# Introduction

It is free software and available for GNU/Linux, Microsoft Windows and Mac OS X.

Unlike most free software for creating 3D models (such as the well-known application Blender), OpenSCAD does not focus on the artistic aspects of 3D modelling, but instead focuses on the CAD aspects. So it might be the application you are looking for when you are planning to create 3D models of machine parts, but probably is not what you are looking for when you are more interested in creating computer-animated movies or organic life-like models.

OpenSCAD, unlike many CAD products, is not an interactive modeler. Instead it is something like a 2D/3D-compiler that reads in a program file that describes the object and renders the model from this file. This gives you (the designer) full control over the modelling process. This enables you to easily change any step in the modelling process and make designs that are defined by configurable parameters.

OpenSCAD has two main operating modes, Preview and Render. Preview is relatively fast using 3D graphics and the computer's GPU, but is an approximation of the model and can produce artifacts; Preview uses OpenCSG and OpenGL. Render generates exact geometry and a fully tessellated mesh. It is not an approximation and as such it is often a lengthy process, taking minutes or hours for larger designs. Render uses CGAL as its geometry engine.

OpenSCAD provides two types of 3D modelling:

Autocad DXF files are used as the data exchange format for 2D outlines. In addition to 2D paths for extrusion it is also possible to read design parameters from DXF files. Besides DXF files, OpenSCAD can read and create 3D models in the STL and OFF file formats.

# First Steps

For our first model we will create a simple 2 x 3 x 4 cuboid. To get started launch OpenSCAD. You should have a preview window, toolbar, console and editor windows open. If one is hidden you can turn it on by going to the View menu and unselect the hidden items.

To create our cuboid we will use the openSCAD editor window to type our one line command:

 Usage example 1 - simple cuboid: cube([2,3,4]);  OpenSCAD Simple Cuboid

### Compiling and rendering our first model

The cuboid can now be compiled and rendered by pressing F5 or F6 Function key on your keyboard while the OpenSCAD editor has focus. You should now see your object in the preview window as shown above.

Open one of the many examples that come with OpenSCAD (File, Examples). Or you can copy and paste this simple example into the OpenSCAD window:

 Usage example 1 difference() { cube(30, center=true); sphere(20); } translate([0, 0, 30]) { cylinder(h=40, r=10); } 
OpenSCAD after pasting the example code and pressing F5

Then press F5 to get a graphical preview of what you typed (or press F6 to get a graphical view).

You get three types of movement in the preview frame:

1. Drag with left mouse button to rotate the view. The bottom line will change the rotate values.
2. Drag with any other mouse button (or control-drag under OSX) to translate (move) the view. The bottom line will change translate values.
3. Use the mouse scroll to zoom in and out. Alternatively you can use the + and - keys, or right-drag with the mouse while pressing a shift key (or control-shift-drag under OSX). The Viewport line at the bottom of the window will show a change in the distance value.

We have already seen how to create a simple cuboid. Our next task is to attempt to use the translate positioning command to place an identical cuboid next to the existing cuboid. Type the data as shown below. There are a total of 4 lines of code. Press F5 or F6 function key when done to see the preview.

 Usage example 1 - positioning an object: cube([2,3,4]); translate([3,0,0]) { cube([2,3,4]); }  OpenSCAD positioning an object

### There is no semicolon following the translate command

Notice that there is no semicolon following the translate command. This is because the translate command relates to the following object. If the semicolon was in place, then the effect of the position translation would end, and the second cuboid would be placed at the same position as the first cuboid.

We can change the color of an object by giving it RGB values. Instead of the traditional RGB values from 0 to 255 floating point values are used from 0.0 to 1.0. Note: changing the colors only works in Preview mode (F5); render mode (F6) does not currently support color.

 Usage example 1 - changing the color of an object: color([1,0,0]) cube([2,3,4]); translate([3,0,0]) color([0,1,0]) cube([2,3,4]); translate([6,0,0]) color([0,0,1]) cube([2,3,4]);  OpenSCAD changing the color of an object

Color names can be used in the 2011.12 version (and newer). The names are the same used for Web colors. For example: color("red") cube();

If you think of the entire command as a sentence, then color() is an "adjective" that describes the "object" of the sentence (which is a "noun"). In this case, the object is the cube() to be created. The adjective is placed before the noun in the sentence, like so: color() cube();. In the same way, translate() can be thought of as a "verb" that acts upon the object, and is placed like this: translate() color() cube();. The following code will produce the same result:

translate([6,0,0])
{
color([0,0,1])    // notice that there is NO semicolon
cube([2,3,4]);    // notice the semicolon is at the end of all related commands
}


The "View" menu at the top of the OpenSCAD application window provides a variety of view options in the OpenSCAD model view window.

## CGAL Surfaces

The surface view is the initial model view that appears when the model code is first rendered. You can get back to this view by choosing "View >> CGAL Surfaces".

## CGAL Grid Only

Designers often choose "View >> CGAL Grid Only" when working with a particularly complex 3D model. The Grid Only view presents only the "scaffolding" beneath the surface, also known as a wireframe. Think of the Eiffel Tower.

A wireframe is a visual presentation of a three dimensional or physical object. This method of modelling consists only of lines, points and curves defining the edges of an object. Using a wireframe model allows visualization of the underlying design structure of a 3D model. Since wireframe renderings are relatively simple and fast to calculate, they are often used in cases where a higher screen frame rate is needed (for instance, when working with a particularly complex 3D model, or in real-time systems that model exterior phenomena). When greater graphical detail is desired, surface textures can be added automatically after completion of the initial rendering of the wireframe. This allows the designer to quickly review changes or rotate the object to new desired views without long delays associated with more realistic rendering. The wireframe format is also well suited and widely used in programming tool paths for DNC (Direct Numerical Control) machine tools. Wireframe models are also used as the input for CAM (computer-Aided Manufacturing). Wireframe is the most abstract and least realistic of the three main CAD views. [1]

## The OpenCSG View

Choosing "View >> OpenCSG" uses the open constructive solid geometry library to generate the model view utilizing OpenGL. If the OpenCSG library is not available or the video card or drivers do not support OpenGL, then this view will produce no visible output.

## The Thrown Together View

Choosing "View >> Thrown Together" overlays all the previous views together on the same screen. Importantly, objects subtracted by the difference() command are rendered as solid objects in green (by default).

## User Interface

The user interface of OpenSCAD has three parts

• The viewing area
• The console window
• The text editor

### Viewing area

Preview and rendering output goes into the viewing area. Using the Show Axes menu entry an indicator for the coordinate axes can be enabled.

### Console window

Status information, warnings and errors are displayed in the console window.

### Text editor

The built-in text editor provides basic editing features like text search & replace and also supports syntax highlighting. There are predefined color schemes which can be selected in the Preferences dialog.

OpenSCAD Editor with Find / Replace functionality.

The viewing area is navigated primarily using the mouse:

Action Icons Description
rotating the view Dragging with the left mouse button rotates the view along the axes of the viewing area. It preserves the vertical axis' direction.
⇧ Shift + Dragging with the left mouse button when the shift key is pressed rotates the view along the vertical axis and the axis pointing towards the user.
moving the viewing area Dragging with the right mouse button moves the viewing area.
zooming using the scroll wheel
dragging with the middle mouse button
⇧ Shift + dragging with the right or middle mouse button and the shift key pressed
⇧ Shift +
+ and - the keys + and -
rotation reset Ctrl+0 Rotation can be reset using the shortcut Ctrl+0.
movement reset Ctrl+P Movement can be reset using the shortcut Ctrl+P.

## View setup

The viewing area can be configured to use different rendering methods and other options using the View menu. Most of the options described here are available using shortcuts as well.

### Render modes

#### OpenCSG (F9)

This method produces instantaneous results, but has low frame rates when working with highly nonconvex objects.

Note that selecting the OpenCSG mode using F9 will switch to the last generated OpenCSG view, but will not re-evaluate the source code. You may want to use the Compile function (F5, found in the Design menu) to re-evaluate the source code, build the OpenCSG objects and then switch to OpenCSG view.

##### Implementation Details

In OpenCSG mode, the OpenCSG library is used for generating the visible model. This library uses advanced OpenGL features (2.0) like the Z buffer and does not require an explicit description of the resulting mesh – instead, it tracks how objects are to be combined. For example, when rendering a spherical dent in a cube, it will first render the cube on the graphics card and then render the sphere, but instead of using the Z buffer to hide the parts of the sphere that are covered by the cube, it will render only those parts of the sphere, visually resulting in a cube with a spherical dent.

#### CGAL (Surfaces and Grid, F10 and F11)

This method might need some time when first used with a new program, but will then have higher framerates.

As before with OpenCSG, F10 and F11 only enable CGAL display mode and don't update the underlying objects; for that, use the Compile and Render function (F6, found in the Design menu).

To combine the benefits of those two display methods, you can selectively wrap parts of your program in a render function and force them to be baken into a mesh even with OpenCSG mode enabled.

##### Implementation Details

The acronym CGAL refers to The Open Source Computational Geometry Algorithms Library.

In CGAL mode, the CGAL library is used to compute the mesh of the root object, which is then displayed using simple OpenGL.

### View options

#### Show Edges (Ctrl+1)

The difference between the CGAL and OpenCSG approaches can be seen at edges created by boolean operations.

If Show Edges is enabled, both OpenCSG and CGAL mode will render edges as well as faces, CGAL will even show vertices. In CGAL grid mode, this option has no effect.

Enabling this option shows the difference between OpenCSG and CGAL quite clearly: While in CGAL mode you see an edge drawn everywhere it "belongs", OpenCSG will not show edges resulting from boolean operations – this is because they were never explicitly calculated but are just where one object's Z clipping begins or ends.

#### Show Axes (Ctrl+2)

If Show Axes is enabled, the origin of the global coordinate system will be indicated by an orthogonal axes indicator. Additionally, a smaller axes indicator with axes names will be shown in the lower left corner of the viewing area. The smaller axes indicator is marked x, y, z and coloured red, green, blue respectively.

#### Show Crosshairs (Ctrl+3)

If Show Crosshairs is enabled, the center of the viewport will be indicated by four lines pointing in the room diagonal directions of the global coordinate system. This is useful when aligning the viewing area to a particular point in the model to keep it centered on screen during rotation.

### Animation

The Animate option adds an animation bar to the lower edge of the screen. As soon as FPS and Steps are set (reasonable values to begin with are 10 and 100, respectively), the current Time is incremented by 1/Steps, FPS times per second, until it reaches 1, when it wraps back to 0.

Every time Time is changed, the program is re-evaluated with the variable $t set to the current time. Read more about how$t is used in section Other_Language_Features.

### View alignment

The menu items Top, Bottom, …, Diagonal and Center (Ctrl+4, Ctrl+5, …, Ctrl+0, Ctrl+P) align the view to the global coordinate system.

Top, Bottom, Left, Right, Front and Back align it in parallel to the axes, the Diagonal option aligns it diagonally as it is aligned when OpenSCAD starts.

The Center option will put the coordinate center in the middle of the screen (but not rotate the view).

By default, the view is in Perspective mode, meaning that distances far away from the viewer will look shorter, as it is common with eyes or cameras. When the view mode is changed to Orthogonal, visible distances will not depend on the camera distance (the view will simulate a camera in an infinite distance with an infinite focal length). This is especially useful in combination with the Top etc. options described above, as this will result in a 2D image similar to what one would see in an engineering drawing.

### Introduction

OpenSCAD is a 2D/3D and solid modeling program which is based on a Functional programming language used to create models that are previewed on the screen, and rendered into 3D mesh which allows the model to be exported in a variety of 2D/3D file formats.

A script in the OpenSCAD language is used to create 2D or 3D models. This script is a free format list of action statements.

 object();
variable = value;
operator()   action();
operator() { action();    action(); }
operator()   operator() { action(); action(); }
operator() { operator()   action();
operator() { action(); action(); } }

Objects

Objects are the building blocks for models, created by 2D and 3D primitives. Objects end in a semicolon ';'.

Actions

Action statements include creating objects using primitives and assigning values to variables. Action statements also end in a semicolon ';'.

Operators

Operators, or transformations, modify the location, color and other properties of objects. Operators use braces '{}' when their scope covers more than one action. More than one operator may be used for the same action or group of actions. Multiple operators are processed Right to Left, that is, the operator closest to the action is processed first. Operators do not end in semicolons ';', but the individual actions they contain do.

 Examples

cube(5);
x = 4+y;
rotate(40) square(5,10);
translate([10,5]) { circle(5); square(4); }
rotate(60) color("red") { circle(5); square(4); }
color("blue") { translate([5,3,0]) sphere(5); rotate([45,0,45]) { cylinder(10); cube([5,6,7]); } }


Comments are a way of leaving notes within the script, or code, (either to yourself or to future programmers) describing how the code works, or what it does. Comments are not evaluated by the compiler, and should not be used to describe self-evident code.

// This is a comment

myvar = 10; // The rest of the line is a comment

/*
can span multiple lines.
*/


### Values and Data Types

A value in OpenSCAD is either a Number (like 42), a Boolean (like true), a String (like "foo"), a Range (like [0: 1: 10]), a Vector (like [1,2,3]), or the Undefined value (undef). Values can be stored in variables, passed as function arguments, and returned as function results.

[OpenSCAD is a dynamically typed language with a fixed set of data types. There are no type names, and no user defined types. Functions are not values. In fact, variables and functions occupy disjoint namespaces.]

#### Numbers

Numbers are the most important type of value in OpenSCAD, and they are written in the familiar decimal notation used in other languages. Eg, -1, 42, 0.5, 2.99792458e+8. [OpenSCAD does not support octal or hexadecimal notation for numbers.]

In additional to decimal numerals, the following names for special numbers are defined:

• PI

OpenSCAD has only a single kind of number, which is a 64 bit IEEE floating point number. [OpenSCAD does not distinguish integers and floating point numbers as two different types, nor does it support complex numbers.] Because OpenSCAD uses the IEEE floating point standard, there are a few deviations from the behaviour of numbers in mathematics:

• We use binary floating point. A fractional number is not represented exactly unless the denominator is a power of 2. For example, 0.2 (2/10) does not have an exact internal representation, but 0.25 (1/4) and 0.125 (1/8) are represented exactly.
• The largest representable number is about 1e308. If a numeric result is too large, then the result can be infinity (printed as inf by echo).
• The smallest representable number is about -1e308. If a numeric result is too small, then the result can be -infinity (printed as -inf by echo).
• If a numeric result is invalid, then the result can be Not A Number (printed as nan by echo).
• If a non-zero numeric result is too close to zero to be representable, then the result will be -0 if the result is negative, otherwise it will be 0. Zero (0) and negative zero (-0) are treated as two distinct numbers by some of the math operations, and are printed differently by 'echo', although they compare equal.

Note that 'inf' and 'nan' are not supported as numeric constants by OpenSCAD, even though you can compute numbers that are printed this way by 'echo'. You can define variables with these values by using:

inf = 1e200 * 1e200;
nan = 0 / 0;
echo(inf,nan);


Note that 'nan' is the only OpenSCAD value that is not equal to any other value, including itself. Although you can test if a variable 'x' has the undefined value using 'x == undef', you can't use 'x == 0/0' to test if x is Not A Number. Instead, you must use 'x != x' to test if x is nan.

#### Boolean Values

Booleans are truth values. There are two Boolean values, namely true and false. A Boolean is passed as the argument to conditional statement 'if()'. conditional operator '? :', and logical operators '!' (not), '&&' (and), and '||' (or). In all of these contexts, you can actually pass any quantity. Most values are converted to 'true' in a Boolean context, the values that count as 'false' are:

• false
• 0 and -0
• ""
• []
• undef

Note that "false" (the string), [0] (a numeric vector), [ [] ] (a vector containing an empty vector), [false] (a vector containing the Boolean value false) and 0/0 (Not A Number) all count as true.

#### Strings

A string is a sequence of zero or more unicode characters. String values are used to specify file names when importing a file, and to display text for debugging purposes when using echo(). Strings can also be used with the new text() primitive added in 2015.03.

A string literal is written as a sequence of characters enclosed in quotation marks ", like this: "" (an empty string), or "this is a string".

To include a " character in a string literal, use \". To include a \ character in a string literal, use \\. The following escape sequences beginning with \ can be used within string literals:

• \" → "
• \\ → \
• \t → tab
• \n → newline
• \r → carriage return
• \u03a9 → Ω - see text() for further information on unicode characters

 Example:

echo("The quick brown fox \tjumps \"over\" the lazy dog.\rThe quick brown fox.\nThe \\lazy\\ dog.");

result
ECHO: "The quick brown fox     jumps "over" the lazy dog.
The quick brown fox.
The \lazy\ dog."

old result
ECHO: "The quick brown fox \tjumps \"over\" the lazy dog.
The quick brown fox.\nThe \\lazy\\ dog."


#### Ranges

Ranges are used by for() loops and children(). They have 2 varieties:

[<start>:<end>]
[<start>:<increment>:<end>]

Although enclosed in square brackets [] , they are not vectors. They use colons : for separators rather than commas.

r1 = [0:10];
r2 = [0.5:2.5:20];
echo(r1); // ECHO: [0: 1: 10]
echo(r2); // ECHO: [0.5: 2.5: 20]


You should avoid step values that cannot be represented exactly as binary floating point numbers. Integers are okay, as are fractional values whose denominator is a power of two. For example, 0.25 (1/4) and 0.125 (1/8) are safe, but 0.2 (2/10) should be avoided. The problem with these step values is that your range may have too many or too few elements, due to inexact arithmetic.

A missing <increment> defaults to 1. A range in the form [<start>:<end>] with <start> greater than <end> will generate a warning and is equivalent to [<end>: 1: <start>]. A range in the form [<start>:1:<end>] with <start> greater than <end> will not generate a warning and is equivalent to []. The <increment> in a range may be negative (for versions after 2014).

#### The Undefined Value

The undefined value is a special value written as undef. It's the initial value of a variable that hasn't been assigned a value, and it is often returned as a result by functions or operations that are passed illegal arguments. Finally, undef can be used as a null value, equivalent to null or NULL in other programming languages.

All arithmetic expressions containing undef values evaluate as undef. In logical expressions, undef is equivalent to false. Relational operator expressions with undef evaluate as false except for undef==undef which is true.

Note that numeric operations may also return 'nan' (not-a-number) to indicate an illegal argument. For example, 0/false is undef, but 0/0 is 'nan'. Relational operators like < and > return false if passed illegal arguments. Although undef is a language value, 'nan' is not.

### Variables

OpenSCAD variables are created by a statement with a name or identifier, assignment via an expression and a semicolon. The role of arrays, found in many imperative languages, is handled in OpenSCAD via vectors.

var = 25;
xx = 1.25 * cos(50);
y = 2*xx+var;
logic = true;
MyString = "This is a string";
a_vector = [1,2,3];
rr = a_vector[2];      // member of vector
range1 = [-1.5:0.5:3]; // for() loop range
xx = [0:5];            // alternate for() loop range


OpenSCAD is a Functional programming language, as such variables are bound to expressions and keep a single value during their entire lifetime due to the requirements of referential transparency. In imperative languages, such as C, the same behavior is seen as constants, which are typically contrasted with normal variables.

In other words OpenSCAD variables are more like constants, but with an important difference. If variables are assigned a value multiple times, only the last assigned value is used in all places in the code. See further discussion at Variables are set at compile-time, not run-time. This behavior is due to the need to supply variable input on the command line, via the use of -D variable=value option. OpenSCAD currently places that assignment at the end of the source code, and thus must allow a variables value to be changed for this purpose.

The variable retains its last assigned value at compile time, in line with Functional programming languages. Unlike Imperative languages, such as C, OpenSCAD is not an iterative language, as such the concept of x = x + 1  is not valid, get to understand this concept and you will understand the beauty of OpenSCAD.

Before version 2015.03

It was not possible to do assignments at any place except the file top-level and module top-level. Inside an if/else  or for  loop, assign() was needed.

Since version 2015.03

Variables can now be assigned in any scope. Note that assignments are only valid within the scope in which they are defined - you are still not allowed to leak values to an outer scope. See Scope of variables for more details.

a=0;
if (a==0)
{
a=1; //  before 2015.03 this line would generate a Compile Error
//  since 2015.03  no longer an error, but the value a=1 is confined to within the braces {}
}


#### Undefined variable

A non assigned variable has the special value undef. It could be tested in conditional expression, and returned by a function.

 Example

echo("Variable a is ", a);                // Variable a is undef
if (a==undef) {
echo("Variable a is tested undefined"); // Variable a is tested undefined
}


#### Scope of variables

When operators such as translate() and color() need to encompass more than one action ( actions end in ;), braces {} are needed to group the actions, creating a new, inner scope. When there is only one semicolon, braces are usually optional.

Each pair of braces creates a new scope inside the scope where they were used. Since 2015.03, new variables can be created within this new scope. New values can be given to variables which were created in an outer scope . These variables and their values are also available to further inner scopes created within this scope, but are not available to any thing outside this scope. Variables still have only the last value assigned within a scope.

                       // scope 1
a = 6;                // create a
echo(a,b);            //                6, undef
translate([5,0,0]){   // scope 1.1
a= 10;
b= 16;              // create b
echo(a,b);          //              100, 16   a=10; was overridden by later a=100;
color("blue") {     // scope 1.1.1
echo(a,b);        //              100, 20
cube();
b=20;
}                   // back to 1,1
echo(a,b);          //              100, 16
a=100;              // override a in 1.1
}                     // back to 1
echo(a,b);            //                6, undef
color("red"){         // scope 1.2
cube();
echo(a,b);          //                6, undef
}                   // back to 1
echo(a,b);            //                6, undef

//In this example, scopes 1 and 1.1 are outer scopes to 1.1.1 but 1.2 is not.

Anonymous scopes are not considered scopes:
 {
angle = 45;
}
rotate(angle) square(10);


For() loops are not an exception to the rule about variables having only one value within a scope. A copy of loop contents is created for each pass. Each pass is given its own scope, allowing any variables to have unique values for that pass. No, you still can't do a=a+1;

#### Variables are set at compile-time, not run-time

Because OpenSCAD calculates its variable values at compile-time, not run-time, the last variable assignment, within a scope will apply everywhere in that scope, or inner scopes thereof. It may be helpful to think of them as override-able constants rather than as variables.

// The value of 'a' reflects only the last set value
a = 0;
echo(a);  // 5
a = 3;
echo(a);  // 5
a = 5;


While this appears to be counter-intuitive, it allows you to do some interesting things: For instance, if you set up your shared library files to have default values defined as variables at their root level, when you include that file in your own code, you can 're-define' or override those constants by simply assigning a new value to them.

#### Special Variables

Special variables provide an alternate means of passing arguments to modules and functions. All variables starting with a '$' are special variables, similar to special variables in lisp. As such they are more dynamic than regular variables. (for more details see Other Language Features) ### Vectors A vector is a sequence of zero or more OpenSCAD values. Vectors are a collection (or list or table) of numeric or boolean values, variables, vectors, strings or any combination thereof. They can also be expressions which evaluate to one of these. Vectors handle the role of arrays found in many imperative languages. The information here also applies to lists and tables which use vectors for their data. A vector has square brackets, [] enclosing zero or more items (elements or members), separated by commas. A vector can contain vectors, which contain vectors, etc. examples  [1,2,3] [a,5,b] [] [5.643] ["a","b","string"] [[1,r],[x,y,z,4,5]] [3, 5, [6,7], [[8,9],[10,[11,12],13], c, "string"] [4/3, 6*1.5, cos(60)]  use in OpenSCAD:  cube( [width,depth,height] ); // optional spaces shown for clarity translate( [x,y,z] ) polygon( [ [x0,y0], [x1,y1], [x2,y2] ] );  creation Vectors are created by writing the list of elements, separated by commas, and enclosed in square brackets. Variables are replaced by their values.  cube([10,15,20]); a1 = [1,2,3]; a2 = [4,5]; a3 = [6,7,8,9]; b = [a1,a2,a3]; // [ [1,2,3], [4,5], [6,7,8,9] ] note increased nesting depth  elements within vectors Elements within vectors are numbered from 0 to n-1 where n is the length returned by len(). Address elements within vectors with the following notation: e[5] // element no 5 (sixth) at 1st nesting level e[5][2] // element 2 of element 5 2nd nesting level e[5][2][0] // element 0 of 2 of 5 3rd nesting level e[5][2][0][1] // element 1 of 0 of 2 of 5 4th nesting level  example elements with lengths from len() e = [ [1], [], [3,4,5], "string", "x", [[10,11],[12,13,14],[[15,16],[17]]] ]; // length 6 address length element e[0] 1 [1] e[1] 0 [] e[5] 3 [ [10,11], [12,13,14], [[15,16],[17]] ] e[5][1] 3 [ 12, 13, 14 ] e[5][2] 2 [ [15,16], [17] ] e[5][2][0] 2 [ 15, 16 ] e[5][2][0][1] undef 16 e[3] 6 "string" e[3 ][2] 1 "r" s = [2,0,5]; a = 2; s[a] undef 5 e[s[a]] 3 [ [10,11], [12,13,14], [[15,16],[17]] ]  alternate dot notation The first three elements of a vector can be accessed with an alternate dot notation: e.x //equivalent to e[0] e.y //equivalent to e[1] e.z //equivalent to e[2]  ##### vector operators ###### concat [Note: Requires version 2015.03 or later] concat() combines the elements of 2 or more vectors into a single vector. No change in nesting level is made.  vector1 = [1,2,3]; vector2 = [4]; vector3 = [5,6]; new_vector = concat(vector1, vector2, vector3); // [1,2,3,4,5,6] string_vector = concat("abc","def"); // ["abc", "def"] one_string = str(string_vector[0],string_vector[1]); // "abcdef"  ###### len len() is a function which returns the length of vectors or strings. Indices of elements are from [0] to [length-1]. vector Returns the number of elements at this level. Single values, which are not vectors, return undef. string Returns the number of characters in string.  a = [1,2,3]; echo(len(a)); // 3  ##### Matrix A matrix is a vector of vectors. Example which defines a 2D rotation matrix mr = [ [cos(angle), -sin(angle)], [sin(angle), cos(angle)] ];  ### Getting input Now we have variables, it would be nice to be able to get input into them instead of setting the values from code. There are a few functions to read data from DXF files, or you can set a variable with the -D switch on the command line. Getting a point from a drawing Getting a point is useful for reading an origin point in a 2D view in a technical drawing. The function dxf_cross will read the intersection of two lines on a layer you specify and return the intersection point. This means that the point must be given with two lines in the DXF file, and not a point entity. OriginPoint = dxf_cross(file="drawing.dxf", layer="SCAD.Origin", origin=[0, 0], scale=1);  Getting a dimension value You can read dimensions from a technical drawing. This can be useful to read a rotation angle, an extrusion height, or spacing between parts. In the drawing, create a dimension that does not show the dimension value, but an identifier. To read the value, you specify this identifier from your program: TotalWidth = dxf_dim(file="drawing.dxf", name="TotalWidth", layer="SCAD.Origin", origin=[0, 0], scale=1);  For a nice example of both functions, see Example009 and the image on the homepage of OpenSCAD. ### For loop Evaluate each value in a range or vector, applying it to the following Action.  for(variable = [start : increment : end]) for(variable = [start : end]) for(variable = [vector])  parameters As a range [ start : <increment : > end ] (see section on range) Note: For range, values are separated by colons rather than commas used in vectors. start - initial value increment or step - amount to increase the value, optional, default = 1 end - stop when next value would be past end examples:  for (a =[3:5])echo(a); // 3 4 5 for (a =[3:0]){echo(a);} // 0 1 2 3 start > end is invalid, deprecated by 2015.3 for (a =[3:0.5:5])echo(a); // 3 3.5 4 4.5 5 for (a =[0:2:5])echo(a); // 0 2 4 a never equals end for (a =[3:-2:-1])echo(a); // 3 1 -1 negative increment requires 2015.3 be sure end > start  As a vector The Action is evaluated for each element of the vector  for (a =[3,4,1,5])echo(a); // 3 4 1 5 for (a =[0.3,PI,1,99]){echo(a);} // 0.3 3.14159 1 99 x1=2; x2=8; x3=5.5; for (a =[x1,x2,x3]){echo(a);} // 2 8 5.5 for (a =[[1,2],6,"s",[[3,4],[5,6]]])echo(a); // [1,2] 6 "s" [[3,4],[5,6]]  for() is an Operator. Operators require braces {} if more than one Action is within it scope. Actions end in semicolons, Operators do not. for() is not an exception to the rule about variables having only one value within a scope. Each evaluation is given its own scope, allowing any variables to have unique values. No, you still can't do a=a+1; Remember this is not an iterative language, the for() does not loop in the programmatic sense, it builds a tree of objects one branch for each item in the range/vector, inside each branch the 'variable' is a specific and separate instantiation or scope. Hence: for (i=[0:3]) translate([i*10,0,0]) cube(i+1);  Produces: [See Design/Display-CSG-Tree menu]  group() { group() { multmatrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) { cube(size = [1, 1, 1], center = false); } multmatrix([[1, 0, 0, 10], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) { cube(size = [2, 2, 2], center = false); } multmatrix([[1, 0, 0, 20], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) { cube(size = [3, 3, 3], center = false); } multmatrix([[1, 0, 0, 30], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) { cube(size = [4, 4, 4], center = false); } } }  All instances of the for() exist at the same time, they do not iterate sequentially. Nested for() While it is reasonable to nest multiple for() statements such as: for(z=[-180:45:+180]) for(x=[10:5:50]) rotate([0,0,z]) translate([x,0,0]) cube(1);  instead, all ranges/vectors can be include in the same for() operator. for ( variable1 = <range or vector> , variable2 = <range or vector> ) <do something using both variables>  for() loops nested 3 deep  example for() nested 3 deep color_vec = ["black","red","blue","green","pink","purple"]; for (x = [-20:10:20] ) for (y = [0:4] )color(color_vec[y]) for (z = [0,4,10] ) {translate([x,y*5-10,z])cube();} shorthand nesting for same result color_vec = ["black","red","blue","green","pink","purple"]; for (x = [-20:10:20], y = [0:4], z = [0,4,10] ) translate([x,y*5-10,z]){color(color_vec[y])cube();}  Examples using vector of vectors example 1 for() loop vector of vectors (rotation) example 1 - iteration over a vector of vectors (rotation) for(i = [ [ 0, 0, 0], [ 10, 20, 300], [200, 40, 57], [ 20, 88, 57] ]) { rotate(i) cube([100, 20, 20], center = true); }  example 2 for() loop vector of vectors (translation) example 2 - iteration over a vector of vectors (translation) for(i = [ [ 0, 0, 0], [10, 12, 10], [20, 24, 20], [30, 36, 30], [20, 48, 40], [10, 60, 50] ]) { translate(i) cube([50, 15, 10], center = true); }  example 3 for() loop vector of vectors example 3 - iteration over a vector of vectors for(i = [ [[ 0, 0, 0], 20], [[10, 12, 10], 50], [[20, 24, 20], 70], [[30, 36, 30], 10], [[20, 48, 40], 30], [[10, 60, 50], 40] ]) { translate([i[0][0], 2*i[0][1], 0]) cube([10, 15, i[1]]); }  ### Intersection For Loop Iterate over the values in a range or vector and create the intersection of objects created by each pass. Besides creating separate instances for each pass, the standard for() also groups all these instances creating an implicit union. intersection_for() is a work around because the implicit union prevents getting the expected results using a combination of the standard for() and intersection() statements. intersection_for() uses the same parameters, and works the same as a For Loop, other than eliminating the implicit union.  example 1 - loop over a range: intersection_for(n = [1 : 6]) { rotate([0, 0, n * 60]) { translate([5,0,0]) sphere(r=12); } }  intersection_for() either intersection() for() or for() intersection()  example 2 - rotation :  intersection_for(i = [ [ 0, 0, 0], [ 10, 20, 300], [200, 40, 57], [ 20, 88, 57] ]) { rotate(i) cube([100, 20, 20], center = true); }  intersection_for() intersection() for() In ### If Statement Performs a test to determine if the actions in a sub scope should be performed or not. if (test) scope1 if (test){scope1} if (test) scope1 else scope2 if (test){scope1} else {scope2}  Parameters test: Usually a boolean expression, but can be any value or variable. See here for true or false state of values. See here for boolean and logical operators Do not confuse the assignment operator '=' with the equal operator '==' scope1: one or more actions to take when test is true. scope2: one or more actions to take when test is false. if (b==a) cube(4); if (b<a) {cube(4); cylinder(6);} if (b&&a) {cube(4); cylinder(6);} if (b!=a) cube(4); else cylinder(3); if (b) {cube(4); cylinder(6);} else {cylinder(10,5,5);} if (!true){cube(4); cylinder(6);} else cylinder(10,5,5); if (x>y) cube(1, center=false); else {cube(size = 2, center = true);} if (a==4) {} else echo("a is not 4"); if ((b<5)&&(a>8)) {cube(4); else cylinder(3);} if (b<5&&a>8) cube(4); else cylinder(3);  Since 2015.03 variables can now be assigned in any scope. Note that assignments are only valid within the scope in which they are defined - you are still not allowed to leak values to an outer scope. See Scope of variables for more details. Nested if The scopes of both the if() portion and the else portion, can in turn contain if() statements. This nesting can be to many depths.  if (test1) { scope1 if (test2) {scope2.1} else {scope2.2} } else { scope2 if (test3) {scope3.1} else {scope3.2} }  When scope1 and scope2 contain only the if() statement, the outer sets of braces can be removed.  if (test1) if (test2) {scope2.1} else {scope2.2} else if (test3) {scope3.1} else {scope3.2}  One evolution is this: #### else if  if(test1) {scope1} else if(test2) {scope2} else if(test3) {scope3} else if(test4) {scope4} else {scope5}  Note that else and if are two separate words. When working down the chain of tests, the first true will use its scope. All further tests will be skipped. example if((k<8)&&(m>1)) cube(10); else if(y==6) {sphere(6);cube(10);} else if(y==7) color("blue")sphere(5); else if(k+m!=8) {cylinder(15,5,0);sphere(8);} else color("green"){cylinder(12,5,0);sphere(8);}  ### Conditional ? : A function which uses a test to determine which of 2 values to return.  a = test ? TrueValue : FalseValue ; echo( test ? TrueValue : FalseValue );  Parameters test: Usually a boolean expression, but can be any value or variable. See here for true or false state of values. See here for boolean and logical operators Do not confuse assignment '=' with equal '==' TrueValue: the value to return when test is true. FalseValue: the value to return when test is false. A value in OpenSCAD is either a Number (like 42), a Boolean (like true), a String (like "foo"), a Vector (like [1,2,3]), or the Undefined value (undef). Values can be stored in variables, passed as function arguments, and returned as function results. This works like the ?: operator from the family of C-like programming languages. Examples  a=1; b=2; c= a==b ? 4 : 5 ; // 5 a=1; b=2; c= a==b ? "a==b" : "a!=b" ; // "a!=b" TrueValue = true; FalseValue = false; a=5; test = a==1; echo( test ? TrueValue : FalseValue ); // false L = 75; R = 2; test = (L/R)>25; TrueValue = [test,L,R,L/R,cos(30)]; FalseValue = [test,L,R,sin(15)]; a1 = test ? TrueValue : FalseValue ; // [true, 75, 2, 37.5, 0.866025]  #### Recursive function calls Recursive function calls are supported. Using the Conditional "... ? ... : ... " it's possible to ensure the recursion is terminated. Note: There is a built-in recursion limit to prevent an application crash. If the limit is hit, the function returns undef. example  // recursion - find the sum of the values in a vector (array) by calling itself // from the start (or s'th element) to the i'th element - remember elements are zero based function sumv(v,i,s=0) = (i==s ? v[i] : v[i] + sumv(v,i-1,s)); vec=[ 10, 20, 30, 40 ]; echo("sum vec=", sumv(vec,2,1)); // calculates 20+30=50  Some forms of tail-recursion elimination are supported. ### Assign Statement Set variables to a new value for a sub-tree. Since 2015.03 assign() is deprecated, as variables can now be assigned anywhere, see 2nd example below. If you prefer this way of setting values, the new Let Statement can be used instead. Parameters The variables that should be (re-)assigned example: for (i = [10:50]) { assign (angle = i*360/20, distance = i*10, r = i*2) { rotate(angle, [1, 0, 0]) translate([0, distance, 0]) sphere(r = r); } }  for (i = [10:50]) { angle = i*360/20; distance = i*10; r = i*2; rotate(angle, [1, 0, 0]) translate([0, distance, 0]) sphere(r = r); }  ### Let Statement [Note: Requires version 2016.XX] (ie a development version) Set variables to a new value for a sub-tree. The parameters are evaluated sequentially and may depend on each other (as opposed to the deprecated assign() statement). Parameters The variables that should be set example: for (i = [10:50]) { let (angle = i*360/20, r= i*2, distance = r*5) { rotate(angle, [1, 0, 0]) translate([0, distance, 0]) sphere(r = r); } }  ### Scalar Arithmetical Operators The scalar arithmetical operators take numbers as operands and produce a new number.  + add - subtract * multiply / divide % modulo The "-" can also be used as prefix operator to negate a number. ### Relational Operators Relational operators produce a Boolean result from two operands.  < less than <= less equal == equal != not equal >= greater equal > greater than If both operands are simple numbers, the meaning is self-evident. If both operands are strings, alphabetical sorting determines equality and order. E.g., "ab" > "aa" > "a". If both operands are Booleans, true > false. If one operand is Boolean, the other operand is converted to Boolean before the comparison is made. If both operands are vectors, OpenSCAD performs an element-by-element comparison and can only result in true if the vectors are equal in size and each and every pair of elements results in true upon the comparison. Otherwise, false is returned. Vectors of different sizes are treated as unequal for '==' and '!=' operators, and always result in false for '>', '>=', '<' and '<=' operators. In fact the same principle applies for all comparison between dissimilar types of operand, e.g. comparing a string with a number. Note that [1] ≠ 1. undef doesn't equal anything but undef. undef compares ('>' etc.) anything result in false. nan doesn't equal anything. See Numbers. ### Logical Operators All logical operators take Booleans as operands and produce a Boolean. Non-Boolean quantities are converted to Booleans before the operator is evaluated.  && logical AND || logical OR ! logical unary NOT Since [false] is true, false || [false] is also true. Note that how logical operators deal with vectors is different than relational operators: [1, 1] > [0, 2] is false, but [false, false] && [false, false] is true. ### Conditional Operator The ?: operator can be used to conditionally evaluate one or another expression. It works like the ?: operator from the family of C-like programming languages.  ? : Conditional operator  Usage Example: a=1; b=2; c= a==b ? 4 : 5;  If a equals b, then c is set to 4, else c is set to 5. The part "a==b" must be something that evaluates to a boolean value. ### Vector-Number Operators The vector-number operators take a vector and a number as operands and produce a new vector.  * multiply all vector elements by number / divide all vector elements by number Example L = [1, [2, [3, "a"] ] ]; echo(5*L); // ECHO: [5, [10, [15, undef]]]  ### Vector Operators The vector operators take vectors as operands and produce a new vector.  + add element-wise - subtract element-wise The "-" can also be used as prefix operator to element-wise negate a vector. Example L1 = [1, [2, [3, "a"] ] ]; L2 = [1, [2, 3] ]; echo(L1+L1); // ECHO: [2, [4, [6, undef]]] echo(L1+L2); // ECHO: [2, [4, undef]]  ### Vector Dot-Product Operator If both operands of multiplication are simple vectors, the result is a number according to the linear algebra rule for dot product. c = u*v; results in ${\displaystyle c=\sum u_{i}v_{i}}$. If the operands' sizes don't match, the result is undef. ### Matrix Multiplication If one or both operands of multiplication are matrices, the result is a simple vector or matrix according to the linear algebra rules for matrix product. In the following, A, B, C... are matrices, u, v, w... are vectors. Subscripts i, j denote element indices. For A a matrix of size n × m and B a matrix of size m × p, their product C = A*B; is a matrix of size n × p with elements ${\displaystyle C_{ij}=\sum _{k=0}^{m-1}A_{ik}B_{kj}}$. C = B*A; results in undef unless n = p. For A a matrix of size n × m and v a vector of size m, their product u = A*v; is a vector of size n with elements ${\displaystyle u_{i}=\sum _{k=0}^{m-1}A_{ik}v_{k}}$. In linear algebra, this is the product of a matrix and a column vector. For v a vector of size n and A a matrix of size n × m, their product u = v*A; is a vector of size m with elements ${\displaystyle u_{j}=\sum _{k=0}^{n-1}v_{k}A_{kj}}$. In linear algebra, this is the product of a row vector and a matrix. Matrix multiplication is not commutative: ${\displaystyle AB\neq BA}$, ${\displaystyle Av\neq vA}$. ## Trigonometric Functions The trig functions use the C Language mathematics functions, which are based in turn on Binary Floating Point mathematics, which use approximations of Real Numbers during calculation. OpenSCAD's math functions use the C++ 'double' type, inside Value.h/Value.cc, A good resource for the specifics of the C library math functions, such as valid inputs/output ranges, can be found at the Open Group website math.h & acos ### cos Mathematical cosine function of degrees. See Cosine Parameters <degrees> Decimal. Angle in degrees.  Usage Example:  for(i=[0:36]) translate([i*10,0,0]) cylinder(r=5,h=cos(i*10)*50+60);  OpenSCAD Cos Function‎ ### sin Mathematical sine function. See Sine Parameters <degrees> Decimal. Angle in degrees.  Usage example 1:  for (i = [0:5]) { echo(360*i/6, sin(360*i/6)*80, cos(360*i/6)*80); translate([sin(360*i/6)*80, cos(360*i/6)*80, 0 ]) cylinder(h = 200, r=10); }   Usage example 2:  for(i=[0:36]) translate([i*10,0,0]) cylinder(r=5,h=sin(i*10)*50+60);  OpenSCAD Sin Function ### tan Mathematical tangent function. See Tangent Parameters <degrees> Decimal. Angle in degrees.  Usage example:  for (i = [0:5]) { echo(360*i/6, tan(360*i/6)*80); translate([tan(360*i/6)*80, 0, 0 ]) cylinder(h = 200, r=10); }  ### acos Mathematical arccosine, or inverse cosine, expressed in degrees. See: Inverse trigonometric functions ### asin Mathematical arcsine, or inverse sine, expressed in degrees. See: Inverse trigonometric functions ### atan Mathematical arctangent, or inverse tangent, function. Returns the principal value of the arc tangent of x, expressed in degrees. See: Inverse trigonometric functions ### atan2 Mathematical two-argument atan function, taking y as its first argument. Returns the principal value of the arc tangent of y/x, expressed in degrees. See: atan2 ## Other Mathematical Functions ### abs Mathematical absolute value function. Returns the positive value of a signed decimal number. Usage examples: abs(-5.0); abs(0); abs(8.0);  Results: 5.0 0.0 8.0  ### ceil Mathematical ceiling function. Returns the next highest integer value by rounding up value if necessary. See: Ceil Function echo(ceil(4.4),ceil(-4.4)); // produces ECHO: 5, -4  ### concat [Note: Requires version 2015.03] Return a vector containing the arguments. Where an argument is a vector the elements of the vector are individually added to the result vector. Strings are distinct from vectors in this case. Usage examples: echo(concat("a","b","c","d","e","f")); // produces ECHO: ["a", "b", "c", "d", "e", "f"] echo(concat(["a","b","c"],["d","e","f"])); // produces ECHO: ["a", "b", "c", "d", "e", "f"] echo(concat(1,2,3,4,5,6)); // produces ECHO: [1, 2, 3, 4, 5, 6]  Vector of vectors echo(concat([ [1],[2] ], [ [3] ])); // produces ECHO: [[1], [2], [3]]  Contrast with strings echo(concat([1,2,3],[4,5,6])); // produces ECHO: [1, 2, 3, 4, 5, 6] echo(concat("abc","def")); // produces ECHO: ["abc", "def"] echo(str("abc","def")); // produces ECHO: "abcdef"  ### cross Calculates the cross product of two vectors in 3D space. The result is a vector that is perpendicular to both of the input vectors. Using invalid input parameters (e.g. vectors with a length different from 3 or other types) will produce an undefined result. Usage examples: echo(cross([2, 3, 4], [5, 6, 7])); // produces ECHO: [-3, 6, -3] echo(cross([2, 1, -3], [0, 4, 5])); // produces ECHO: [17, -10, 8] echo(cross([2, 3, 4], "5")); // produces ECHO: undef  ### exp Mathematical exp function. Returns the base-e exponential function of x, which is the number e raised to the power x. See: Exponent echo(exp(1),exp(ln(3)*4)); // produces ECHO: 2.71828, 81  ### floor Mathematical floor function. floor(x) = is the largest integer not greater than x See: Floor Function echo(floor(4.4),floor(-4.4)); // produces ECHO: 4, -5  ### ln Mathematical natural logarithm. See: Natural logarithm ### len Mathematical length function. Returns the length of an array, a vector or a string parameter. Usage examples: str1="abcdef"; len_str1=len(str1); echo(str1,len_str1); a=6; len_a=len(a); echo(a,len_a); array1=[1,2,3,4,5,6,7,8]; len_array1=len(array1); echo(array1,len_array1); array2=[[0,0],[0,1],[1,0],[1,1]]; len_array2=len(array2); echo(array2,len_array2); len_array2_2=len(array2[2]); echo(array2[2],len_array2_2);  Results: ECHO: "abcdef", 6 ECHO: 6, undef ECHO: [1, 2, 3, 4, 5, 6, 7, 8], 8 ECHO: [[0, 0], [0, 1], [1, 0], [1, 1]], 4 ECHO: [1, 0], 2  This function allows (e.g.) the parsing of an array, a vector or a string. Usage examples: str2="4711"; for (i=[0:len(str2)-1]) echo(str("digit ",i+1," : ",str2[i]));  Results: ECHO: "digit 1 : 4" ECHO: "digit 2 : 7" ECHO: "digit 3 : 1" ECHO: "digit 4 : 1"  Note that the len() function is not defined when a simple variable is passed as the parameter. This is useful when handling parameters to a module, similar to how shapes can be defined as a single number, or as an [x,y,z] vector; i.e. cube(5) or cube([5,5,5]) For example module doIt(size) { if (len(size) == undef) { // size is a number, use it for x,y & z. (or could be undef) do([size,size,size]); } else { // size is a vector, (could be a string but that would be stupid) do(size); } } doIt(5); // equivalent to [5,5,5] doIt([5,5,5]); // similar to cube(5) v's cube([5,5,5])  ### let [Note: Requires version 2015.03] Sequential assignment of variables inside an expression. The following expression is evaluated in context of the let assignments and can use the variables. This is mainly useful to make complicated expressions more readable by assigning interim results to variables. Parameters let (var1 = value1, var2 = f(var1), var3 = g(var1, var2)) expression  Usage Example: echo(let(a = 135, s = sin(a), c = cos(a)) [ s, c ]); // ECHO: [0.707107, -0.707107]  ### log Mathematical logarithm to the base 10. Example: log(1000) = 3. See: Logarithm ### lookup Look up value in table, and linearly interpolate if there's no exact match. The first argument is the value to look up. The second is the lookup table -- a vector of key-value pairs. Parameters key A lookup key <key,value> array keys and values Notes There is a bug where out-of-range keys will return the first value in the list. Newer versions of Openscad should use the top or bottom end of the table as appropriate instead.  Usage example: Will create a sort of 3D chart made out of cylinders of different height.  function get_cylinder_h(p) = lookup(p, [ [ -200, 5 ], [ -50, 20 ], [ -20, 18 ], [ +80, 25 ], [ +150, 2 ] ]); for (i = [-100:5:+100]) { // echo(i, get_cylinder_h(i)); translate([ i, 0, -30 ]) cylinder(r1 = 6, r2 = 2, h = get_cylinder_h(i)*3); }  OpenSCAD Lookup Function ### max Returns the maximum of the parameters. If a single vector is given as parameter, returns the maximum element of that vector. Parameters max(n,n{,n}...) max(vector)  <n> Two or more decimals <vector> Single vector of decimals (requires OpenSCAD version 2014.06 or later). Usage Example: max(3.0,5.0) max(8.0,3.0,4.0,5.0) max([8,3,4,5])  Results: 5 8 8  ### min Returns the minimum of the parameters. If a single vector is given as parameter, returns the minimum element of that vector. Parameters min(n,n{,n}...) min(vector)  <n> Two or more decimals <vector> Single vector of decimals (requires OpenSCAD version 2014.06 or later). Usage Example: min(3.0,5.0) min(8.0,3.0,4.0,5.0) min([8,3,4,5])  Results: 3 3 3  Looking for mod - it's not a function, see modulo operator (%) ### norm Returns the euclidean norm of a vector. Note this returns the actual numeric length while len returns the number of elements in the vector or array. Usage examples: a=[1,2,3,4]; b="abcd"; c=[]; d=""; e=[[1,2,3,4],[1,2,3],[1,2],[1]]; echo(norm(a)); //5.47723 echo(norm(b)); //undef echo(norm(c)); //0 echo(norm(d)); //undef echo(norm(e[0])); //5.47723 echo(norm(e[1])); //3.74166 echo(norm(e[2])); //2.23607 echo(norm(e[3])); //1  Results: ECHO: 5.47723 ECHO: undef ECHO: 0 ECHO: undef ECHO: 5.47723 ECHO: 3.74166 ECHO: 2.23607 ECHO: 1  ### pow Mathematical power function. Parameters <base> Decimal. Base. <exponent> Decimal. Exponent. Usage examples: for (i = [0:5]) { translate([i*25,0,0]) { cylinder(h = pow(2,i)*5, r=10); echo (i, pow(2,i)); } }  echo(pow(10,2)); // means 10^2 or 10*10 // result: ECHO: 100 echo(pow(10,3)); // means 10^3 or 10*10*10 // result: ECHO: 1000 echo(pow(125,1/3)); // means 125^(0.333...) which equals calculating the cube root of 125 // result: ECHO: 5  ### rands Random number generator. Generates a constant vector of pseudo random numbers, much like an array. The numbers are doubles not integers. When generating only one number, you still call it with variable[0] Parameters min_value Minimum value of random number range max_value Maximum value of random number range value_count Number of random numbers to return as a vector seed_value (optional) Seed value for random number generator for repeatable results. On versions before late 2015, seed_value gets rounded to the nearest integer Usage Examples: // get a single number single_rand = rands(0,10,1)[0]; echo(single_rand);  // get a vector of 4 numbers seed=42; random_vect=rands(5,15,4,seed); echo( "Random Vector: ",random_vect); sphere(r=5); for(i=[0:3]) { rotate(360*i/4) { translate([10+random_vect[i],0,0]) sphere(r=random_vect[i]/2); } } // ECHO: "Random Vector: ", [8.7454, 12.9654, 14.5071, 6.83435]  ### round The "round" operator returns the greatest or least integer part, respectively, if the numeric input is positive or negative. Some examples: round(x.5) = x+1. round(x.49) = x. round(-(x.5)) = -(x+1). round(-(x.49)) = -x. round(5.4); //-> 5 round(5.5); //-> 6 round(5.6); //-> 6  ### sign Mathematical signum function. Returns a unit value that extracts the sign of a value see: Signum function Parameters <x> Decimal. Value to find the sign of. Usage examples: sign(-5.0); sign(0); sign(8.0);  Results: -1.0 0.0 1.0  ### sqrt Mathematical square root function. Usage Examples: translate([sqrt(100),0,0])sphere(100);  ## Infinities and NaNs How does OpenSCAD deal with inputs like (1/0)? Basically, the behavior is inherited from the language OpenSCAD was written in, the C++ language, and its floating point number types and the associated C math library. This system allows representation of both positive and negative infinity by the special values "Inf" or "-Inf". It also allow representation of creatures like sqrt(-1) or 0/0 as "NaN", an abbreviation for "Not A Number". Some very nice explanations can be found on the web, for example the Open Group's site on math.h or Wikipedia's page on the IEEE 754 number format. However OpenSCAD is it's own language so it may not exactly match everything that happens in C. For example, OpenSCAD uses degrees instead of radians for trigonometric functions. Another example is that sin() does not throw a "domain error" when the input is 1/0, although it does return NaN. Here are some examples of infinite input to OpenSCAD math functions and the resulting output, taken from OpenSCAD's regression test system in late 2015.  0/0: nan sin(1/0): nan asin(1/0): nan ln(1/0): inf round(1/0): inf -0/0: nan cos(1/0): nan acos(1/0): nan ln(-1/0): nan round(-1/0): -inf 0/-0: nan tan(1/0): nan atan(1/0): 90 log(1/0): inf sign(1/0): 1 1/0: inf ceil(-1/0): -inf atan(-1/0): -90 log(-1/0): nan sign(-1/0): -1 1/-0: -inf ceil(1/0): inf atan2(1/0, -1/0): 135 max(-1/0, 1/0): inf sqrt(1/0): inf -1/0: -inf floor(-1/0): -inf exp(1/0): inf min(-1/0, 1/0): -inf sqrt(-1/0): nan -1/-0: inf floor(1/0): inf exp(-1/0): 0 pow(2, 1/0): inf pow(2, -1/0): 0 ### str Convert all arguments to strings and concatenate. Usage examples: number=2; echo ("This is ",number,3," and that's it."); echo (str("This is ",number,3," and that's it."));  Results: ECHO: "This is ", 2, 3, " and that's it." ECHO: "This is 23 and that's it."  ### chr [Note: Requires version 2015.03] Convert numbers to a string containing character with the corresponding code. OpenSCAD uses Unicode, so the number is interpreted as Unicode code point. Numbers outside the valid code point range will produce an empty string. Parameters chr(Number) Convert one code point to a string of length 1 (number of bytes depending on UTF-8 encoding) if the code point is valid. chr(Vector) Convert all code points given in the argument vector to a string. chr(Range) Convert all code points produced by the range argument to a string. Examples echo(chr(65), chr(97)); // ECHO: "A", "a" echo(chr(65, 97)); // ECHO: "Aa" echo(chr([66, 98])); // ECHO: "Bb" echo(chr([97 : 2 : 102])); // ECHO: "ace" echo(chr(-3)); // ECHO: "" echo(chr(9786), chr(9788)); // ECHO: "☺", "☼" echo(len(chr(9788))); // ECHO: 1  Note: When used with echo() the output to the console for character codes greater than 127 is platform dependent. ### ord [Note: Requires version nightly build] Convert a character to a number representing the Unicode code point. If the parameter is not a string, the ord() will return undef. Parameters ord(String) Convert the first character of the given string to a Unicode code point. Examples echo(ord("a")); // ECHO: 97 echo(ord("BCD")); // ECHO: 66 echo([for (c = "Hello! 🙂") ord(c)]); // ECHO: [72, 101, 108, 108, 111, 33, 32, 128578]  ### Also See search() search() for text searching. ### cube Creates a cube in the first octant. When center is true, the cube is centered on the origin. Argument names are optional if given in the order shown here. cube(size = [x,y,z], center = true/false); cube(size = x , center = true/false);  parameters: size single value, cube with all sides this length 3 value array [x,y,z], cube with dimensions x, y and z. center false (default), 1st (positive) octant, one corner at (0,0,0) true, cube is centered at (0,0,0) default values: cube(); yields: cube(size = [1, 1, 1], center = false);  examples: equivalent scripts for this example cube(size = 18); cube(18); cube([18,18,18]); . cube(18,false); cube([18,18,18],false); cube([18,18,18],center=false); cube(size = [18,18,18], center = false); cube(center = false,size = [18,18,18] );  equivalent scripts for this example cube([18,28,8],true); box=[18,28,8];cube(box,true);  ### sphere Creates a sphere at the origin of the coordinate system. The r argument name is optional. To use d instead of r, d must be named. Parameters Radius. This is the radius of the sphere. The resolution of the sphere will be based on the size of the sphere and the$fa, $fs and$fn variables. For more information on these special variables look at: OpenSCAD_User_Manual/Other_Language_Features
Diameter. This is the diameter of the sphere.

(NOTE: d is only available in versions later than 2014.03. Debian is currently known to be behind this)

$fa Fragment angle in degrees$fs
Fragment size in mm
$fn Resolution  default values: sphere(); yields: sphere($fn = 0, $fa = 12,$fs = 2, r = 1);


Usage Examples

sphere(r = 1);
sphere(r = 5);
sphere(r = 10);
sphere(d = 2);
sphere(d = 10);
sphere(d = 20);

// this will create a high resolution sphere with a 2mm radius
sphere(2, $fn=100);  // will also create a 2mm high resolution sphere but this one // does not have as many small triangles on the poles of the sphere sphere(2,$fa=5, $fs=0.1);  ### cylinder Creates a cylinder or cone centered about the z axis. When center is true, it is also centered vertically along the z axis. Parameter names are optional if given in the order shown here. If a parameter is named, all following parameters must also be named. NOTE: If r, d, d1 or d2 are used they must be named. cylinder(h = height, r1 = BottomRadius, r2 = TopRadius, center = true/false);  Parameters h : height of the cylinder or cone r : radius of cylinder. r1 = r2 = r. r1 : radius, bottom of cone. r2 : radius, top of cone. d : diameter of cylinder. r1 = r2 = d /2. d1 : diameter, bottom of cone. r1 = d1 /2 d2 : diameter, top of cone. r2 = d2 /2 (NOTE: d,d1,d2 require 2014.03 or later. Debian is currently known to be behind this) center false (default), z ranges from 0 to h true, z ranges from -h/2 to +h/2$fa : minimum angle (in degrees) of each fragment.
$fs : minimum circumferential length of each fragment.$fn : fixed number of fragments in 360 degrees. Values of 3 or more override $fa and$fs
$fa,$fs and $fn must be named. click here for more details,. defaults: cylinder(); yields: cylinder($fn = 0, $fa = 12,$fs = 2, h = 1, r1 = 1, r2 = 1, center = false);


equivalent scripts
cylinder(h=15, r1=9.5, r2=19.5, center=false);
cylinder(  15,    9.5,    19.5, false);
cylinder(  15,    9.5,    19.5);
cylinder(  15,    9.5, d2=39  );
cylinder(  15, d1=19,  d2=39  );
cylinder(  15, d1=19,  r2=19.5);


equivalent scripts
cylinder(h=15, r1=10, r2=0, center=true);
cylinder(  15,    10,    0,        true);
cylinder(h=15, d1=20, d2=0, center=true);

equivalent scripts
cylinder(h=20, r=10, center=true);
cylinder(  20,   10, 10,true);
cylinder(  20, d=20, center=true);
cylinder(  20,r1=10, d2=20, center=true);
cylinder(  20,r1=10, d2=2*10, center=true);

use of $fn Larger values of$fn create smoother, more circular, surfaces at the cost of longer rendering time. Some use medium values during development for the faster rendering, then change to a larger value for the final F6 rendering.

However, use of small values can produce some interesting non circular objects. A few examples are show here:

scripts for these examples
cylinder(20,20,20,$fn=3); cylinder(20,20,00,$fn=4);
cylinder(20,20,10,$fn=4);  undersized holes When using cylinder() with difference() to place holes in objects, the holes will be undersized. This is because circular paths are approximated with polygons inscribed within in a circle. The points of the polygon are on the circle, but straight lines between are inside. To have all of the hole larger than the true circle, the polygon must lie wholly outside of the circle (circumscribed). Modules for circumscribed holes Notes on accuracy Circle objects are approximated. The algorithm for doing this matters when you want 3d printed holes to be the right size. Current behavior is illustrated in a diagram . Discussion regarding optionally changing this behavior happening in a Pull Request ### polyhedron A polyhedron is the most general 3D primitive solid. It can be used to create any regular or irregular shape including those with concave as well as convex features. Curved surfaces are approximated by a series of flat surfaces. polyhedron( points = [ [X0, Y0, Z0], [X1, Y1, Z1], ... ], triangles = [ [P0, P1, P2], ... ], convexity = N); // before 2014.03 polyhedron( points = [ [X0, Y0, Z0], [X1, Y1, Z1], ... ], faces = [ [P0, P1, P2, P3, ...], ... ], convexity = N); // 2014.03 & later  Parameters points Vector of 3d points or vertices. Each point is in turn a vector, [x,y,z], of its coordinates. Points may be defined in any order. N points are referenced, in the order defined, as 0 to N-1. triangles (deprecated in version 2014.03, use faces) Vector of faces which collectively enclose the solid. Each face is a vector containing the indices (0 based) of 3 points from the points vector. faces (introduced in version 2014.03) Vector of faces which collectively enclose the solid. Each face is a vector containing the indices (0 based) of 3 or more points from the points vector. Faces may be defined in any order. Define enough faces to fully enclose the solid, with no overlap. Points which describe a single face must all be on the same plane. convexity Integer. The convexity parameter specifies the maximum number of faces a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode. It has no effect on the polyhedron rendering. For display problems, setting it to 10 should work fine for most cases.  default values: polyhedron(); yields: polyhedron(points = undef, faces = undef, convexity = 1);  All faces must have points ordered in the same direction . OpenSCAD prefers clockwise when looking at each face from outside inwards. The back is viewed from the back, the bottom from the bottom, etc.. Example 1 Using polyhedron to generate cube( [ 10, 7, 5 ] ); point numbers for cube unfolded cube faces CubePoints = [ [ 0, 0, 0 ], //0 [ 10, 0, 0 ], //1 [ 10, 7, 0 ], //2 [ 0, 7, 0 ], //3 [ 0, 0, 5 ], //4 [ 10, 0, 5 ], //5 [ 10, 7, 5 ], //6 [ 0, 7, 5 ]]; //7 CubeFaces = [ [0,1,2,3], // bottom [4,5,1,0], // front [7,6,5,4], // top [5,6,2,1], // right [6,7,3,2], // back [7,4,0,3]]; // left polyhedron( CubePoints, CubeFaces );  equivalent descriptions of the bottom face [0,1,2,3], [0,1,2,3,0], [1,2,3,0], [2,3,0,1], [3,0,1,2], [0,1,2],[2,3,0], // 2 triangles with no overlap [1,2,3],[3,0,1], [1,2,3],[0,1,3],  Example 2 A square base pyramid: A simple polyhedron, square base pyramid polyhedron( points=[ [10,10,0],[10,-10,0],[-10,-10,0],[-10,10,0], // the four points at base [0,0,10] ], // the apex point faces=[ [0,1,4],[1,2,4],[2,3,4],[3,0,4], // each triangle side [1,0,3],[2,1,3] ] // two triangles for square base );  Example 3 A triangular prism: A polyhedron triangular prism  module prism(l, w, h){ polyhedron( points=[[0,0,0], [l,0,0], [l,w,0], [0,w,0], [0,w,h], [l,w,h]], faces=[[0,1,2,3],[5,4,3,2],[0,4,5,1],[0,3,4],[5,2,1]] ); // preview unfolded (do not include in your function z = 0.08; separation = 2; border = .2; translate([0,w+separation,0]) cube([l,w,z]); translate([0,w+separation+w+border,0]) cube([l,h,z]); translate([0,w+separation+w+border+h+border,0]) cube([l,sqrt(w*w+h*h),z]); translate([l+border,w+separation+w+border+h+border,0]) polyhedron( points=[[0,0,0],[h,0,0],[0,sqrt(w*w+h*h),0], [0,0,z],[h,0,z],[0,sqrt(w*w+h*h),z]], faces=[[0,1,2], [3,5,4], [0,3,4,1], [1,4,5,2], [2,5,3,0]] ); translate([0-border,w+separation+w+border+h+border,0]) polyhedron( points=[[0,0,0],[0-h,0,0],[0,sqrt(w*w+h*h),0], [0,0,z],[0-h,0,z],[0,sqrt(w*w+h*h),z]], faces=[[1,0,2],[5,3,4],[0,1,4,3],[1,2,5,4],[2,0,3,5]] ); } prism(10, 5, 3);  #### Debugging polyhedra Mistakes in defining polyhedra include not having all faces with the same order, overlap of faces and missing faces or portions of faces. As a general rule, the polyhedron faces should also satisfy (manifold conditions): • exactly two faces should meet at any polyhedron edge. • if two faces have a vertex in common, they should be in the same cycle face-edge around the vertex. The first rule eliminates polyhedron like two cubes with a common edge and not watertight models; the second excludes polyhedron like two cubes with a common vertex. When viewed from the outside, the points describing each face must be in the same order . OpenSCAD prefers CW, and provides a mechanism for detecting CCW. When the thrown together view (F12) is used with F5, CCW faces are shown in pink. Reorder the points for incorrect faces. Rotate the object to view all faces. The pink view can be turned off with F10. OpenSCAD allows, temporarily, commenting out part of the face descriptions so that only the remaining faces are displayed. Use // to comment out the rest of the line. Use /* and */ to start and end a comment block. This can be part of a line or extend over several lines. Viewing only part of the faces can be helpful in determining the right points for an individual face. Note that a solid is not shown, only the faces. If using F12, all faces have one pink side. Commenting some faces helps also to show any internal face. example 1 showing only 2 faces CubeFaces = [ /* [0,1,2,3], // bottom [4,5,1,0], // front */ [7,6,5,4], // top /* [5,6,2,1], // right [6,7,3,2], // back */ [7,4,0,3]]; // left  After defining a polyhedron, its preview may seem correct. The polyhedron alone may even render fine. However to be sure it is a valid manifold and that it will generate a valid STL file, union it with any cube and render it (F6). If the polyhedron disappears, it means that it is not correct. Revise the winding order of all faces and the two rules stated above. #### Mis-ordered faces Example 4 a more complex polyhedron with mis-ordered faces When you select 'Thrown together' from the view menu and compile the design (not compile and render!) you will see a preview with the mis-oriented polygons highlighted. Unfortunately this highlighting is not possible in the OpenCSG preview mode because it would interfere with the way the OpenCSG preview mode is implemented.) Below you can see the code and the picture of such a problematic polyhedron, the bad polygons (faces or compositions of faces) are in pink. // Bad polyhedron polyhedron (points = [ [0, -10, 60], [0, 10, 60], [0, 10, 0], [0, -10, 0], [60, -10, 60], [60, 10, 60], [10, -10, 50], [10, 10, 50], [10, 10, 30], [10, -10, 30], [30, -10, 50], [30, 10, 50] ], faces = [ [0,2,3], [0,1,2], [0,4,5], [0,5,1], [5,4,2], [2,4,3], [6,8,9], [6,7,8], [6,10,11], [6,11,7], [10,8,11], [10,9,8], [0,3,9], [9,0,6], [10,6, 0], [0,4,10], [3,9,10], [3,10,4], [1,7,11], [1,11,5], [1,7,8], [1,8,2], [2,8,11], [2,11,5] ] );  Polyhedron with badly oriented polygons A correct polyhedron would be the following: polyhedron (points = [ [0, -10, 60], [0, 10, 60], [0, 10, 0], [0, -10, 0], [60, -10, 60], [60, 10, 60], [10, -10, 50], [10, 10, 50], [10, 10, 30], [10, -10, 30], [30, -10, 50], [30, 10, 50] ], faces = [ [0,3,2], [0,2,1], [4,0,5], [5,0,1], [5,2,4], [4,2,3], [6,8,9], [6,7,8], [6,10,11],[6,11,7], [10,8,11], [10,9,8], [3,0,9], [9,0,6], [10,6, 0],[0,4,10], [3,9,10], [3,10,4], [1,7,11], [1,11,5], [1,8,7], [2,8,1], [8,2,11], [5,11,2] ] );  Beginner's tip: If you don't really understand "orientation", try to identify the mis-oriented pink faces and then invert the sequence of the references to the points vectors until you get it right. E.g. in the above example, the third triangle ([0,4,5]) was wrong and we fixed it as [4,0,5]. Remember that a face list is a circular list. In addition, you may select "Show Edges" from the "View Menu", print a screen capture and number both the points and the faces. In our example, the points are annotated in black and the faces in blue. Turn the object around and make a second copy from the back if needed. This way you can keep track. Clockwise Technique: Orientation is determined by clockwise circular indexing. This means that if you're looking at the triangle (in this case [4,0,5]) from the outside you'll see that the path is clockwise around the center of the face. The winding order [4,0,5] is clockwise and therefore good. The winding order [0,4,5] is counter-clockwise and therefore bad. Likewise, any other clockwise order of [4,0,5] works: [5,4,0] & [0,5,4] are good too. If you use the clockwise technique, you'll always have your faces outside (outside of OpenSCAD, other programs do use counter-clockwise as the outside though). Think of it as a Left Hand Rule: If you hold the face and the fingers of your right hand curls is the same order as the points, then your thumb points outwards. Polyhedron with badly oriented polygons Succinct description of a 'Polyhedron' * Points define all of the points/vertices in the shape. * Faces is a list of flat polygons that connect up the points/vertices.  Each point, in the point list, is defined with a 3-tuple x,y,z position specification. Points in the point list are automatically enumerated starting from zero for use in the faces list (0,1,2,3,... etc). Each face, in the faces list, is defined by selecting 3 or more of the points (using the point order number) out of the point list. e.g. faces=[ [0,1,2] ] defines a triangle from the first point (points are zero referenced) to the second point and then to the third point. When looking at any face from the outside, the face must list all points in a clockwise order. #### Alternate Face Descriptions Before 2014.03, faces could only be described via triangles. Since 2014.03, a face description can have any number of points. The points, all in the same plane, must be listed in the proper order. Since version ???, the face vertices do not have to be planar: OpenSCAD will do its best to internally subdivide the face in triangles. Note that this may lead to different results depending on the chosen face triangulation. If a specific result is needed, the non planar face should be broken in triangular pieces by the user. An alternate (correct) face definition for example 4: faces = [ [0,3,2,1], [0,1,5,4], [2,3,4,5], // outside [6,7,8,9], [7,6,10,11], [11,10,9,8], // inside [0,4,3,0,6,9,10,6], // front [1,2,5,1,7,11,8,7] // back ]  #### Point repetitions in a polyhedron point list The point list of the polyhedron definition may have repetitions. When two or more points have the same coordinates they are considered the same polyhedron vertex. So, the following polyhedron: points = [[ 0, 0, 0], [10, 0, 0], [ 0,10, 0], [ 0, 0, 0], [10, 0, 0], [ 0,10, 0], [ 0,10, 0], [10, 0, 0], [ 0, 0,10], [ 0, 0, 0], [ 0, 0,10], [10, 0, 0], [ 0, 0, 0], [ 0, 0,10], [ 0,10, 0]]; polyhedron(points, [[0,1,2], [3,4,5], [6,7,8], [9,10,11]] );  define the same tetrahedron as: points = [[0,0,0], [0,10,0], [10,0,0], [0,0,10]]; polyhedron(points, [[0,2,1], [0,1,3], [1,2,3], [0,3,2]] );  ### Basic concept Transformation affect the child nodes and as the name implies transforms them in various ways such as moving/rotating or scaling the child. Cascading transformations are used to apply a variety of transforms to a final child. Cascading is achieved by nesting statements i.e. rotate([45,45,45]) translate([10,20,30]) cube(10);  Transformations can be applied to a group of child nodes by using '{' and '}' to enclose the subtree e.g. translate([0,0,-5]) { cube(10); cylinder(r=5,h=10); }  Transformations are written before the object they affect. Imagine command like translate, mirror and scale as verbs. Commands like color are like adjectives that describe the object. Notice that there is no semicolon following transformation command. ### Advanced concept As OpenSCAD uses different libraries to implement capabilities this can introduce some inconsistencies to the F5 preview behaviour of transformations. Traditional transforms (translate, rotate, scale, mirror & multimatrix) are performed using OpenGL in preview, while other more advanced transforms, such as resize, perform a CGAL operation, behaving like a CSG operation affecting the underlying object, not just transforming it. In particular this can affect the display of modifier characters, specifically "#" and "%", where the highlight may not display intuitively, such as highlighting the pre-resized object, but highlighting the post-scaled object. ### scale Scales its child elements using the specified vector. The argument name is optional. Usage Example: scale(v = [x, y, z]) { ... }  cube(10); translate([15,0,0]) scale([0.5,1,2]) cube(10);  Note: Do not use negative scale values. Negative scale values appear to work for previews, but they lead to unpredictable errors when rendering through CGAL. Use the mirror() function instead. ### resize Modifies the size of the child object to match the given x,y, and z. resize() is a CGAL operation, and like others such as render() operates with full geometry, so even in preview will take time to process. Usage Example: // resize the sphere to extend 30 in x, 60 in y, and 10 in the z directions. resize(newsize=[30,60,10]) sphere(r=10);  If x,y, or z is 0 then that dimension is left as-is. // resize the 1x1x1 cube to 2x2x1 resize([2,2,0]) cube();  If the 'auto' parameter is set to true, it will auto-scale any 0-dimensions to match. For example. // resize the 1x2x0.5 cube to 7x14x3.5 resize([7,0,0], auto=true) cube([1,2,0.5]);  The 'auto' parameter can also be used if you only wish to auto-scale a single dimension, and leave the other as-is. // resize to 10x8x1. Note that the z dimension is left alone. resize([10,0,0], auto=[true,true,false]) cube([5,4,1]);  ### rotate Rotates its child 'a' degrees about the axis of the coordinate system or around an arbitrary axis. The argument names are optional if the arguments are given in the same order as specified. //Usage: rotate(a = deg_a, v = [x, y, z]) { ... } // or rotate(deg_a, [x, y, z]) { ... } rotate(a = [deg_x, deg_y, deg_z]) { ... } rotate([deg_x, deg_y, deg_z]) { ... }  The 'a' argument (deg_a) can be an array, as expressed in the later usage above; when deg_a is an array, the 'v' argument is ignored. Where 'a' specifies multiple axes then the rotation is applied in the following order: x, y, z. That means the code: rotate(a=[ax,ay,az]) {...}  is equivalent to: rotate(a=[0,0,az]) rotate(a=[0,ay,0]) rotate(a=[ax,0,0]) {...}  The optional argument 'v' is a vector and allows you to set an arbitrary axis about which the object will be rotated. For example, to flip an object upside-down, you can rotate your object 180 degrees around the 'y' axis. rotate(a=[0,180,0]) { ... }  This is frequently simplified to rotate([0,180,0]) { ... }  When specifying a single axis the 'v' argument allows you to specify which axis is the basis for rotation. For example, the equivalent to the above, to rotate just around y rotate(a=180, v=[0,1,0]) { ... }  When specifying a single axis, 'v' is a vector defining an arbitrary axis for rotation; this is different from the multiple axis above. For example, rotate your object 45 degrees around the axis defined by the vector [1,1,0], rotate(a=45, v=[1,1,0]) { ... }  Rotate with a single scalar argument rotates around the Z axis. This is useful in 2D contexts where that is the only axis for rotation. For example: rotate(45) square(10);  ##### Rotation rule help Right-hand grip rule For the case of: rotate([a, b, c]) { ... };  "a" is a rotation about the X axis, from the +Y axis, toward the +Z axis. "b" is a rotation about the Y axis, from the +Z axis, toward the +X axis. "c" is a rotation about the Z axis, from the +X axis, toward the +Y axis. These are all cases of the Right Hand Rule. Point your right thumb along the positive axis, your fingers show the direction of rotation. Thus if "a" is fixed to zero, and "b" and "c" are manipulated appropriately, this is the spherical coordinate system. So, to construct a cylinder from the origin to some other point (x,y,z): x= 10; y = 10; z = 10; // point coordinates of end of cylinder length = norm([x,y,z]); // radial distance b = acos(z/length); // inclination angle c = atan2(y,x); // azimuthal angle rotate([0, b, c]) cylinder(h=length, r=0.5); %cube([x,y,z]); // corner of cube should coincide with end of cylinder  ### translate Translates (moves) its child elements along the specified vector. The argument name is optional. Example: translate(v = [x, y, z]) { ... }  cube(2,center = true); translate([5,0,0]) sphere(1,center = true);  ### mirror Mirrors the child element on a plane through the origin. The argument to mirror() is the normal vector of a plane intersecting the origin through which to mirror the object. #### Function signature: mirror(v= [x, y, z] ) { ... }  #### Examples The original is on the right side. Note that mirror doesn't make a copy. Like rotate and scale, it changes the object. rotate([0,0,10]) cube([3,2,1]); mirror([1,0,0]) translate([1,0,0]) rotate([0,0,10]) cube([3,2,1]);  ### multmatrix Multiplies the geometry of all child elements with the given 4x4 transformation matrix. Usage: multmatrix(m = [...]) { ... } This is a breakdown of what you can do with the independent elements in the matrix (for the first three rows):  [Scale X] [Scale X sheared along Y] [Scale X sheared along Z] [Translate X] [Scale Y sheared along X] [Scale Y] [Scale Y sheared along Z] [Translate Y] [Scale Z sheared along X] [Scale Z sheared along Y] [Scale Z] [Translate Z] the fourth row is used in 3D environments to define a view of the object. it is not used in OpenSCAD and should be [0,0,0,1] Example which rotates by 45 degrees in XY plane and translates by [10,20,30], ie the same as translate([10,20,30]) rotate([0,0,45]) would do. angle=45; multmatrix(m = [ [cos(angle), -sin(angle), 0, 10], [sin(angle), cos(angle), 0, 20], [ 0, 0, 1, 30], [ 0, 0, 0, 1] ]) union() { cylinder(r=10.0,h=10,center=false); cube(size=[10,10,10],center=false); }  Example that skews a model, something that is not possible with the other transformations. Also shows you can have the matrix in a variable. M = [ [ 1 , 0 , 0 , 0 ], [ 0 , 1 , 0.7, 0 ], // The "0.7" is the skew value; pushed along the y axis [ 0 , 0 , 1 , 0 ], [ 0 , 0 , 0 , 1 ] ] ; multmatrix(M) { union() { cylinder(r=10.0,h=10,center=false); cube(size=[10,10,10],center=false); } }  #### More? Learn more about it here: ### color Displays the child elements using the specified RGB color + alpha value. This is only used for the F5 preview as CGAL and STL (F6) do not currently support color. The alpha value will default to 1.0 (opaque) if not specified. #### Function signature: color( c = [r, g, b, a] ) { ... } color( c = [r, g, b], alpha = 1.0 ) { ... } color( "colorname", 1.0 ) { ... }  Note that the r, g, b, a values are limited to floating point values in the range [0,1] rather than the more traditional integers { 0 ... 255 }. However, nothing prevents you to using R, G, B values from {0 ... 255} with appropriate scaling: color([ R/255, G/255, B/255 ]) { ... }  Since version 2011.12, colors can also be defined by name (case insensitive). For example, to create a red sphere, you can write color("red") sphere(5);. Alpha is specified as an extra parameter for named colors: color("Blue",0.5) cube(5); The available color names are taken from the World Wide Web consortium's SVG color list. A chart of the color names is as follows, (note that both spellings of grey/gray including slategrey/slategray etc are valid):  Purples Lavender Thistle Plum Violet Orchid Fuchsia Magenta MediumOrchid MediumPurple BlueViolet DarkViolet DarkOrchid DarkMagenta Purple Indigo DarkSlateBlue SlateBlue MediumSlateBlue Pinks Pink LightPink HotPink DeepPink MediumVioletRed PaleVioletRed  Blues Aqua Cyan LightCyan PaleTurquoise Aquamarine Turquoise MediumTurquoise DarkTurquoise CadetBlue SteelBlue LightSteelBlue PowderBlue LightBlue SkyBlue LightSkyBlue DeepSkyBlue DodgerBlue CornflowerBlue RoyalBlue Blue MediumBlue DarkBlue Navy MidnightBlue Reds IndianRed LightCoral Salmon DarkSalmon LightSalmon Red Crimson FireBrick DarkRed  Greens GreenYellow Chartreuse LawnGreen Lime LimeGreen PaleGreen LightGreen MediumSpringGreen SpringGreen MediumSeaGreen SeaGreen ForestGreen Green DarkGreen YellowGreen OliveDrab Olive DarkOliveGreen MediumAquamarine DarkSeaGreen LightSeaGreen DarkCyan Teal Oranges LightSalmon Coral Tomato OrangeRed DarkOrange Orange  Yellows Gold Yellow LightYellow LemonChiffon LightGoldenrodYellow PapayaWhip Moccasin PeachPuff PaleGoldenrod Khaki DarkKhaki Browns Cornsilk BlanchedAlmond Bisque NavajoWhite Wheat BurlyWood Tan RosyBrown SandyBrown Goldenrod DarkGoldenrod Peru Chocolate SaddleBrown Sienna Brown Maroon  Whites White Snow Honeydew MintCream Azure AliceBlue GhostWhite WhiteSmoke Seashell Beige OldLace FloralWhite Ivory AntiqueWhite Linen LavenderBlush MistyRose Grays Gainsboro LightGrey Silver DarkGray Gray DimGray LightSlateGray SlateGray DarkSlateGray Black #### Example A 3-D multicolor sine wave Here's a code fragment that draws a wavy multicolor object  for(i=[0:36]) { for(j=[0:36]) { color( [0.5+sin(10*i)/2, 0.5+sin(10*j)/2, 0.5+sin(10*(i+j))/2] ) translate( [i, j, 0] ) cube( size = [1, 1, 11+10*cos(10*i)*sin(10*j)] ); } }  ↗ Being that -1<=sin(x)<=1 then 0<=(1/2 + sin(x)/2)<=1 , allowing for the RGB components assigned to color to remain within the [0,1] interval. #### Example 2 In cases where you want to optionally set a color based on a parameter you can use the following trick:  module myModule(withColors=false) { c=withColors?"red":undef; color(c) circle(r=10); }  Setting the colorname to undef will keep the default colors. ### offset [Note: Requires version 2015.03] Offset allows moving 2D outlines outward or inward by a given amount. • This is useful for making thin walls, by differencing a positive-offset exterior and a negative-offset interior. • Fillet: offset(r=-3) offset(delta=+3) rounds all inside (concave) corners, and leaves flat walls unchanged. However, holes less than 2*r in diameter will vanish. • Round: offset(r=+3) offset(delta=-3) rounds all outside (convex) corners, and leaves flat walls unchanged. However, walls less than 2*r thick will vanish. Parameters r | delta Double. Amount to offset the polygon. When negative, the polygon is offset inwards. The parameter r specifies the radius that is used to generate rounded corners, using delta gives straight edges. chamfer Boolean. (default false) When using the delta parameter, this flag defines if edges should be chamfered (cut off with a straight line) or not (extended to their intersection). Positive r/delta value Negative r/delta value Result for different parameters. The black polygon is the input for the offset() operation. Examples Example 1: Result. // Example 1 linear_extrude(height = 60, twist = 90, slices = 60) { difference() { offset(r = 10) { square(20, center = true); } offset(r = 8) { square(20, center = true); } } }  // Example 2 module fillet(r) { offset(r = -r) { offset(delta = r) { children(); } } }  ### minkowski A box and a cylinder Minkowski sum of the box and cylinder Displays the minkowski sum of child nodes. Usage example: Say you have a flat box, and you want a rounded edge. There are many ways to do this, but minkowski is very elegant. Take your box, and a cylinder: $fn=50;
cube([10,10,1]);
cylinder(r=2,h=1);


Then, do a minkowski sum of them (note that the outer dimensions of the box are now 10+2+2 = 14 units by 14 units by 2 units high as the heights of the objects are summed):

rotate ([90,0,0]) cylinder (h = 4, r=0.9, center = true, $fn=100); }  Remark: union is implicit when not used. But it is mandatory, for example, in difference to group first child nodes into one. ### difference Subtracts the 2nd (and all further) child nodes from the first one (logical and not). May be used with either 2D or 3D objects, but don't mix them. Usage example: difference() { cylinder (h = 4, r=1, center = true,$fn=100);
rotate ([90,0,0]) cylinder (h = 4, r=0.9, center = true, $fn=100); }  ##### difference with multiple children Note, in the second instance, the result of adding a union of the 1st and 2nd children. // Usage example for difference of multiple children:$fn=90;
difference(){
cylinder(r=5,h=20,center=true);
rotate([00,140,-45]) color("LightBlue") cylinder(r=2,h=25,center=true);
rotate([00,40,-50])                     cylinder(r=2,h=30,center=true);
translate([0,0,-10])rotate([00,40,-50]) cylinder(r=1.4,h=30,center=true);
}

// second instance with added union
translate([10,10,0]){
difference(){
union(){        // combine 1st and 2nd children
cylinder(r=5,h=20,center=true);
rotate([00,140,-45]) color("LightBlue") cylinder(r=2,h=25,center=true);
}
rotate([00,40,-50])                       cylinder(r=2,h=30,center=true);
translate([0,0,-10])rotate([00,40,-50])   cylinder(r=1.4,h=30,center=true);
}
}


### intersection

Creates the intersection of all child nodes. This keeps the overlapping portion (logical and).
Only the area which is common or shared by all children is retained.
May be used with either 2D or 3D objects, but don't mix them.

//Usage example:
intersection() {
cylinder (h = 4, r=1, center = true, $fn=100); rotate ([90,0,0]) cylinder (h = 4, r=0.9, center = true,$fn=100);
}


### render

• Warning:** Using render, always calculates the CSG model for this tree (even in OpenCSG preview mode).

This can make previewing very slow and OpenSCAD to appear to hang/freeze.

Usage example:
render(convexity = 1) { ... }

 convexity Integer. The convexity parameter specifies the maximum number of front and back sides a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode and has no effect on the polyhedron rendering.

This image shows a 2D shape with a convexity of 4, as the ray indicated in red crosses the 2D shape a maximum of 4 times. The convexity of a 3D shape would be determined in a similar way. Setting it to 10 should work fine for most cases.

Modifier characters are used to change the appearance or behaviours of child nodes. They are particularly useful in debugging where they can be used to highlight specific objects, or include or exclude them from rendering.

As OpenSCAD uses different libraries to implement capabilities this can introduce some inconsistencies to the F5 preview behaviour of transformations. Traditional transforms (translate, rotate, scale, mirror & multimatrix) are performed using OpenGL in preview, while other more advanced transforms, such as resize, perform a CGAL operation, behaving like a CSG operation affecting the underlying object, not just transforming it. In particular this can affect the display of modifier characters, specifically "#" and "%", where the highlight may not display intuitively, such as highlighting the pre-resized object, but highlighting the post-scaled object.

Note: The color changes triggered by character modifiers will only be shown in "Compile" mode not "Compile and Render (CGAL)" mode. (As per the color section.)

### Background Modifier

Ignore this subtree for the normal rendering process and draw it in transparent gray (all transformations are still applied to the nodes in this tree).

Because the marked subtree is completely ignored, it might have unexpected effects in case it's used, for example, with the first object in a difference(). In that case this object will be rendered in transparent gray, but it will not be the base for the difference()!

Usage

 % { ... }


Example

difference() {
cylinder (h = 12, r=5, center = true, $fn=100); // first object that will be subtracted rotate ([90,0,0]) cylinder (h = 15, r=1, center = true,$fn=100);
// second object that will be subtracted
%rotate ([0,90,0]) cylinder (h = 15, r=3, center = true, $fn=100); }  Example Output Output without the modifier. Output with modifier added. Rendered Model. ### Debug Modifier Use this subtree as usual in the rendering process but also draw it unmodified in transparent pink. Usage  # { ... }  Example difference() { // start objects cylinder (h = 12, r=5, center = true,$fn=100);
// first object that will subtracted
#rotate ([90,0,0]) cylinder (h = 15, r=1, center = true, $fn=100); // second object that will be subtracted #rotate ([0,90,0]) cylinder (h = 15, r=3, center = true,$fn=100);
}


Example Output

Output without the modifier.

### Root Modifier

Ignore the rest of the design and use this subtree as design root.

Usage

 ! { ... }


Example

difference() {
cube(10, center = true);
translate([0, 0, 5]) {
!rotate([90, 0, 0]) {
#cylinder(r = 2, h = 20, center = true, $fn = 40); } } }  Example Output Output without the modifier. Output with modifier added. As shown in the example output with the root modifier active, the rotate() is executed as it's part of the subtree marked with the root modifier, but the translate() has no effect. ### Disable Modifier Simply ignore this entire subtree. Usage  * { ... }  Example difference() { cube(10, center = true); translate([0, 0, 5]) { rotate([0, 90, 0]) { cylinder(r = 2, h = 20, center = true,$fn = 40);
}
*rotate([90, 0, 0]) {
#cylinder(r = 2, h = 20, center = true, $fn = 40); } } }  Example Output Output without the modifier. Output with modifier added. The disable modifier allows to comment out one or multiple subtrees. Compared to using the usual line or multi-line comments, it's aware of the hierarchical structure which makes it easier to disable even larger trees without the need to search for the end of the subtree. ### Echo Statements see also OpenSCAD User Manual/Other Language Features#Echo Statements This function prints the contents to the compilation window (aka Console). Useful for debugging code. Also see the String function str(). Numeric values are rounded to 5 significant digits. The OpenSCAD console supports a subset of HTML markup language. See here for details. It can be handy to use 'variable=variable' as the expression to easily label the variables, see the example below. Usage examples: my_h=50; my_r=100; echo("This is a cylinder with h=", my_h, " and r=", my_r); echo(my_h=my_h,my_r=my_r); // shortcut cylinder(h=my_h, r=my_r); // echo("<b>Hello</b> <i>Qt!</i>");  Shows in the Console as ECHO: "This is a cylinder with h=", 50, " and r=", 100 ECHO: my_h = 50, my_r = 100 ECHO: "Hello Qt!"  ### Introduction Users can extend the language by defining their own modules and functions. This allows grouping portions of script for easy reuse with different values. Well chosen names also help document your script. OpenSCAD provides: functions which return values. modules which perform actions, but do not return values. OpenSCAD calculates the value of variables at compile-time, not run-time. The last variable assignment within a scope will apply everywhere in that scope. It also applies to any inner scopes, or children, thereof. See Scope of variables for more details. It may be helpful to think of them as override-able constants rather than as variables. For functions and modules OpenSCAD makes copies of pertinent portions of the script for each use. Each copy has its own scope, which contains fixed values for variables and expressions unique to that instance. The name of functions and modules is case sensitive, therefore test() and TEST() refer to different functions/modules. ### Functions Functions operate on values to calculate and return new values. function definition function name ( parameters ) = value ;  name Your name for this function. A meaningful name is helpful later. parameters Zero or more arguments. Parameters can be assigned default values, to use in case they are omitted in the call. Parameter names are local and do not conflict with external variables of the same name. value an expression which calculates a value. This value can be a vector. function use When used, functions are treated as values, and do not themselves end with a semi-colon ';'. //example 1 function func0() = 5; function func1(x=3) = 2*x+1; function func2() = [1,2,3,4]; function func3(y=7) = (y==7) ? 5 : 2 ; function func4(p0,p1,p2,p3) = [p0,p1,p2,p3]; echo (func0()); // 5 a = func1(); // 7 b= func1(5); // 11 echo (func2()); // [1, 2, 3, 4] echo( func3(2),func3()); // 2, 5 z= func4(func0(),func1(),func2(),func3()); // [5, 7, [1, 2, 3, 4], 5] translate([0,-4*func0(),0])cube([func0(),2*func0(),func0()]); // same as translate([0,-20,0])cube([5,10,5]);  //example 2 creates for() range to give desired no of steps to cover range function steps( start, no_steps, end) = [start:(end-start)/(no_steps-1):end]; echo( steps(10,3,5)); // [10 : -2.5 : 5] for( i=steps(10,3,5))echo(i); // 10 7.5 5 echo(steps(10,3,15)); //[10 : 2.5 : 15] for( i=steps(10,3,15))echo(i); // 10 12.5 15 echo(steps(0,5,5)); // [0 : 1.25 : 5] for( i=steps(0,5,5))echo(i); // 0 1.25 2.5 3.75 5  Example 3 //example 3 rectangle with top pushed over, keeping same y function rhomboid(x=1,y=1,angle=90) = [[0,0],[x,0], [x+x*cos(angle)/sin(angle),y], [x*cos(angle)/sin(angle),y]]; echo (v1); v1 = rhomboid(10,10,35); // [[0, 0], // [10, 0], // [24.2815, 10], // [14.2815, 10]] polygon(v1); polygon(rhomboid(10,10,35)); // alternate  //performing the same action with a module module parallelogram(x=1,y=1,angle=90) {polygon([[0,0],[x,0], [x+x*cos(angle)/sin(angle),y], [x*cos(angle)/sin(angle),y]]);}; parallelogram(10,10,35);  You can also use the let statement: function get_square_triangle_perimeter(p1, p2) = let(hypotenuse=sqrt(p1*p1+p2*p2)) p1+p2+hypotenuse;  It can be used to store variables in recursive functions. #### Recursive functions Recursive function calls are supported. Using the Conditional Operator "... ? ... : ... ", it is possible to ensure the recursion is terminated.  // recursion example: add all integers up to n function add_up_to(n) = ( n==0 ? 0 : n + add_up_to(n-1) );  There is a built-in recursion limit to prevent an application crash (a few thousands). If the limit is hit, you get an error like: ERROR: Recursion detected calling function ... . For some special cases of tail-recursive functions, OpenSCAD is able to eliminate internally the recursion transforming it in an iterative loop. The special forms are: function recurse(...) = <test> ? <result> : recurse(...);  and function recurse(...) = <test> ? recurse(...) : <result>;  The previous example code does not match any of these forms. But the following is entitled to tail-recursion elimination: // tail-recursion elimination example: add all integers up to n function add_up_to(n, sum=0) = n==0 ? sum : add_up_to(n-1, sum+n); echo(sum=add_up_to(100000)); // ECHO: sum = 5.00005e+009  Tail-recursion elimination allows much higher recursion limits. ### Modules Modules can be used to define objects or, using children(), define operators. Once defined, modules are temporarily added to the language. module definition module name ( parameters ) { actions }  name Your name for this module. Try to pick something meaningful. parameters Zero or more arguments. Parameters may be assigned default values, to use in case they are omitted in the call. Parameter names are local and do not conflict with external variables of the same name. actions Nearly any statement valid outside a module can be included within a module. This includes the definition of functions and other modules. Such functions and modules can only be called from within the enclosing module. Variables can be assigned, but their scope is limited to within each individual use of the module. There is no mechanism in OpenSCAD for modules to return values to the outside. See Scope of variables for more details. #### Object modules Object modules use one or more primitives, with associated operators, to define new objects. In use, object modules are actions ending with a semi-colon ';'. name ( parameter values );  Color bar //example 1 translate([-30,-20,0]) ShowColorBars(Expense); ColorBreak=[[0,""], [20,"lime"], // upper limit of color range [40,"greenyellow"], [60,"yellow"], [75,"LightCoral"], [200,"red"]]; Expense=[16,20,25,85,52,63,45]; module ColorBar(value,period,range){ // 1 color on 1 bar RangeHi = ColorBreak[range][0]; RangeLo = ColorBreak[range-1][0]; color( ColorBreak[range][1] ) translate([10*period,0,RangeLo]) if (value > RangeHi) cube([5,2,RangeHi-RangeLo]); else if (value > RangeLo) cube([5,2,value-RangeLo]); } module ShowColorBars(values){ for (month = [0:len(values)-1], range = [1:len(ColorBreak)-1]) ColorBar(values[month],month,range); }  House //example 2 module house(roof="flat",paint=[1,0,0]) { color(paint) if(roof=="flat") { translate([0,-1,0]) cube(); } else if(roof=="pitched") { rotate([90,0,0]) linear_extrude(height=1) polygon(points=[[0,0],[0,1],[0.5,1.5],[1,1],[1,0]]); } else if(roof=="domical") { translate([0,-1,0]){ translate([0.5,0.5,1]) sphere(r=0.5,$fn=20); cube(); }
} }

house();
translate([2,0,0]) house("pitched");
translate([4,0,0]) house("domical",[0,1,0]);
translate([6,0,0]) house(roof="pitched",paint=[0,0,1]);
translate([0,3,0]) house(paint=[0,0,0],roof="pitched");
translate([2,3,0]) house(roof="domical");
translate([4,3,0]) house(paint=[0,0.5,0.5]);

//example 3

element_data = [[0,"","",0],  // must be in order
[1,"Hydrogen","H",1.008],   // indexed via atomic number
[2,"Helium",  "He",4.003]   // redundant atomic number to preserve your sanity later
];

Hydrogen = 1;
Helium   = 2;

module coaster(atomic_number){
element     = element_data[atomic_number][1];
symbol      = element_data[atomic_number][2];
atomic_mass = element_data[atomic_number][3];
//rest of script
}


#### Operator Modules

Use of children() allows modules to act as operators applied to any or all of the objects within this module instantiation. In use, operator modules do not end with a semi-colon.

name ( parameter values ){scope of operator}


#### Children

Objects are indexed via integers from 0 to $children-1. OpenSCAD sets$children to the total number of objects within the scope. Objects grouped into a sub scope are treated as one child. See example of separate children below and Scope of variables.

 children();                         all children
children(index);                    value or variable to select one child
children([start : step : end]);     select from start to end incremented by step
children([start : end]);            step defaults to 1 or -1
children([vector]);                 selection of several children


Deprecated child() module

Up to release 2013.06 the now deprecated child() module was used instead. This can be translated to the new children() according to the table:

up to 2013.06 2014.03 and later
child() children(0)
child(x) children(x)
for (a = [0:$children-1]) child(a) children([0:$children-1])
Use all children

Examples

//Use all children

module move(x=0,y=0,z=0,rx=0,ry=0,rz=0)
{ translate([x,y,z])rotate([rx,ry,rz]) children(); }

move(10)           cube(10,true);
move(-10)          cube(10,true);
move(z=7.07, ry=45)cube(10,true);
move(z=-7.07,ry=45)cube(10,true);

Use only the first child, multiple times
//Use only the first child, multiple times

module lineup(num, space) {
for (i = [0 : num-1])
translate([ space*i, 0, 0 ]) children(0);
}

lineup(5, 65){ sphere(30);cube(35);}

Separate action for each child
  //Separate action for each child

module SeparateChildren(space){
for ( i= [0:1:$children-1]) // step needed in case$children < 2
translate([i*space,0,0]) {children(i);text(str(i));}
}

SeparateChildren(-20){
cube(5);              // 0
sphere(5);            // 1
translate([0,20,0]){  // 2
cube(5);
sphere(5);
}
cylinder(15);         // 3
cube(8,true);         // 4
}
translate([0,40,0])color("lightblue")
SeparateChildren(20){cube(3,true);}

Multiple ranges
//Multiple ranges
module MultiRange(){
color("lightblue") children([0:1]);
color("lightgreen")children([2:$children-2]); color("lightpink") children($children-1);
}

MultiRange()
{
cube(5);              // 0
sphere(5);            // 1
translate([0,20,0]){  // 2
cube(5);
sphere(5);
}
cylinder(15);         // 3
cube(8,true);         // 4
}


#### Further Module Examples

Objects
module arrow(){
cylinder(10);
cube([4,.5,3],true);
cube([.5,4,3],true);
translate([0,0,10]) cylinder(4,2,0,true);
}

module cannon(){
difference(){union()
{sphere(10);cylinder(40,10,8);} cylinder(41,4,4);
} }

module base(){
difference(){
cube([40,30,20],true);
translate([0,0,5])  cube([50,20,15],true);
} }

Operators
Rotary Clusters
module aim(elevation,azimuth=0)
{ rotate([0,0,azimuth])
{ rotate([0,90-elevation,0]) children(0);
children([1:1:$children-1]); // step needed in case$children < 2
} }

aim(30,20)arrow();
aim(35,270)cannon();
aim(15){cannon();base();}

for (azimuth =[0:360/number:359])
rotate([0,0,azimuth])
translate([40,0,30]) text(str(azimuth)); }

RotaryCluster(200,7) color("lightgreen") aim(15){cannon();base();}
rotate([0,0,110]) RotaryCluster(100,4.5) aim(35)cannon();
color("LightBlue")aim(55,30){cannon();base();}


#### Recursive Modules

Like functions, modules may contain recursive calls. However, there is no tail-recursion elimination for recursive modules.

The code below generates a crude model of a tree. Each tree branch is itself a modified version of the tree and produced by recursion. Be careful to keep the recursion depth (branching) n below 7 as the number of primitives and the preview time grow exponentially.

A simple tree created with a recursive OpenSCAD module
    module simple_tree(size, dna, n) {
if (n > 0) {
// trunk
cylinder(r1=size/10, r2=size/12, h=size, $fn=24); // branches translate([0,0,size]) for(bd = dna) { angx = bd[0]; angz = bd[1]; scal = bd[2]; rotate([angx,0,angz]) simple_tree(scal*size, dna, n-1); } } else // leaves color("green") scale([1,1,3]) translate([0,0,size/6]) rotate([90,0,0]) cylinder(r=size/6,h=size/10); } // dna is a list of branching data bd of the tree: // bd[0] - inclination of the branch // bd[1] - Z rotation angle of the branch // bd[2] - relative scale of the branch dna = [ [12, 80, 0.85], [55, 0, 0.6], [62, 125, 0.6], [57, -125, 0.6] ]; simple_tree(50, dna, 5);  Another example of recursive module may be found in Tips and Tricks ### Overwriting built-in modules It is possible to overwrite the built-in modules. A simple, but pointless example would be: module sphere(){ square(); } sphere();  Note that the built-in sphere module can not be called when over written. A more sensible way to use this language feature is to overwrite the 3D primitives with extruded 2D-primitives. This allows additional to customize the default parameters and to add additional parameters. ### Overwriting built-in functions It is possible to overwrite the built-in functions. Source Code Console output echo (sin(1)); function sin() = true; echo (sin(1)); Compiling design (CSG Tree generation)... ECHO: true ECHO: true Compiling design (CSG Products generation)... For including code from external files in OpenSCAD, there are two commands available: • include <filename> acts as if the contents of the included file were written in the including file, and • use <filename> imports modules and functions, but does not execute any commands other than those definitions. Library files are searched for in the same folder as the design was open from, or in the library folder of the OpenSCAD installation. You can use a relative path specification to either. If they lie elsewhere you must give the complete path. Newer versions have predefined user libraries, see the OpenSCAD_User_Manual/Libraries page, which also documents a number of library files included in OpenSCAD. Wildcards (*, for e.g. include <MCAD/*.scad>) can not be used to include multiple files. #### Directory separators Windows and Linux/Mac use different separators for directories. Windows uses \, e.g. directory\file.ext, while the others use /, e.g. directory/file.ext. This could lead to cross platform issues. However OpenSCAD on Windows correctly handles the use of /, so using / in all include or use statements will work on all platforms. To access the parent directory ../ can be used under Linux. #### Variables ##### Scope of variables Using include <filename> allows default variables to be specified in the library. These defaults can be overridden in the main code. An OpenSCAD variable only has one value during the life of the program. When there are multiple assignments it takes the last value, but assigns when the variable is first created. This has an effect when assigning in a library, as any variables which you later use to change the default, must be assigned before the include statement. See the second example below. ##### Overwriting variables Default variables in an include can be overridden, for example lib.scad i=1; k=3; module x() { echo("hello world"); echo("i=",i,"j=",j,"k=",k); }  hello.scad j=4; include <lib.scad>; x(); i=5; x(); k=j; x();  Produces the following ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", 4 ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", 4 ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", 4  However, placing j=4; after the include fails, producing ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", undef ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", undef ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", undef  #### Example "Ring-Library" A library file for generating rings might look like this (defining a function and providing an example): ring.scad: module ring(r1, r2, h) { difference() { cylinder(r = r1, h = h); translate([ 0, 0, -1 ]) cylinder(r = r2, h = h+2); } } ring(5, 4, 10);  Including the library using include <ring.scad>; rotate([90, 0, 0]) ring(10, 1, 1);  would result in the example ring being shown in addition to the rotated ring, but use <ring.scad>; rotate([90, 0, 0]) ring(10, 1, 1);  only shows the rotated ring. If using the use function, make sure to place the use statements at top of the file, or at least not within a module! This will work fine:  // a.scad use <ring.scad>; module a() { ring(); }  but this will result in an syntax error:  //a.scad module a() { use <ring.scad>; ring(); }  #### Nested Include and Use OpenSCAD will execute nested calls to include and use. There is one caveat to this, that use only brings functions and modules into the local file context. As a result, nested calls to use will have no effect on the environment of the base file; the child use call will work in the parent use context, but the modules and functions so imported will fall out of context before they are seen by the base context. ### Special variables Special variables provide an alternate means of passing arguments to modules and functions. All user, or OpenSCAD, defined variables starting with a '$' are special variables, similar to special variables in lisp. Modules and function see all outside variables in addition to those passed as arguments or defined internally.

The value for a regular variable is assigned at compile time and is thus static for all calls.

Special variables pass along their value from within the scope (see scope of variables) from which the module or function is called. This means that special variables can potentially have a different value each time a module or function is called.

regular  = "regular global";
$special = "special global"; module show() echo(" in show ", regular," ",$special );

echo ("         outside    ", regular,"   ", $special ); // ECHO: " outside ", "regular global", " ", "special global" for ( regular = [0:1] ){ echo("in regular loop ", regular," ",$special ); show();}
// ECHO: "in regular loop     ", 0, "   ", "special global"
// ECHO: "         in show    ", "regular global", "   ", "special global"
// ECHO: "in regular loop     ", 1, "   ", "special global"
// ECHO: "         in show    ", "regular global", "   ", "special global"

for ( $special = [5:6] ){ echo("in special loop ", regular," ",$special ); show();}
// ECHO: "in special loop     ", "regular global", "   ", 5
// ECHO: "         in show    ", "regular global", "   ", 5
// ECHO: "in special loop     ", "regular global", "   ", 6
// ECHO: "         in show    ", "regular global", "   ", 6

show();
// ECHO: "         in show    ", "regular global", "   ", "special global"


This is useful when multiple arguments need to be passed thru several layers of module calls.

#### $fa,$fs and $fn The$fa, $fs and$fn special variables control the number of facets used to generate an arc:

$fa is the minimum angle for a fragment. Even a huge circle does not have more fragments than 360 divided by this number. The default value is 12 (i.e. 30 fragments for a full circle). The minimum allowed value is 0.01. Any attempt to set a lower value will cause a warning.$fs is the minimum size of a fragment. Because of this variable very small circles have a smaller number of fragments than specified using $fa. The default value is 2. The minimum allowed value is 0.01. Any attempt to set a lower value will cause a warning.$fn is usually 0. When this variable has a value greater than zero, the other two variables are ignored and full circle is rendered using this number of fragments. The default value is 0.

The higher the number of fragments, the more memory and CPU consumed, large values will bring many systems to their knees. Depending on the design, $fn values, and the corresponding results of$fa & $fs, should be kept small, at least until the design is finalised when it can be increased for the final result. A$fn over 100 is not recommended or only for specific circumstances, and below 50 would be advisable for performance.

TIP: If you want to create a circle/cylinder/sphere which has a axis aligned integer bounding box (i.e. a bounding box that has integral dimensions, and an integral position) use a value of $fn that is divisible by 4. When$fa and $fs are used to determine the number of fragments for a circle, then OpenSCAD will never use fewer than 5 fragments. This is the C code that calculates the number of fragments in a circle:  int get_fragments_from_r(double r, double fn, double fs, double fa) { if (r < GRID_FINE) return 3; if (fn > 0.0) return (int)(fn >= 3 ? fn : 3); return (int)ceil(fmax(fmin(360.0 / fa, r*2*M_PI / fs), 5)); }  Spheres are first sliced into as many slices as the number of fragments being used to render a circle of the sphere's radius, and then every slice is rendered into as many fragments as are needed for the slice radius. You might have recognized already that the pole of a sphere is usually a pentagon. This is why. The number of fragments for a cylinder is determined using the greater of the two radii. The method is also used when rendering circles and arcs from DXF files. The variables have no effect when importing STL files. You can generate high resolution spheres by resetting the$fX values in the instantiating module:

      $fs = 0.01; sphere(2);  or simply by passing the special variable as parameter:  sphere(2,$fs = 0.01);


You can even scale the special variable instead of resetting it:

      sphere(2, $fs =$fs * 0.01);


#### $t The$t variable is used for animation. If you enable the animation frame with view->animate and give a value for "FPS" and "Steps", the "Time" field shows the current value of $t. With this information in mind, you can animate your design. The design is recompiled every 1/"FPS" seconds with$t incremented by 1/"Steps" for "Steps" times, ending at either $t=1 or$t=1-1/steps.

If "Dump Pictures" is checked, then images will be created in the same directory as the .scad file, using the following $t values, and saved in the following files: •$t=0/Steps filename="frame00001.png"
• $t=1/Steps filename="frame00002.png •$t=2/Steps filename="frame00003.png"
• . . .
• $t=1-3/Steps filename="frame<Steps-2>.png" •$t=1-2/Steps filename="frame<Steps-1>.png"
• $t=1-1/Steps filename="frame00000.png" Or, for other values of Steps, it follows this pattern: •$t=0/Steps filename="frame00001.png"
• $t=1/Steps filename="frame00002.png •$t=2/Steps filename="frame00003.png"
• . . .
• $t=1-3/Steps filename="frame<Steps-2>.png" •$t=1-2/Steps filename="frame<Steps-1>.png"
• $t=1-1/Steps filename="frame<Steps-0>.png" •$t=1-0/Steps filename="frame00000.png"

Which pattern it chooses appears to be an unpredictable, but consistent, function of Steps. For example, when Steps=4, it follows the first pattern, and outputs a total of 4 files. When Steps=3, it follows the second pattern, and also outputs 4 files. It will always output either Steps or Steps+1 files, though it may not be predictable which. When finished, it will wrap around and recreate each of the files, looping through and recreating them forever.

#### $vpr,$vpt and $vpd These contain the current viewport rotation and translation and camera distance - at the time of doing the rendering. Moving the viewport does not update them. During an animation they are updated for each frame. •$vpr shows rotation
• $vpt shows translation (i.e. won't be affected by rotate and zoom) •$vpd shows the camera distance [Note: Requires version 2015.03]

Example

 cube([10, 10, $vpr[0] / 10]);  which makes the cube change size based on the view angle, if an animation loop is active (which does not need to use the$t variable)

You can also make bits of a complex model vanish as you change the view.

All three variables are writable but only assignments at the top-level of the main file will have an effect on the viewport. [Note: Requires version 2015.03]

Example

 $vpr = [0, 0,$t * 360];


which allows a simple 360 degree rotation around the Z axis in animation mode.

The menu command Edit - Paste Viewport Rotation/Translation copies the current value of the viewport, but not the current $vpr or$vpt.

#### $preview [Note: Requires version nightly build]$preview is true, when in OpenCSG preview (F5). $preview is false, when in render (F6). This can, for example, be used to reduce detail during preview to save time, without losing detail in the final rendered result: $fn = $preview ? 12 : 72; sphere(r = 1);  Note that the render function does not affect$preview:

render(){
$fn =$preview ? 12 : 72;
sphere(r = 1);
}


Another use could be to make the preview show an assembly view and the render generate just the printed parts laid out for printing.[1]

If printed parts need extra features that are removed post printing, for example support for suspended holes, then the preview can omit these to show the finished part after post processing.

$parent_modules contains the number of modules in the instantiation stack. parent_module(i) returns the name of the module i levels above the current module in the instantiation stack. The stack is independent of where the modules are defined. It's where they're instantiated that counts. This can be used to e.g. build BOMs. Example:  module top() { children(); } module middle() { children(); } top() middle() echo(parent_module(0)); // prints "middle" top() middle() echo(parent_module(1)); // prints "top"  ### assert [Note: Requires version nightly build] see also Assertion (software development) Assert evaluates a logical expression. If the expression evaluates to false, the generation of the preview/render is stopped with an error. A string representation of the expression and, if given, the message is output to the console. Parameters condition Expression. The expression to be evaluated as check for the assertion. message String. Optional message to be output in case the assertion failed. #### Example The simplest example is a simple assert(false);, e.g. in a file named assert_example1.scad. cube(); assert(false); sphere(); // ERROR: Assertion 'false' failed in file assert_example1.scad, line 2  This example has little use, but the simple assert(false); can be used in code sections that should be unreachable. #### Checking parameters A useful example is checking the validity of input parameters: module row(cnt = 3){ // Count has to be a positive integer greater 0 assert(cnt > 0); for (i = [1 : cnt]) { translate([i * 2, 0, 0]) sphere(); } } row(0); // ERROR: Assertion '(cnt > 0)' failed in file assert_example2.scad, line 3  #### Adding message When writing a library, it could be useful to output additional information to the user in case of an failed assertion. module row(cnt = 3){ assert(cnt > 0, "Count has to be a positive integer greater 0"); for(i = [1 : cnt]) { translate([i * 2, 0, 0]) sphere(); } } row(0); // ERROR: Assertion '(cnt > 0)': "Count has to be a positive integer greater 0" failed in file assert_example3.scad, line 2  # Using the 2D Subsystem All 2D primitives can be transformed with 3D transformations. Usually used as part of a 3D extrusion. Although infinitely thin, they are rendered with a 1 thickness. ## square Creates a square or rectangle in the first quadrant. When center is true the square is centered on the origin. Argument names are optional if given in the order shown here. square(size = [x, y], center = true/false); square(size = x , center = true/false);  parameters: size single value, square with both sides this length 2 value array [x,y], rectangle with dimensions x and y center false (default), 1st (positive) quadrant, one corner at (0,0) true, square is centered at (0,0) default values: square(); yields: square(size = [1, 1], center = false);  examples: equivalent scripts for this example square(size = 10); square(10); square([10,10]); . square(10,false); square([10,10],false); square([10,10],center=false); square(size = [10, 10], center = false); square(center = false,size = [10, 10] );  equivalent scripts for this example square([20,10],true); a=[20,10];square(a,true);  ## circle Creates a circle at the origin. All parameters, except r, must be named. circle(r=radius | d=diameter);  Parameters r : circle radius. r name is the only one optional with circle. circle resolution is based on size, using$fa or $fs. For a small, high resolution circle you can make a large circle, then scale it down, or you could set$fn or other special variables. Note: These examples exceed the resolution of a 3d printer as well as of the display screen.
scale([1/100, 1/100, 1/100]) circle(200); // create a high resolution circle with a radius of 2.
circle(2, $fn=50); // Another way.  d : circle diameter (only available in versions later than 2014.03).$fa : minimum angle (in degrees) of each fragment.
$fs : minimum circumferential length of each fragment.$fn : fixed number of fragments in 360 degrees. Values of 3 or more override $fa and$fs
$fa,$fs and $fn must be named. click here for more details,. defaults: circle(); yields: circle($fn = 0, $fa = 12,$fs = 2, r = 1);


equivalent scripts for this example
circle(10);
circle(r=10);
circle(d=20);
circle(d=2+9*2);


### ellipse

An ellipse can be created from a circle by using either scale() or resize() to make the x and y dimensions unequal. See OpenSCAD User Manual/Transformations

equivalent scripts for this example
resize([30,10])circle(d=20);
scale([1.5,.5])circle(d=20);


### regular polygon

A regular polygon of 3 or more sides can be created by a hack of using circle() with $fn set to the number of sides. But DON'T USE IT! The only purpose of circle is creating circles and ellipses. Software is free to render and process them as circles. Also$fn can be redefined and your "polygons" will become true circles. Use the code below instead:

 module regular_polygon(order, r=1){
angles=[ for (i = [0:order-1]) i*(360/order) ];
coords=[ for (th=angles) [r*cos(th), r*sin(th)] ];
polygon(coords);
}


The polygon is inscribed within the circle with all sides (and angles) equal. One corner points to the positive x direction. For irregular shapes see the polygon primitive below.

script for these examples
translate([-42,  0]){circle(20,$fn=3);%circle(20,$fn=90);}
translate([  0,  0]) circle(20,$fn=4); translate([ 42, 0]) circle(20,$fn=5);
translate([-42,-42]) circle(20,$fn=6); translate([ 0,-42]) circle(20,$fn=8);
translate([ 42,-42]) circle(20,$fn=12);   color("black"){ translate([-42, 0,1])text("3",7,,center); translate([ 0, 0,1])text("4",7,,center); translate([ 42, 0,1])text("5",7,,center); translate([-42,-42,1])text("6",7,,center); translate([ 0,-42,1])text("8",7,,center); translate([ 42,-42,1])text("12",7,,center); }  ## polygon Creates a multiple sided shape from a list of x,y coordinates. A polygon is the most powerful 2D object. It can create anything that circle and squares can, as well as much more. This includes irregular shapes with both concave and convex edges. In addition it can place holes within that shape. polygon(points = [ [x, y], ... ], paths = [ [p1, p2, p3..], ...], convexity = N);  Parameters points The list of x,y points of the polygon. : A vector of 2 element vectors. Note: points are indexed from 0 to n-1. paths default If no path is specified, all points are used in the order listed. single vector The order to traverse the points. Uses indices from 0 to n-1. May be in a different order and use all or part, of the points listed. multiple vectors Creates primary and secondary shapes. Secondary shapes are subtracted from the primary shape (like difference). Secondary shapes may be wholly or partially within the primary shape. A closed shape is created by returning from the last point specified to the first. convexity Integer number of "inward" curves, ie. expected path crossings of an arbitrary line through the polygon. See below. defaults: polygon(); yields: polygon(points = undef, paths = undef, convexity = 1);  Example no holes equivalent scripts for this example polygon(points=[[0,0],[100,0],[130,50],[30,50]]); polygon([[0,0],[100,0],[130,50],[30,50]], paths=[[0,1,2,3]]); polygon([[0,0],[100,0],[130,50],[30,50]],[[3,2,1,0]]); polygon([[0,0],[100,0],[130,50],[30,50]],[[1,0,3,2]]); a=[[0,0],[100,0],[130,50],[30,50]]; b=[[3,0,1,2]]; polygon(a); polygon(a,b); polygon(a,[[2,3,0,1,2]]);  Example one hole equivalent scripts for this example polygon(points=[[0,0],[100,0],[0,100],[10,10],[80,10],[10,80]], paths=[[0,1,2],[3,4,5]],convexity=10); triangle_points =[[0,0],[100,0],[0,100],[10,10],[80,10],[10,80]]; triangle_paths =[[0,1,2],[3,4,5]]; polygon(triangle_points,triangle_paths,10);  The 1st path vector, [0,1,2], selects the points, [0,0],[100,0],[0,100], for the primary shape. The 2nd path vector, [3,4,5], selects the points, [10,10],[80,10],[10,80], for the secondary shape. The secondary shape is subtracted from the primary ( think difference() ). Since the secondary is wholly within the primary, it leaves a shape with a hole.  Example multi hole NOTE: concat() requires 2015.03 or later  //example polygon with multiple holes a0 = [[0,0],[100,0],[130,50],[30,50]]; // main b0 = [1,0,3,2]; a1 = [[20,20],[40,20],[30,30]]; // hole 1 b1 = [4,5,6]; a2 = [[50,20],[60,20],[40,30]]; // hole 2 b2 = [7,8,9]; a3 = [[65,10],[80,10],[80,40],[65,40]]; // hole 3 b3 = [10,11,12,13]; a4 = [[98,10],[115,40],[85,40],[85,10]]; // hole 4 b4 = [14,15,16,17]; a = concat (a0,a1,a2,a3,a4); b = [b0,b1,b2,b3,b4]; polygon(a,b); //alternate polygon(a,[b0,b1,b2,b3,b4]);  convexity The convexity parameter specifies the maximum number of front sides (back sides) a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode and has no effect on the polyhedron rendering. This image shows a 2D shape with a convexity of 4, as the ray indicated in red crosses the 2D shape a maximum of 4 times. The convexity of a 3D shape would be determined in a similar way. Setting it to 10 should work fine for most cases. ## import_dxf DEPRECATED: The import_dxf() module will be removed in future releases. Use import() instead. Read a DXF file and create a 2D shape. Example linear_extrude(height = 5, center = true, convexity = 10) import_dxf(file = "example009.dxf", layer = "plate");  Using the projection() function, you can create 2d drawings from 3d models, and export them to the dxf format. It works by projecting a 3D model to the (x,y) plane, with z at 0. If cut=true, only points with z=0 will be considered (effectively cutting the object), with cut=false(the default), points above and below the plane will be considered as well (creating a proper projection). Example: Consider example002.scad, that comes with OpenSCAD. Then you can do a 'cut' projection, which gives you the 'slice' of the x-y plane with z=0. projection(cut = true) example002();  You can also do an 'ordinary' projection, which gives a sort of 'shadow' of the object onto the xy plane. projection(cut = false) example002();  Another Example You can also use projection to get a 'side view' of an object. Let's take example002, and move it up, out of the X-Y plane, and rotate it: translate([0,0,25]) rotate([90,0,0]) example002();  Now we can get a side view with projection() projection() translate([0,0,25]) rotate([90,0,0]) example002();  Links: Extrusion is the process of creating an object with a fixed cross-sectional profile. OpenSCAD provides two commands to create 3D solids from a 2D shape: linear_extrude() and rotate_extrude(). Linear extrusion is similar to pushing Playdoh through a press with a die of a specific shape. linear_extrude() works like a Playdoh extrusion press Rotational extrusion is similar to the process of turning or "throwing" a bowl on the Potter's wheel. rotate_extrude() emulates throwing a vessel Both extrusion methods work on a (possibly disjointed) 2D shape which exists on the X-Y plane. While transformations that operates on both 2D shapes and 3D solids can move a shape off the X-Y plane, when the extrusion is performed the end result is not very intuitive. What actually happens is that any information in the third coordinate (the Z coordinate) is ignored for any 2D shape, this process amounts to an implicit projection() performed on any 2D shape before the extrusion is executed. It is recommended to perform extrusion on shapes that remains strictly on the X-Y plane. See also 3D and 2D objects. ### Linear Extrude Linear Extrusion is a modeling operation that takes a 2D polygon as input and extends it in the third dimension. This way a 3D shape is created. Keep in mind that extrusion is always performed from XY plane to the height indicate along Z axis; so if you rotate or apply other transformations before extrusion, the extrusion is applied to the projection of the 2D polygon to the XY plane. #### Usage linear_extrude(height = fanwidth, center = true, convexity = 10, twist = -fanrot, slices = 20, scale = 1.0) {...}  You must use parameter names due to a backward compatibility issue. height must be positive. If the extrusion fails for a non-trivial 2D shape, try setting the convexity parameter (the default is not 10, but 10 is a "good" value to try). See explanation further down. #### Twist Twist is the number of degrees of through which the shape is extruded. Setting the parameter twist = 360 will extrude through one revolution. The twist direction follows the left hand rule. 0° of Twist linear_extrude(height = 10, center = true, convexity = 10, twist = 0) translate([2, 0, 0]) circle(r = 1);  -100° of Twist linear_extrude(height = 10, center = true, convexity = 10, twist = -100) translate([2, 0, 0]) circle(r = 1);  100° of Twist linear_extrude(height = 10, center = true, convexity = 10, twist = 100) translate([2, 0, 0]) circle(r = 1);  -500° of Twist linear_extrude(height = 10, center = true, convexity = 10, twist = -500) translate([2, 0, 0]) circle(r = 1);  #### Center It is similar to the parameter center of cylinders. If center is false the linear extrusion Z range is from 0 to height; if it is true, the range is from -height/2 to height/2. center = true linear_extrude(height = 10, center = true, convexity = 10, twist = -500) translate([2, 0, 0]) circle(r = 1);  center = false linear_extrude(height = 10, center = false, convexity = 10, twist = -500) translate([2, 0, 0]) circle(r = 1);  #### Mesh Refinement The slices parameter defines the number of intermediate points along the Z axis of the extrusion. Its default increases with the value of twist. Explicitly setting slices may improve the output refinement. linear_extrude(height = 10, center = false, convexity = 10, twist = 360, slices = 100) translate([2, 0, 0]) circle(r = 1);  The special variables$fn, $fs and$fa can also be used to improve the output. If slices is not defined, its value is taken from the defined $fn value. linear_extrude(height = 10, center = false, convexity = 10, twist = 360,$fn = 100)
translate([2, 0, 0])
circle(r = 1);


#### Scale

Scales the 2D shape by this value over the height of the extrusion. Scale can be a scalar or a vector:

 linear_extrude(height = 10, center = true, convexity = 10, scale=3)
translate([2, 0, 0])
circle(r = 1);


 linear_extrude(height = 10, center = true, convexity = 10, scale=[1,5], $fn=100) translate([2, 0, 0]) circle(r = 1);  Note that if scale is a vector, the resulting side walls may be nonplanar. Use twist=0 and the slices parameter to avoid asymmetry.  linear_extrude(height=10, scale=[1,0.1], slices=20, twist=0) polygon(points=[[0,0],[20,10],[20,-10]]);  ### Rotate Extrude Rotational extrusion spins a 2D shape around the Z-axis to form a solid which has rotational symmetry. One way to think of this operation is to imagine a Potter's wheel placed on the X-Y plane with its axis of rotation pointing up towards +Z. Then place the to-be-made object on this virtual Potter's wheel (possibly extended down below the X-Y plane towards -Z, take the cross-section of this object on the X-Z plane but keep only the right half (X >= 0). That is the 2D shape that need to be fed to rotate_extrude() as the child in order to generate this solid. Since a 2D shape is rendered by OpenSCAD on the X-Y plane, an alternative way to think of this operation is as follows: spins a 2D shape around the Y-axis to form a solid. The resultant solid is placed so that its axis of rotation lies along the Z-axis. It can not be used to produce a helix or screw threads. The 2D shape needs to lie completely on either the right (recommended) or the left side of the Y-axis. More precisely speaking, each vertex of the shape must have either x >= 0 or x <= 0. If the shape crosses the X axis a warning will be shown in the console windows and the rotate_extrude() will be ignored. For OpenSCAD versions prior to 2016.xxxx, if the shape is in the negative axis the faces will be inside-out, which may cause undesired effects. Parameters #### Usage rotate_extrude(angle = 360, convexity = 2) {...}  Right-hand grip rule You must use parameter names due to a backward compatibility issue. convexity If the extrusion fails for a non-trival 2D shape, try setting the convexity parameter (the default is not 10, but 10 is a "good" value to try). See explanation further down. angle [Note: Requires version 2016.XX Defaults to 360. Specifies the number of degrees to sweep, starting at the positive X axis. The direction of the sweep follows the Right Hand Rule, hence a negative angle will sweep clockwise. #### Examples A simple torus can be constructed using a rotational extrude. rotate_extrude(convexity = 10) translate([2, 0, 0]) circle(r = 1);  #### Mesh Refinement Increasing the number of fragments that the 2D shape is composed of will improve the quality of the mesh, but take longer to render. rotate_extrude(convexity = 10) translate([2, 0, 0]) circle(r = 1,$fn = 100);


The number of fragments used by the extrusion can also be increased.

rotate_extrude(convexity = 10, $fn = 100) translate([2, 0, 0]) circle(r = 1,$fn = 100);


Using the parameter angle (with OpenSCAD versions 2016.xx), a hook can be modeled .

translate([0,60,0])
rotate_extrude(angle=270, convexity=10)
translate([40, 0]) circle(10);
rotate_extrude(angle=90, convexity=10)
translate([20, 0]) circle(10);
translate([20,0,0])
rotate([90,0,0]) cylinder(r=10,h=80);


#### Extruding a Polygon

Extrusion can also be performed on polygons with points chosen by the user.

Here is a simple polygon and its 200 step rotational extrusion. (Note it has been rotated 90 degrees to show how the rotation will look; the rotate_extrude() needs it flat).

rotate([90,0,0])        polygon( points=[[0,0],[2,1],[1,2],[1,3],[3,4],[0,5]] );

rotate_extrude($fn=200) polygon( points=[[0,0],[2,1],[1,2],[1,3],[3,4],[0,5]] );  For more information on polygons, please see: 2D Primitives: Polygon. ### Description of extrude parameters #### Extrude parameters for all extrusion modes  convexity Integer. The convexity parameter specifies the maximum number of front sides (back sides) a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode and has no effect on the polyhedron rendering. This image shows a 2D shape with a convexity of 4, as the ray indicated in red crosses the 2D shape a maximum of 4 times. The convexity of a 3D shape would be determined in a similar way. Setting it to 10 should work fine for most cases. #### Extrude parameters for linear extrusion only  height The extrusion height center If true the solid will be centered after extrusion twist The extrusion twist in degrees slices Similar to special variable$fn without being passed down to the child 2D shape. scale Scales the 2D shape by this value over the height of the extrusion.

With the import() and extrusion modules it is possible to convert 2D objects read from DXF files to 3D objects. See also 2D to 3D Extrusion.

### Linear Extrude

Example of linear extrusion of a 2D object imported from a DXF file.

linear_extrude(height = fanwidth, center = true, convexity = 10)
import (file = "example009.dxf", layer = "fan_top");


### Rotate Extrude

Example of rotational extrusion of a 2D object imported from a DXF file.

rotate_extrude(convexity = 10)
import (file = "example009.dxf", layer = "fan_side", origin = fan_side_center);


### Getting Inkscape to work

Inkscape is an open source drawing program. Tutorials for transferring 2d DXF drawings from Inkscape to OpenSCAD are available here:

Currently, OpenSCAD only supports DXF as a graphics format for 2D graphics. Other common formats are PS/EPS, SVG and AI.

### PS/EPS

The pstoedit program can convert between various vector graphics formats. OpenSCAD needs the -polyaslines option passed to the dxf output plugin to understand the file. The -mm option sets one mm to be one unit in the dxf; include this if you use one unit in OpenSCAD as equal to one millimeter. The -dt options instructs pstoedit to render texts, which is usually what you want if you include text. (If the rendered text's resolution in terms of polygon count is too low, the easiest solution is to scape up the eps before converting; if you know a more elegant solution, please add it to the example.)

pstoedit -dt -f "dxf: -polyaslines -mm" infile.eps outfile.dxf


### SVG

Inkscape can convert SVG to EPS. Then pstoedit can convert the EPS to DXF.

inkscape -E intermediate.eps infile.svg
pstoedit -dt -f dxf:-polyaslines\ -mm intermediate.eps outfile.dxf


### Makefile automation

The conversion can be automated using the make system; put the following lines in your Makefile:

 all: my_first_file.dxf my_second_file.dxf another_file.dxf

%.eps: %.svg
inkscape -E $@$<

%.dxf: %.eps
pstoedit -dt -f dxf:-polyaslines\ -mm $<$@


The first line specifies which dxf files are to be generated when make is called in the current directory. The second paragraph specifies how to convert a file ending in .svg to a file ending in .eps, and the third from .eps to .dxf.

A more complete makefile could autogenerate dxf files from the any svg in the folder. In which case, put the following lines into your Makefile:

SVG := $(wildcard *.svg) DXF :=$(SVG:%.svg=%.dxf)
EPS := $(SVG:%.svg=%.eps) .PHONY: all clean clean-eps clean-dxf all:$(DXF)

%.eps: %.svg
inkscape -E $*.eps$*.svg

%.dxf: %.eps
pstoedit -dt -f "dxf: -polyaslines -mm" $*.eps$*.dxf

clean: clean-dxf clean-eps

clean-dxf:
rm -f $(DXF) clean-eps: rm -f$(EPS)


It's still possible to call make filename.dxf to build a particular file, but this code also allows for (re)building of all dxf files in a folder just by calling make or make all.

This code is also universal enough that it's possible to put the code in a single file and symlink every makefile in any directory that has svg files for dxf conversion by running:

ln -s /path/to/this/svg_to_dxf_makefile makefile


in each respective directory.

Although Adobe Illustrator CC/CC.2014 allows you to export illustrations as DXF (and select DXF format versions as early as 12), it will use DXF entities that are not supported by OpenSCAD, such as POLYLINE and SPLINE.

### Command line usage

OpenSCAD can not only be used as a GUI, but also handles command line arguments. Its usage line says:

openscad     [ -o output_file [ -d deps_file ] ]\
[ -m make_command ] [ -D var=val [..] ] \
[ --help ] print this help message and exit \
[ --version ] [ --info ] \
[ --camera=translatex,y,z,rotx,y,z,dist | \
--camera=eyex,y,z,centerx,y,z ] \
[ --autocenter ] \
[ --viewall ] \
[ --imgsize=width,height ] [ --projection=(o)rtho|(p)ersp] \
[ --render | --preview[=throwntogether] ] \
[ --colorscheme=[Cornfield|Sunset|Metallic|Starnight|BeforeDawn|Nature|DeepOcean] ] \
[ --csglimit=num ]\
filename


openscad     [ -o output_file [ -d deps_file ] ]\
[ -m make_command ] [ -D var=val [..] ] \
[ --version ] [ --info ] \
[ --camera=translatex,y,z,rotx,y,z,dist | \
--camera=eyex,y,z,centerx,y,z ] \
[ --imgsize=width,height ] [ --projection=(o)rtho|(p)ersp] \
[ --render | --preview[=throwntogether] ] \
[ --csglimit=num ] \
filename


openscad     [ -o output_file [ -d deps_file ] ]\
[ -m make_command ] [ -D var=val [..] ] [ --render ] \
[ --camera=translatex,y,z,rotx,y,z,dist | \
--camera=eyex,y,z,centerx,y,z ] \
[ --imgsize=width,height ] [ --projection=(o)rtho|(p)ersp] \
filename


openscad [ -o output_file [ -d deps_file ] ] \
[ -m make_command ] [ -D var=val [..] ] filename


The usage on OpenSCAD version 2011.09.30 (now deprecated) was:

openscad [ { -s stl_file | -o off_file | -x dxf_file } [ -d deps_file ] ]\
[ -m make_command ] [ -D var=val [..] ] filename


### Export options

When called with the -o option, OpenSCAD will not start the GUI, but execute the given file and export the to the output_file in a format depending on the extension (.stl / .off / .dxf, .csg).

Some versions use -s/-d/-o to determine the output file format instead; check with "openscad --help".

If the option -d is given in addition to an export command, all files accessed while building the mesh are written in the argument of -d in the syntax of a Makefile.

For at least 2015.03-2+, specifying the extension .echo causes openscad to produce a text file containing error messages and the output of all echo() calls in filename as they would appear in the console window visible in the GUI. Multiple output files are not supported, so using this option you cannot also obtain the model that would have normally been generated.

#### Camera and image output

For 2013.05+, the option to output a .png image was added. There are two types of cameras available for the generation of images.

The first camera type is a 'gimbal' camera that uses Euler angles, translation, and a camera distance, like OpenSCAD's GUI viewport display at the bottom of the OpenSCAD window.

The second camera type is a 'vector' camera, with an 'eye' camera location vector and a 'lookat' center vector.

--imgsize chooses the .png dimensions and --projection chooses orthogonal or perspective, as in the GUI.

By default, cmdline .png output uses Preview mode (f5) with OpenCSG. For some situations it will be desirable instead to use the full render, with CGAL. This is done by adding '--render' as an option.

### Constants

In order to pre-define variables, use the -D option. It can be given repeatedly. Each occurrence of -D must be followed by an assignment. Unlike normal OpenSCAD assignments, these assignments don't define variables, but constants, which can not be changed inside the program, and can thus be used to overwrite values defined in the program at export time.

If you want to assign the -D variable to another variable, the -D variable MUST be initialised in the main .scad program

param1=17;       // must be initalized
val=param1;      // param1 passed via -D on cmd-line
echo(val,param1); // outputs 17,17


without the first line, val would be undefined.

The right hand sides can be arbitrary OpenSCAD expressions, including mathematical operations and strings. Be aware that strings have to be enclosed in quotes, which have to be escaped from the shell. To render a model that takes a quality parameter with the value "production", one has to run

openscad -o my_model_production.stl -D 'quality="production"' my_model.scad


When executing OpenSCAD from another process in Unix, the single-quotes shouldn't be used e.g. from within a Java application:

   pb = new ProcessBuilder("/usr/bin/openscad",
"-o", "my_model_production.stl",
"-D", "quality=\"production\"",


On Windows you may need to escape the inner quotes instead:

openscad -o my_model_production.stl -D "quality=\"production\"" my_model.scad


### Command to build required files

In a complex build process, some files required by an OpenSCAD file might be currently missing, but can be generated, for example if they are defined in a Makefile. If OpenSCAD is given the option -m make, it will start make file the first time it tries to access a missing file.

### Processing all .scad files in a folder

Example to convert all the .scad in a folder into .stl:

In a folder with .scad files, make a .bat file with text:

   FOR %%f in (*.scad)  DO openscad -o "%%~nf.stl" "%%f"


If it closes without processing, check to set the PATH by adding openscad directory to:

     Start - Settings - Control Panel - System - Advanced tab - Environment Variables - System Variables, select Path, then click Edit.


### Makefile example

The -d and -m options only make sense together. (-m without -d would not consider modified dependencies when building exports, -d without -m would require the files to be already built for the first run that generates the dependencies.)

Here is an example of a basic Makefile that creates an .stl file from an .scad file of the same name:

# explicit wildcard expansion suppresses errors when no files are found
include $(wildcard *.deps) %.stl: %.scad openscad -m make -o$@ -d $@.deps$<


When make my_example.stl is run for the first time, it finds no .deps files, and will just depend on my_example.scad; since my_example.stl is not yet preset, it will be created unconditionally. If OpenSCAD finds missing files, it will call make to build them, and it will list all used files in my_example.stl.deps.

When make my_example.stl is called subsequently, it will find and include my_example.stl.deps and check if any of the files listed there, including my_example.scad, changed since my_example.stl was built, based on their time stamps. Only if that is the case, it will build my_example.stl again.

#### Automatic targets

When building similar .stl files from a single .scad file, there is a way to automate that too:

# match "module foobar() { // make me"
TARGETS=$(shell sed '/^module [a-z0-9_-]*().*make..\?me.*$$/!d;s/module //;s/().*/.stl/' base.scad) all:${TARGETS}

# auto-generated .scad files with .deps make make re-build always. keeping the
# scad files solves this problem. (explanations are welcome.)
.SECONDARY: $(shell echo "${TARGETS}" | sed 's/\.stl/.scad/g')

# explicit wildcard expansion suppresses errors when no files are found
include $(wildcard *.deps) %.scad: echo -ne 'use <base.scad>\n$*();' > $@ %.stl: %.scad openscad -m make -o$@ -d $@.deps$<


All objects that are supposed to be exported automatically have to be defined in base.scad in an own module with their future file name (without the ".stl"), and have a comment like "// make me" in the line of the module definition. The "TARGETS=" line picks these out of the base file and creates the file names. These will be built when make all (or make, for short) is called.

As the convention from the last example is to create the .stl files from .scad files of the same base name, for each of these files, an .scad file has to be generated. This is done in the "%.scad:" paragraph; my_example.scad will be a very simple OpenSCAD file:

use <base.scad>
my_example();


The ".SECONDARY" line is there to keep make from deleting the generated .scad files. If it deleted it, it would not be able to automatically determine which files need no rebuild any more; please post ideas about what exactly goes wrong there (or how to fix it better) on the talk page!

### Windows notes

On Windows, openscad.com should be called from the command line as a wrapper for openscad.exe. This is because Openscad uses the 'devenv' solution to the Command-Line/GUI output issue. Typing 'openscad' at the cmd.exe prompt will, by default, call the .com program wrapper.

### MacOS notes

On MacOS the binary is normally hidden inside the App folder. If OpenSCAD is installed in the global Applications folder, it can be called from command line like in the following example that just shows the OpenSCAD version:

macbook:/$/Applications/OpenSCAD.app/Contents/MacOS/OpenSCAD -v OpenSCAD version 2013.06  Alternatively, you may create a symbolic link to the binary to make calls from the command line easier:  macbook:/$ sudo ln -sf /Applications/OpenSCAD.app/Contents/MacOS/OpenSCAD /usr/local/bin/openscad


Now you can call openscad directly without having to type in the full path.

 macbook:/$openscad -v OpenSCAD version 2015.03-3  # Building OpenSCAD from Sources ## Prebuilt binary packages If you are lucky, you won't have to build it. Many Linux and BSD systems have pre-built OpenSCAD packages including Debian, Ubuntu, Fedora, Arch, NetBSD and OpenBSD. Check your system's package manager for details. ### generic linux binary package There is also a generic linux binary package at http://www.openscad.org that can be unpacked and run from within most linux systems. It is self contained and includes the required libraries. ### nightly builds ### chrysn's Ubuntu packages For Ubuntu systems you can also try chrysn's Ubuntu packages at his launchpad PPA, or you can just copy/paste the following onto the command line: sudo add-apt-repository ppa:chrysn/openscad sudo apt-get update sudo apt-get install openscad  His repositories for OpenSCAD and OpenCSG are here and here. ## Building OpenSCAD yourself If you wish to build OpenSCAD for yourself, start by installing git on your system using your package manager. Git is sometimes packaged under the name 'scmgit' or 'git-core'. Then, use git to download the OpenSCAD source code cd ~/ git clone https://github.com/openscad/openscad.git cd openscad  Then get the MCAD library, which is now included with OpenSCAD binary distributions git submodule init git submodule update  ### Installing dependencies OpenSCAD uses a large number of third-party libraries and tools. These are called dependencies. An up to date list of dependencies can usually be found in the README.md in openscad's main directory, here: https://github.com/openscad/openscad/ A brief list follows: Eigen, GCC or Clang, Bison, Flex, CGAL, Qt, GMP, MPFR, boost, cmake, OpenCSG, GLEW, QScintilla, glib2, harfbuzz, freetype2, pkg-config, fontconfig #### Prepackaged dependencies Most systems are set up to install pre-built dependencies using a 'package manager', such as apt on ubuntu or pacman on Arch Linux. OpenSCAD comes with a 'helper script' that will attempt to automatically run your package manager for you and download and install these pre-built packages if they exist. Note you must be running as root and/or using sudo to try this. Note that these scripts will likely fail on Sun, Solaris, AIX, IRIX, etc (skip to the 'building dependencies' section below). ./scripts/uni-get-dependencies.sh  #### Verifying dependencies After attempting to install dependencies, you should double check them. Exit any shells and perhaps reboot. Now verify that the version numbers are up to those listed in openscad/README.md file. Also verify that no packages were accidentally missed. For example open a shell and run 'flex --version' or 'gcc --version'. These are good sanity checks to make sure your environment is proper. OpenSCAD comes with another helper script that attempts to automate this process on many Linux and BSD systems (Again, it won't work on Sun/Solaris/Irix/AIX/etc). ./scripts/check-dependencies.sh  If you cannot verify that your dependencies are installed properly and of a sufficient version, then you may have to install some 'by hand' (see the section below on building your own dependencies). If your system has all the proper versions of dependencies, then continue to the 'Building OpenSCAD' section. ### Building the dependencies yourself On systems that lack updated dependency libraries or tools, you will need to download each and build it and install it by hand. You can do this by downloading and following installation instructions for each package separately. However OpenSCAD comes with scripts that attempt to automate this process on Linux and BSD systems, by installing everything into a folder created under$HOME/openscad_deps. This script will not build typical development dependencies like X11, Qt4, gcc, bash etc. But it will attempt things like OpenCSG, CGAL, boost, etc.

To run the automated script, first set up the environment variables (if you don't use bash, replace "source" with a single ".")

source scripts/setenv-unibuild.sh


./scripts/uni-build-dependencies.sh


(If you only need CGAL or OpenCSG, you can just run ' ./scripts/uni-build-dependencies.sh cgal' or opencsg and it will only build a single library.)

The complete download and build process can take several hours, depending on your network connection speed and system speed. It is recommended to have at least 2 Gigabyte of free disk space to do the full dependency build. Each time you log into a new shell and wish to re-compile OpenSCAD you need to re-run the 'source scripts/setenv-unibuild.sh' script.

After completion, return to the section above on 'verifying dependencies' to see if they installed correctly.

qmake       # or qmake-qt4, depending on your distribution
make


You can also install OpenSCAD to /usr/local/ if you wish. The 'openscad' binary will be put under /usr/local/bin, the libraries and examples will be under something like /usr/local/share/openscad possibly depending on your system. Note that if you have previously installed a binary linux package of openscad, you should take care to delete /usr/local/lib/openscad and /usr/local/share/openscad because they are not the same paths as what the standard qmake-built 'install' target uses.

sudo make install


 Note: on Debian-based systems create a package and install OpenSCAD using: sudo checkinstall -D make install 

If you prefer not to install you can run "./openscad" directly whilst still in the ~/openscad directory.

### Experimental

all experimental features enabled

To enable the experimental features, remake the project with CONFIG+=experimental:

qmake CONFIG+=experimental
make -B


The -B is only required once (when you have changed the config).

The experimental features are disabled by default, even when explicitly build as experimental build.

When you successfully build, you find a "features" tab in the preferences, where you can enable individual experimental features.

CONFIG+=experimental


as the first line of openscad.pro.

## Compiling the test suite

OpenSCAD comes with over 740 regression tests. To build and run them, it is recommended to first build the GUI version of OpenSCAD by following the steps above, including the downloading of MCAD. Then, from the same login, run these commands:

 cd tests
mkdir build && cd build
cmake ..
make
ctest -C All


The file 'openscad/doc/testing.txt' has more information. Full test logs are under tests/build/Testing/Temporary. A pretty-printed index.html web view of the tests can be found under a machine-specific subdirectory thereof and opened with a browser.

## Troubleshooting

### Compiling fails with an Internal compiler error from GCC or GAS

This can happen if you run out of virtual memory, which means all of physical RAM as well as virtual swap space from the disk. See below under "horribly slow" for reasons. If you are non-root, there are a few things you can try. The first is to use the 'clang' compiler, as it uses much less RAM than gcc. The second thing is to edit the Makefile and remove the '-g' and '-pipe' flags from the compiler flags section.

If, on the other hand, you are root, then you can expand your swap space. On Linux this is pretty standard procedure and easily found in a web search. Basically you do these steps (after verifying you have no file named /swapfile already):

   sudo dd if=/dev/zero of=/swapfile bs=1M count=2000  # create a roughly 2 gig swapfile
sudo chmod 0600 /swapfile # set proper permissions for security
sudo mkswap /swapfile  # format as a swapfile
sudo swapon /swapfile  # turn on swap


For permanent swap setup in /etc/fstab, instructions are easily found through web search. If you are building on an SSD (solid state drive) machine the speed of a swapfile will allow a very reasonable build time.

### Compiling is horribly slow and/or grinds the disk

It is recommended to have at least 1.5 Gbyte of RAM to compile OpenSCAD. There are a few workarounds in case you don't. The first is to use the experimental support for the Clang Compiler (described below) as Clang uses much less RAM than GCC. Another workaround is to edit the Makefile generated by qmake and search/replace the optimization flags (-O2) with -O1 or blank, and to remove any '-g' debug flags from the compiler line, as well as '-pipe'.

If you have plenty of RAM and just want to speed up the build, you can try a paralell multicore build with

  make -jx


Where 'x' is the number of cores you want to use. Remember you need x times the amount of RAM to avoid possible disk thrashing.

The reason the build is slow is because OpenSCAD uses template libraries like CGAL, Boost, and Eigen, which use large amounts of RAM to compile - especially CGAL. GCC may take up 1.5 Gigabytes of RAM on some systems during the build of certain CGAL modules. There is more information at StackOverflow.com.

### BSD issues

The build instructions above are designed to work unchanged on FreeBSD and NetBSD. However the BSDs typically require special environment variables set up to build any QT project - you can set them up automatically by running

   source ./scripts/setenv-unibuild.sh


NetBSD 5.x, requires a patched version of CGAL. It is recommended to upgrade to NetBSD 6 instead as it has all dependencies available from pkgin. NetBSD also requires the X Sets to be installed when the system was created (or added later).

On OpenBSD it may fail to build after running out of RAM. OpenSCAD requires at least 1 Gigabyte to build with GCC. You may have need to be a user with 'staff' level access or otherwise alter required system parameters. The 'dependency build' sequence has also not been ported to OpenBSD so you will have to rely on the standard OpenBSD system package tools (in other words you have to have root).

### Sun / Solaris / IllumOS / AIX / IRIX / Minix / etc

The OpenSCAD dependency builds have been mainly focused on Linux and BSD systems like Debian or FreeBSD. The 'helper scripts' likely will fail on other types of Un*x. Furthermore the OpenSCAD build system files (qmake .pro files for the GUI, cmake CMakeFiles.txt for the test suite) have not been tested thoroughly on non-Linux non-BSD systems. Extensive work may be required to get a working build on such systems.

### Test suite problems

The test suite will try to automatically detect if you have an X11 DISPLAY environment variable set. If not, it will try to automatically start Xvfb or Xvnc (virtual X framebuffers) if they are available.

If you want to run these servers manually, you can attempt the following:

$Xvfb :5 -screen 0 800x600x24 &$ DISPLAY=:5 ctest


Alternatively:

### Setup environment to start developing OpenSCAD in Ubuntu 11.04

The following paragraph describes an easy way to setup a development environment for OpenSCAD in Ubuntu 11.04. After executing the following steps QT Creator can be used to graphically start developing/debugging OpenSCAD.

# sudo add-apt-repository ppa:chrysn/openscad

• Update and install required packages:
# sudo apt-get update
# sudo apt-get install git build-essential qtcreator libglew1.5-dev libopencsg-dev libcgal-dev libeigen2-dev bison flex

# mkdir ~/src
# cd ~/src

• Build OpenSCAD using the command line:
# cd ~/src/openscad
# qmake
# make

• Build OpenSCAD using QT Creator:

Just open the project file openscad.pro (CTRL+O) in QT Creator and hit the build all (CTRL+SHIFT+B) and run button (CTRL+R).

### The Clang Compiler

There is experimental support for building with the Clang compiler under linux. Clang is faster, uses less RAM, and has different error messages than GCC. To use it, first of all you will need CGAL of at least version 4.0.2, as prior versions have a bug that makes clang unusable. Then, run this script before you build OpenSCAD.

 source scripts/setenv-unibuild.sh clang


Clang support depends on your system's QT installation having a clang enabled qmake.conf file. For example, on Ubuntu, this is under /usr/share/qt4/mkspecs/unsupported/linux-clang/qmake.conf. BSD clang-building may require a good deal of fiddling and is untested, although eventually it is planned to move in this direction as the BSDs (not to mention OSX) are moving towards favoring clang as their main compiler. OpenSCAD includes convenience scripts to cross-build Windows installer binaries using the MXE system (http://mxe.cc). If you wish to use them, you can first install the MXE Requirements such as cmake, perl, scons, using your system's package manager (click to view a complete list of requirements). Then you can perform the following commands to download OpenSCAD source and build a windows installer:

 git clone https://github.com/openscad/openscad.git
source ./scripts/setenv-mingw-xbuild.sh
./scripts/mingw-x-build-dependencies.sh
./scripts/release-common.sh mingw32


The x-build-dependencies process takes several hours, mostly to cross-build QT. It also requires several gigabytes of disk space. If you have multiple CPUs you can speed up things by running export NUMCPU=x before running the dependency build script. By default it builds the dependencies in $HOME/openscad_deps/mxe. You can override the mxe installation path by setting the BASEDIR environment variable before running the scripts. The OpenSCAD binaries are built into a separate build path, openscad/mingw32. Note that if you want to then build linux binaries, you should log out of your shell, and log back in. The 'setenv' scripts, as of early 2013, required a 'clean' shell environment to work. If you wish to cross-build manually, please follow the steps below and/or consult the release-common.sh source code. ## Setup The easiest way to cross-compile OpenSCAD for Windows on Linux or Mac is to use mxe (M cross environment). You will need to install git to get it. Once you have git, navigate to where you want to keep the mxe files in a terminal window and run: git clone git://github.com/mxe/mxe.git  Add the following line to your ~/.bashrc file: export PATH=/<where mxe is installed>/usr/bin:$PATH


replacing <where mxe is installed> with the appropriate path.

## Requirements

The requirements to cross-compile for Windows are just the requirements of mxe. They are listed, along with a command for installing them here. You don't need to type 'make'; this will make everything and take up >10 GB of diskspace. You can instead follow the next step to compile only what's needed for openscad.

Now that you have the requirements for mxe installed, you can build OpenSCAD's dependencies (CGAL, Opencsg, MPFR, and Eigen2). Just open a terminal window, navigate to your mxe installation and run:

make mpfr eigen opencsg cgal qt


This will take a few hours, because it has to build things like gcc, qt, and boost. Just go calibrate your printer or something while you wait. To speed things up, you might want do something like "make -j 4 JOBS=2" for parallel building. See the mxe tutorial for more details.

Optional: If you want to build an installer, you need to install the nullsoft installer system. It should be in your package manager, called "nsis".

Now that all the requirements have been met, all that remains is to build OpenSCAD itself. Open a terminal window and enter:

git clone git://github.com/openscad/openscad.git


git submodule init
git submodule update


You need to create a symbolic link here for the build system to find the libraries:

ln -s /<where mxe is installed>/usr/i686-pc-mingw32/ mingw-cross-env


again replacing <where mxe is installed> with the appropriate path

i686-pc-mingw32-qmake CONFIG+=mingw-cross-env openscad.pro
make


When that is finished, you will have openscad.exe in ./release and you can build an installer with it as described in the instructions for building with Microsoft Visual C++, described here.

The difference is that instead of right-clicking on the *.nsi file you will run:

makensis installer.nsis


Note that as of early 2013, OpenSCAD's 'scripts/release-common.sh' automatically uses the version of nsis that comes with the MXE cross build system, so you may wish to investigate the release-common.sh source code to see how it works, if you have troubles. This is a set of instructions for building OpenSCAD with the Microsoft Visual C++ compilers. It has not been used since circa 2012 and is unlikely to work properly. It is maintained here for historical reference purposes.

---

This MSVC build is as static as reasonable, with no external DLL dependencies that are not shipped with Windows

Note: It was last tested on the Dec 2011 build. Newer checkouts of OpenSCAD may not build correctly or require extensive modification to compile under MSVC. OpenSCAD releases of 2012 were typically cross-compiled from linux using the Mingw & MXE system. See Cross-compiling for Windows on Linux or Mac OS X.

## Installing

• Install Visual Studio
• No need for siverlight or mssql express
• You can use a virtual-CD program like MagicDisc to mount the ISO file and install without using a CD
• Install QT
• Install to default location C:\Qt\4.7.2\
• Install Git
• Click Run Git and included Unix tools from the Windows Command Prompt despite the big red letters warning you not to.
• Install Cmake
• Check the 'Add cmake to the system path for the current user' checkbox
• Install to default location C:\Program Files\CMake 2.8
• Install Boost
• Select the VC++ 9.0 vs2008 radio
• Check the 'multithreaded static runtime' checkbox only
• Install into C:\boost_1_46_1\
• Install CGAL
• Note - CGAL 3.9 fixes several bugs in earlier versions of CGAL, but CGAL 3.9 will not compile under MSVC without extensive patching. Please keep that in mind when compiling OpenSCAD with MSVC - there may be bugs due to the outdated version of CGAL required to use MSVC.
• Note its not a binary distribution, just an installer that installs the source.
• No need for CGAL Examples and Demos
• Make sure mpfr and gmp precompiled libs is checked
• The installer wants you to put this in C:\Program Files\CGAL-3.7\ I used C:\CGAL-3.7\
• Make sure CGAL_DIR environment checked.
• Install MinGW
• Make sure you select the MSYS Basic System under components
• Extract downloaded win32_gmp_mpfr.zip file to C:\win32_gmp_mpfr\
• Replace the mpfr and gmp .h files in CGAL with the ones from win32_gmp_mpfr
• Delete, or move to a temp folder, all files in CGAL-3.7\auxiliary\gmp\include folder
• Copy all the .h files in C:\win32_gmp_mpfr\gmp\Win32\Release to CGAL-3.7\auxiliary\gmp\include
• Copy all the .h files in C:\win32_gmp_mpfr\mpfr\Win32\Release to CGAL-3.7\auxiliary\gmp\include
• Replace the mpfr and gmp libs in CGAL with the ones from win32_gmp_mpfr
• Delete, or move to a temp folder, all (06/20/2011 libmpfr-4.lib is needed 7/19/11 - i didnt need it) files in CGAL-3.7\auxiliary\gmp\lib folder.
• Copy C:\win32_gmp_mpfr\gmp\Win32\Release\gmp.lib to CGAL-3.7\auxiliary\gmp\lib
• Copy C:\win32_gmp_mpfr\mpfr\Win32\Release\mpfr.lib to CGAL-3.7\auxiliary\gmp\lib
• Go into CGAL-3.7\auxiliary\gmp\lib and copy gmp.lib to gmp-vc90-mt-s.lib, and mpfr.lib to mpfr-vc90-mt-s.lib (so the linker can find them in the final link of openscad.exe)

• Open "Git Bash" (or MingW Shell) (the installer may have put a shortcut on your desktop). This launches a command line window.
• Type cd c: to change the current directory.

Where to put other files:

I put all the dependencies in C:\ so for example,

• C:\eigen2\
• C:\glew-1.5.8\
• C:\OpenCSG-1.3.2\

.tgz can be extracted with tar -zxvf from the MingW shell, or Windows tools like 7-zip. Rename and move sub-directories if needed. I.e eigen-eigen-0938af7840b0 should become c:\eigen2, with the files like COPYING and CMakeLists.txt directly under it. c:\glew-1.5.8 should have 'include' and 'lib' directly under it.

## Compiling Dependencies

For compilation I use the QT Development Command Prompt

Start->Program Files->Qt by Nokia v4.7.2 (VS2008 OpenSource)->QT 4.7.2 Command Prompt

### Qt

Qt needs to be recompiled to get a static C runtime build. To do so, open the command prompt and do:

configure -static -platform win32-msvc2008 -no-webkit


Configure will take several minutes to finish processing. After it is done, open up the file Qt\4.7.2\mkspecs\win32-msvc2008\qmake.conf and replace every instance of -MD with -MT. Then:

nmake


This takes a very, very long time. Have a nap. Get something to eat. On a Pentium 4, 2.8GHZ CPU with 1 Gigabyte RAM, Windows XP, it took more than 7 hours, (that was with -O2 turned off)

### CGAL

cd C:\CGAL-3.7\
set BOOST_ROOT=C:\boost_1_46_1\
cmake .


Now edit the CMakeCache.txt file. Replace every instance of /MD with /MT . Now, look for a line like this:

CMAKE_BUILD_TYPE:STRING=Debug

Change Debug to Release. Now re-run cmake

cmake .


It should scroll by, watch for lines saying "--Building static libraries" and "--Build type: Release" to confirm the proper settings. Also look for /MT in the CXXFLAGS line. When it's done, you can do the build:

nmake


You should now have a CGAL-vc90-mt-s.lib file under C:\CGAL-3.7\lib . If not, see Troubleshooting, below.

### OpenCSG

Launch Visual Express.

cd C:\OpenCSG-1.3.2
vcexpress OpenCSG.sln
Substitute devenv for vcexpress if you are not using the express version

• Manually step through project upgrade wizard
• Make sure the runtime library settings for all projects is for Release (not Debug)
• Click Build/Configuration Manager
• Select "Release" from "Configuration:" drop down menu
• Hit Close
• Make sure the runtime library setting for OpenCSG project is set to multi-threaded static
• Open the OpenCSG project properties by clicking menu item "Project->OpenCSG Properties" (might be just "Properties")
• Make sure it says "Active(Release)" in the "Configuration:" drop down menu
• Click 'Configuration Properties -> C/C++ -> Code Generation'
• Make sure "Runtime Library" is set to "Multi-threaded (/MT)"
• Click hit OK
• Make sure the runtime library setting for glew_static project is set to multi-threaded static
• In "Solution Explorer - OpenCSG" pane click "glew_static" project
• Open the OpenCSG project properties by clicking menu item "Project->OpenCSG Properties" (might be just "Properties")
• Make sure it says "Active(Release)" in the "Configuration:" drop down menu
• Click C/C++ -> Code Generation
• Make sure "Runtime Library" is set to "Multi-threaded (/MT)"
• Click hit OK
• Close Visual Express saving changes

Build OpenCSG library. You can use the GUI Build/Build menu (the Examples project might fail, but glew and OpenCSG should succeed). Alternatively you can use the command line:

cmd /c vcexpress OpenCSG.sln /build
Again, substitute devenv if you have the full visual studio


The cmd /c bit is needed otherwise you will be returned to the shell immediately and have to Wait for build process to complete (there will be no indication that this is happening appart from in task manager)

• Bison/Flex: Open the mingw shell and type mingw-get install msys-bison. Then do the same for flex: mingw-get install msys-flex
• Open the QT Shell, and copy/paste the following commands
cd C:\openscad
set INCLUDE=%INCLUDE%C:\CGAL-3.7\include;C:\CGAL-3.7\auxiliary\gmp\include;
set INCLUDE=%INCLUDE%C:\boost_1_46_1;C:\glew-1.5.8\include;C:\OpenCSG-1.3.2\include;C:\eigen2
set LIB=%LIB%C:\CGAL-3.7\lib;C:\CGAL-3.7\auxiliary\gmp\lib;
set LIB=%LIB%C:\boost_1_46_1\lib;C:\glew-1.5.8\lib;C:\OpenCSG-1.3.2\lib
qmake
nmake -f Makefile.Release


Wait for the nmake to end. There are usually a lot of non-fatal warnings about the linker. On success, there will be an openscad.exe file in the release folder. Enjoy.

## Building an installer

• Put the FileAssociation.nsh macro from http://nsis.sourceforge.net/File_Association in the NSIS Include directory, C:\Program Files\NSIS\Include
• Copy the OpenSCAD "libraries" and "examples" directory into the "release" directory
• Copy OpenSCAD's "scripts/installer.nsi" to the "release" directory.
• Right-click on the file and compile it with NSIS. It will spit out a nice, easy installer. Enjoy.

## Compiling the regression tests

• Follow all the above steps, build openscad, run it, and test that it basically works.
• Install Python 2.x (not 3.x) from http://www.python.org
• Install Imagemagick from http://www.imagemagick.org
• Go into your QT shell
set PATH=%PATH%;C:\Python27 (or your version of python)
cmake . -DCMAKE_BUILD_TYPE=Release
Edit the CMakeCache.txt file, search/replace /MD to /MT
cmake .
nmake -f Makefile

• This should produce a number of test .exe files in your directory. Now run
ctest


If you have link problems, see Troubleshooting, below.

## Troubleshooting

If you have errors during linking, the first step is to improve debug logging, and redirect to a file. Open Openscad.pro and uncomment this line:

 QMAKE_LFLAGS   += -VERBOSE


Now rerun

 nmake -f Makefile.Release > log.txt


You can use a program like 'less' (search with '/') or wordpad to review the log.

To debug these errors, you must understand basics about Windows linking. Windows links to its standard C library with basic C functions like malloc(). But there are four different ways to do this, as follows:

compiler switch - type - linked runtime C library


All of the libraries that are link together in a final executable must be compiled with the same type of linking to the standard C library. Otherwise, you get link errors like, "LNK2005 - XXX is already defined in YYY". But how can you track down which library wasn't linked properly? 1. Look at the log, and 2. dumpbin.exe

dumpbin.exe

dumpbin.exe can help you determine what type of linking your .lib or .obj files were created with. For example, dumpbin.exe /all CGAL.lib | find /i "DEFAULTLIB"  will give you a list of DEFAULTLIB symbols inside of CGAL.lib. Look for LIBCMT, LIBCMTD, MSVCRT, or MSVCRTD. That will tell you, according to the above table, whether it was built Static Release, Static Debug, DLL Release, or DLL Debug. (DLL, of course means Dynamic Link Library in this conversation.) This can help you track down, for example, linker errors about conflicting symbols in LIBCMT and LIBCMTD.

dumpbin.exe can also help you understand errors involving unresolved external symbols. For example, if you get an error about unresolved external symbol ___GLEW_NV_occlusion_query, but your VERBOSE error log says the program linked in glew32.lib, then you can dumpbin.exe /all glew32.lib | find /i "occlusion" to see if the symbol is actually there. You may see a mangled symbol, with __impl, which gives you another clue with which you can google. In this particular example, glew32s.lib (s=static) should have been linked instead of glew32.lib.

### CGAL

CGAL-vc90-mt-s.lib

After compilation, it is possible that you might get a file named CGAL-vc90-mt.lib or CGAL-vc90-mt-gd.lib instead of CGAL-vc90-mt-s.lib. There are many possibilities: you accidentally built the wrong version, or you may have built the right version and VCExpress named it wrong. To double check, and fix the problem, you can do the following:

cd C:\CGAL-3.7\lib
dumpbin /all CGAL-vc90-mt.lib | find /i "DEFAULTLIB"
(if you have mt-gd, use that name instead)


If this shows lines referencing LIBCMTD, MSVCRT, or MSVCRTD then you accidentally built the debug and/or dynamic version, and you need to clean the build, and try to build again with proper settings to get the multi-threaded static release version. However, if it just says LIBCMT, then you are probably OK. Look for another line saying DEFAULTLIB:CGAL-vc90-mt-s. If it is there, then you can probably just rename the file and have it work.

move CGAL-vc90-mt.lib CGAL-vc90-mt-s.lib


Visual Studio build

You can build CGAL using the GUI of visual studio, as an alternative to nmake. You have to use an alternate cmake syntax. Type 'cmake' by itself and it will give you a list of 'generators' that are valid for your machine; for example Visual Studio Express is cmake -G"Visual Studio 9 2008" .. That should get you a working .sln (solution) file.

Then run this:

vcexpress CGAL.sln


Modify the build configure target to Release (not Debug) and change the properties of the projects to be '/MT' multithreaded static builds. This is the similar procedure used to build OpenCSG, so refer to those instructions above for more detail.

Note for Unix users

The 'MingW Shell' (Start/Programs) provide tools like bash, sed, grep, vi, tar, &c. The C:\ drive is under '/c/'. MingW has packages, for example: mingw-get install msys-unzip downloads and installs the 'unzip' program. Git contains some programs by default, like perl. The windows command shell has cut/paste - hit alt-space. You can also change the scrollback buffer settings.

### References

For making release binaries, see http://svn.clifford.at/openscad/trunk/doc/checklist-macosx.txt

# Library Locations

OpenSCAD uses three library locations, the installation library, built-in library, and user-defined libraries.

1. The Installation library location is the libraries directory under the directory where OpenSCAD is installed.
2. The Built-In library location is O/S dependent. Since version 2014.03, it can be opened in the system specific file manager using the "File->Show Library Folder..." menu entry.
• Windows: My Documents\OpenSCAD\libraries
• Linux: $HOME/.local/share/OpenSCAD/libraries • Mac OS X: $HOME/Documents/OpenSCAD/libraries
3. The User-Defined library path can be created using the OPENSCADPATH Environment Variable to point to the library(s). OPENSCADPATH can contain multiple directories in case you have library collections in more than one place, separate directories with a semi-colon for Windows, and a colon for Linux/Mac OS. For example:
Windows: C:\Users\A_user\Documents\OpenSCAD\MyLib;C:\Thingiverse Stuff\OpenSCAD Things;D:\test_stuff
(Note: For Windows, in versions prior to 2014.02.22 there is a bug preventing multiple directories in OPENSCADPATH as described above, it uses a colon (:) to separate directories. A workaround, if your libraries are on C: is to leave off the drive letter & colon, e.g. \Thingiverse Stuff\OpenSCAD Things:\stuff. For more about setting Windows environment variables, see User Environment Variables.
Linux/Mac OS: /usr/lib:/home/mylib:.
OpenSCAD will need to be restarted to recognise any change to the OPENSCADPATH Environment Variable.

When you specify a non-fully qualified path and filename in the use <...> or include <...> statement OpenSCAD looks for the file in the following directories in the following order:

• the directory of the calling .scad file
• the User-Defined library paths (OPENSCADPATH)
• the Built-In library (i.e. the O/S dependent locations above)
• the Installation library

In the case of a library file itself having use <...> or include <...> the directory of the library .scad file is the 'calling' file, i.e. when looking for libraries within a library, it does not check the directory of the top level .scad file.

For example, with the following locations and files defined: (with OPENSCADPATH=/usr/lib:/home/lib_os:.)

1. <installation library>/lib1.scad


The following include <...> statements will match to the nominated library files

include <lib1.scad>  // #1.


Since 2014.03, the currently active list of locations can be verified in the "Help->Library Info" dialog.

The details info shows both the content of the OPENSCADPATH variable and the list of all library locations. The locations will be searched in the order they appear in this list. For example;

OPENSCADPATH: /data/lib1:/data/lib2
/data/lib1
/data/lib2


In Windows, Environment Variables are set via the Control panel, select System, then Advanced System Settings, click Environment Variables. Create a new User Variable, or edit OPENSCADPATH if it exists.

## Include Statement

After 2010.02

include <filename.scad> (appends whole file)

use <filename.scad>  (appends ONLY modules and functions)


filename could use directory (with / char separator).

Prior to 2010.02

<filename.scad>


## Other Language Features

$fa is the minimum angle for a fragment. The default value is 12 (degrees)  $fs is the minimum size of a fragment. The default value is 1.

$fn is the number of fragments. The default value is 0.  When$fa and $fs are used to determine the number of fragments for a circle, then OpenSCAD will never use less than 5 fragments. $t


The $t variable is used for animation. If you enable the animation frame with view->animate and give a value for "FPS" and "Steps", the "Time" field shows the current value of$t.

function name(<var>) = f(<var>);

echo(<string>, <var>, ...);

render(convexity = <val>) {...}

surface(file = "filename.dat", center = <boolean>, convexity = <val>);


## 2D Primitives

square(size = <val>, center=<boolean>);
square(size = [x,y], center=<boolean>);

circle(r = <val>);

polygon(points = [[x, y], ... ], paths = [[p1, p2, p3..], ... ], convexity = N);


## 3D to 2D Projection

projection(cut = <boolean>)


## 2D to 3D Extrusion

linear_extrude(height = <val>, center = <boolean>, convexity = <val>, twist = <degrees>[, slices = <val>, $fn=...,$fs=...,$fa=...]){...}  rotate_extrude(convexity = <val>[,$fn = ...]){...}


## DXF Extrusion

linear_extrude(height = <val>, center = <boolean>, convexity = <val>, twist = <degrees>[...])
import (file = "filename.dxf", layer = "layername")

rotate_extrude(origin = [x,y], convexity = <val>[, \$fn = ...])
import (file = "filename.dxf", layer = "layername")


## STL Import

import("filename.stl", convexity = <val>);