This is a printable version of only The OpenSCAD Language Everything else is at OpenSCAD_User_Manual/Print_version For the Contents governed by [hide] or [show], what you see is what gets printed. This message will not be printed.

# Chapter 1 -- General

### 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.

Actions

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

Operators

Operators do not end in semicolons ';'. 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.

 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 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 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 Special variables) ### 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], [5,7,8,9] ] 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]] ]  ##### 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  See example elements with lengths ##### 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. # Chapter 2 -- 3D Objects OpenSCAD User Manual/The OpenSCAD Language ## Primitive Solids ### 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 rectangular prism: A polyhedron rectangular 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],[w,0,0],[0,sqrt(w*w+h*h),0], [0,0,z],[w,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-w,0,0],[0,sqrt(w*w+h*h),0], [0,0,z],[0-w,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 polyhedrons Mistakes in defining polyhedrons include not having all faces with the same order, overlap of faces and missing faces or portions of faces. 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. 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  #### 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 permute 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]. 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 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 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 given an identifier starting at 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 identifier) 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. 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 ]  ## 3D to 2D Projection 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, 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: # Chapter 3 -- 2D Objects OpenSCAD User Manual/The OpenSCAD Language 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 $fa must be named. click here for more details,. defaults: circle(); yields: circle($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 using circle() with $fn set to the number of sides. The polygon is inscribed within the circle with all sides (and angles) equal. One corner points to the positive x direction. For irregular shapes see the polygon primitive below. script for these examples translate([-42, 0]){circle(20,$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");


## Text

The text module creates text as a 2D geometric object, using fonts installed on the local system or provided as separate font file.

[Note: Requires version 2015.03]

Parameters

text
String. The text to generate.
size
Decimal. The generated text will have approximately an ascent of the given value (height above the baseline). Default is 10.
Note that specific fonts will vary somewhat and may not fill the size specified exactly, usually slightly smaller.
font
String. The name of the font that should be used. This is not the name of the font file, but the logical font name (internally handled by the fontconfig library). This can also include a style parameter, see below. A list of installed fonts & styles can be obtained using the font list dialog (Help -> Font List).
halign
String. The horizontal alignment for the text. Possible values are "left", "center" and "right". Default is "left".
valign
String. The vertical alignment for the text. Possible values are "top", "center", "baseline" and "bottom". Default is "baseline".
spacing
Decimal. Factor to increase/decrease the character spacing. The default value of 1 will result in the normal spacing for the font, giving a value greater than 1 will cause the letters to be spaced further apart.
direction
String. Direction of the text flow. Possible values are "ltr" (left-to-right), "rtl" (right-to-left), "ttb" (top-to-bottom) and "btt" (bottom-to-top). Default is "ltr".
language
String. The language of the text. Default is "en".
script
String. The script of the text. Default is "latin".
fn used for subdividing the curved path segments provided by freetype Example Example 1: Result. text("OpenSCAD");  Note To allow specification of particular Unicode characters you can specify them in a string with the following escape codes; \x03 - single hex character (only allowed values are 01h - 7fh) \u0123 - unicode char with 4 hexadecimal digits (note: Lowercase) \U012345 - unicode char with 6 hexadecimal digits (note: Uppercase) Example t="\u20AC10 \u263A"; // 10 euro and a smilie  ### Using Fonts & Styles Fonts are specified by their logical font name; in addition a style parameter can be added to select a specific font style like "bold" or "italic", such as: font="Liberation Sans:style=Bold Italic"  The font list dialog shows the font name and the font style for each available font. For reference, the dialog also displays the location of the font file. OpenSCAD font list dialog OpenSCAD includes the fonts Liberation Mono, Liberation Sans, Liberation Sans Narrow and Liberation Serif. Hence, as fonts in general differ by platform type, use of these included fonts is likely to be portable across platforms. For common/casual text usage, the specification of one of these fonts is recommended for this reason. Liberation Sans is the default font to encourage this. In addition to the installed fonts, it's possible to add project specific font files. Supported font file formats are TrueType Fonts (*.ttf) and OpenType Fonts (*.otf). The files need to be registered with use<>.  use <ttf/paratype-serif/PTF55F.ttf>  After the registration, the font will also be listed in the font list dialog, so in case logical name of a font is unknown, it can be looked up there are it was registered. Example Example 2: Result.  square(10); translate([15, 15]) { text("OpenSCAD", font = "Liberation Sans"); } translate([15, 0]) { text("OpenSCAD", font = "Liberation Sans:style=Bold Italic"); }  ### Alignment #### Vertical alignment top The text is aligned with the top of the bounding box at the given Y coordinate. center The text is aligned with the center of the bounding box at the given Y coordinate. baseline The text is aligned with the font baseline at the given Y coordinate. This is the default. bottom The text is aligned with the bottom of the bounding box at the given Y coordinate. OpenSCAD vertical text alignment  text = "Align"; font = "Liberation Sans"; valign = [ [ 0, "top"], [ 40, "center"], [ 75, "baseline"], [110, "bottom"] ]; for (a = valign) { translate([10, 120 - a[0], 0]) { color("red") cube([135, 1, 0.1]); color("blue") cube([1, 20, 0.1]); linear_extrude(height = 0.5) { text(text = str(text,"_",a[1]), font = font, size = 20, valign = a[1]); } } }  #### Horizontal alignment left The text is aligned with the left side of the bounding box at the given X coordinate. This is the default. center The text is aligned with the center of the bounding box at the given X coordinate. right The text is aligned with the right of the bounding box at the given X coordinate. OpenSCAD horizontal text alignment  text = "Align"; font = "Liberation Sans"; halign = [ [10, "left"], [50, "center"], [90, "right"] ]; for (a = halign) { translate([140, a[0], 0]) { color("red") cube([115, 2,0.1]); color("blue") cube([2, 20,0.1]); linear_extrude(height = 0.5) { text(text = str(text,"_",a[1]), font = font, size = 20, halign = a[1]); } } }  ### Renderable 3Dtext It is easy only using the function linear_extrude(height) ## 3D to 2D Projection 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, 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: ## 2D to 3D Extrusion 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. 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. #### 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 false, 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 variablesfn, $fs and$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 it's 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. 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]] );


# Chapter 4 -- Transform

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 '{' & '}' to enclose the subtree e.g.

 translate([0,0,-5]) {
{                                                 cube(10);
cube(10);                                       cylinder(r=5,h=10);
cylinder(r=5,h=10);                           }
}


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);


### resize

resize() is available since OpenSCAD 2013.06. It modifies the size of the child object to match the given x,y, and z.

There is a bug with shrinking in the 2013.06 release, that will be fixed in the next release.

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 origin 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.

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 mutiple 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 coincides with end of cylinder


### translate

Translates (moves) its child elements along the specified vector. The argument name is optional.

IExample

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

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);
} }


### 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( [r, g, b, a] ) { ... }
color( [r, g, b], a=1.0 ) { ... } // since v. 2011.12 (?)
color( colorname, 1 ) { ... } // since v. 2011.12 ( fails in 2014.03; use color( "colorname", #) were # is the alpha )


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.

Chart based on "Web Colors" from Wikipedia

#### Example2

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): $fn=50;
minkowski()
{
cube([10,10,1]);
cylinder(r=2,h=1);
}


### hull

Two cylinders
Convex hull of two cylinders

Displays the convex hull of child nodes.

Usage example:

hull() {
translate([15,10,0]) circle(10);
circle(10);
}


## Combining transformations

When combining transformations, it is a sequential process, but going right-to-left. That is

 rotate( ... ) translate ( ... ) cube(5) ;


would first move the cube, and then move in an arc (turning it the same amount) at the radius given by the translation.

 translate ( ... ) rotate( ... ) cube(5) ;


would first turn the cube and place it at the offset defined by the translate.

Combine two transforms
color("red")   translate([0,10,0] ) rotate([45,0,0])     cube(5);
color("green") rotate([45,0,0])     translate([0,10,0] ) cube(5);


# Chapter 5 -- Boolean combination

### boolean overview

##### 2D examples
union()       {square(10);circle(10);} // square or  circle
difference()  {square(10);circle(10);} // square and not circle
difference()  {circle(10);square(10);} // circle and not square
intersection(){square(10);circle(10);} // square and circle

##### 3D examples
union()       {cube(12, center=true); sphere(8);} // cube or  sphere
difference()  {cube(12, center=true); sphere(8);} // cube and not sphere
difference()  {sphere(8); cube(12, center=true);} // sphere and not cube
intersection(){cube(12, center=true); sphere(8);} // cube and sphere


### union

Creates a union of all its child nodes. This is the sum of all children (logical or).
May be used with either 2D or 3D objects, but don't mix them.

Usage example:
union() {
cylinder (h = 4, r=1, center = true, $fn=100); rotate ([90,0,0]) cylinder (h = 4, r=0.9, center = true,$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 Always calculate the CSG model for this tree (even in OpenCSG preview mode). 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. # Chapter 6 -- Other Functions and Operators OpenSCAD User Manual/The OpenSCAD Language ## Conditional and Iterator Functions ### 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 As a vector The Action is evaluated for each element of the vector 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 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 of 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); } }  ## Mathematical Operators ### 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: ${\displaystyle AB\neq BA}$, ${\displaystyle Av\neq vA}$. ## Mathematical Functions ## 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. ceil(x) is the smallest integer not less than x. 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); //-> 5round(5.5); //-> 6round(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 it's 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 ## String Functions ### 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. ### Also See search() search() for text searching. ## List Comprehensions [Note: Requires version 2015.03] ### Basic Syntax The list comprehensions provide a flexible way to generate lists using the general syntax  [ list-definition expression ]  The following elements are supported to construct the list definition for (i = sequence) Iteration over a range or an existing list if (condition) Selection criteria, when true the expression will be calculated and added to the result list let (x = value) Local variable assignment #### for The for element defines the input values for the list generation, the syntax is the same as used by the for iterator. [ for (i = [start : step : end]) i ] Generate output based on a range definition, this version is mainly useful to calculate list values or access existing lists using the range value as index. Examples // generate a list with all values defined by a range list1 = [ for (i = [0 : 2 : 10]) i ]; echo(list1); // ECHO: [0, 2, 4, 6, 8, 10]  // extract every second character of a string str = "SomeText"; list2 = [ for (i = [0 : 2 : len(str) - 1]) str[i] ]; echo(list2); // ECHO: ["S", "m", "T", "x"]  // indexed list access, using function to map input values to output values function func(x) = x < 1 ? 0 : x + func(x - 1); input = [1, 3, 5, 8]; output = [for (a = [ 0 : len(input) - 1 ]) func(input[a]) ]; echo(output); // ECHO: [1, 6, 15, 36]  [ for (i = [a, b, c, ...]) i ] Use list parameter as input, this version can be used to map input values to calculated output values. Examples // map input list to output list list = [ for (i = [2, 3, 5, 7, 11]) i * i ]; echo(list); // ECHO: [4, 9, 25, 49, 121]  // calculate Fibonacci numbers function func(x) = x < 3 ? 1 : func(x - 1) + func(x - 2); input = [7, 10, 12]; output = [for (a = input) func(a) ]; echo(output); // ECHO: [13, 55, 144]  #### if The if element allows selection if the expression should be allocated and added to the result list or not. In the simplest case this allows filtering of an list. [ for (i = list) if (condition(i)) i ] When the evaluation of the condition returns true, the expression i is added to the result list. Example list = [ for (a = [ 1 : 8 ]) if (a % 2 == 0) a ]; echo(list); // ECHO: [2, 4, 6, 8]  #### let The let element allows sequential assignment of variables inside an list comprehension definition. [ for (i = list) let (assignments) a ] Example list = [ for (a = [ 1 : 4 ]) let (b = a*a, c = 2 * b) [ a, b, c ] ]; echo(list); // ECHO: [[1, 1, 2], [2, 4, 8], [3, 9, 18], [4, 16, 32]]  ### Nested loops There are different ways to define nested loops. Defining multiple loop variables inside one for element and multiple for elements produce both flat result lists. To generate nested result lists an additional [ ] markup is required. // nested loop using multiple variables flat_result1 = [ for (a = [ 0 : 2 ], b = [ 0 : 2 ]) a == b ? 1 : 0 ]; echo(flat_result1); // ECHO: [1, 0, 0, 0, 1, 0, 0, 0, 1]  // nested loop using multiple for elements flat_result2 = [ for (a = [ 0 : 2 ]) for (b = [0 : 2]) a == b ? 1 : 0 ]; echo(flat_result2); // ECHO: [1, 0, 0, 0, 1, 0, 0, 0, 1]  // nested loop to generate nested output list nested_result = [ for (a = [ 0 : 2 ]) [ for (b = [ 0 : 2 ]) a == b ? 1 : 0 ] ]; echo(nested_result); // ECHO: [[1, 0, 0], [0, 1, 0], [0, 0, 1]]  ### Advanced Examples This chapter lists some advanced examples, useful idioms and use-cases for the list comprehension syntax. #### Generating vertices for a polygon Result Using list comprehension, a parametric equation can be calculated at a number of points to approximate many curves, such as the following example for an ellipse (using polygon()): sma = 20; // semi-minor axis smb = 30; // semi-major axis polygon( [ for (a = [0 : 5 : 359]) [ sma * sin(a), smb * cos(a) ] ] );  #### Flattening a nested vector List comprehension can be used in a user-defined function to perform tasks on or for vectors. Here is a user-defined function that flattens a nested vector. // input : nested list // output : list with the outer level nesting removed function flatten(l) = [ for (a = l) for (b = a) b ] ; nested_list = [ [ 1, 2, 3 ], [ 4, 5, 6 ] ]; echo(flatten(nested_list)); // ECHO: [1, 2, 3, 4, 5, 6]  #### Sorting a vector Even a complicated algorithm Quicksort becomes doable with for(), if(), let() and recursion: // input : list of numbers // output : sorted list of numbers function quicksort(arr) = !(len(arr)>0) ? [] : let( pivot = arr[floor(len(arr)/2)], lesser = [ for (y = arr) if (y < pivot) y ], equal = [ for (y = arr) if (y == pivot) y ], greater = [ for (y = arr) if (y > pivot) y ] ) concat( quicksort(lesser), equal, quicksort(greater) ); // use seed in rands() to get reproducable results unsorted = [for (a = rands(0, 10, 6, 3)) ceil(a)]; echo(unsorted); // ECHO: [6, 1, 8, 9, 3, 2] echo(quicksort(unsorted)); // ECHO: [1, 2, 3, 6, 8, 9]  #### Selecting elements of a vector select() performs selection and reordering of elements into a new vector. function select(vector,indices) = [ for (index = indices) vector[index] ]; vector1 = [[0,0],[1,1],[2,2],[3,3],[4,4]]; selector1 = [4,0,3]; vector2 = select(vector1,selector1); // [[4, 4], [0, 0], [3, 3]] vector3 = select(vector1,[0,2,4,4,2,0]);// [[0, 0], [2, 2], [4, 4],[4, 4], [2, 2], [0, 0]] // range also works as indices vector4 = select(vector1, [4:-1:0]); // [[4, 4], [3, 3], [2, 2], [1, 1], [0, 0]]  ## Other Language Features ### 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.

### 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 Qt Docs 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!"


### Render

Forces the generation of a mesh even in preview mode. Useful when the boolean operations become too slow to track.

Needs description.

Usage examples:

render(convexity = 2) difference() {
cube([20, 20, 150], center = true);
translate([-10, -10, 0])
cylinder(h = 80, r = 10, center = true);
translate([-10, -10, +40])
sphere(r = 10);
translate([-10, -10, -40])
sphere(r = 10);
}


### Surface

Surface reads Heightmap information from text or image files.

Parameters

file
String. The path to the file containing the heightmap data.
center
Boolean. This determines the positioning of the generated object. If true, object is centered in X- and Y-axis. Otherwise, the object is placed in the positive quadrant. Defaults to false.
invert
Boolean. Inverts how the color values of imported images are translated into height values. This has no effect when importing text data files. Defaults to false. [Note: Requires version 2015.03]
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 final rendering.

#### Text file format

The format for text based heightmaps is a matrix of numbers that represent the height for a specific point. Rows are mapped to the Y-axis, columns to the X axis. The numbers must be separated by spaces or tabs. Empty lines and lines starting with a # character are ignored.

#### Images

[Note: Requires version 2015.03]

Currently only PNG images are supported. Alpha channel information of the image is ignored and the height for the pixel is determined by converting the color value to Grayscale using the linear luminance for the sRGB color space (Y = 0.2126R + 0.7152G + 0.0722B). The gray scale values are scaled to be in the range 0 to 100.

#### Examples

Example 1:

//surface.scad
surface(file = "surface.dat", center = true, convexity = 5);
%translate([0,0,5])cube([10,10,10], center =true);

#surface.dat
10 9 8 7 6 5 5 5 5 5
9 8 7 6 6 4 3 2 1 0
8 7 6 6 4 3 2 1 0 0
7 6 6 4 3 2 1 0 0 0
6 6 4 3 2 1 1 0 0 0
6 6 3 2 1 1 1 0 0 0
6 6 2 1 1 1 1 0 0 0
6 6 1 0 0 0 0 0 0 0
3 1 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0


Result:

Example 2

 // example010.dat generated using octave:
// d = (sin(1:0.2:10)' * cos(1:0.2:10)) * 10;
// save("example010.dat", "d");
intersection() {
surface(file = "example010.dat", center = true, convexity = 5);
rotate(45, [0, 0, 1]) surface(file = "example010.dat", center = true, convexity = 5);
}


Example 3:

[Note: Requires version 2015.03]

// Example 3a
scale([1, 1, 0.1])
surface(file = "smiley.png", center = true);

// Example 3b
scale([1, 1, 0.1])
surface(file = "smiley.png", center = true, invert = true);

Input image
Example 3a: surface(invert = false)
Example 3b: surface(invert = true)
Example 3: Using surface() with a PNG image as heightmap input.

### Search

The search() function is a general-purpose function to find one or more (or all) occurrences of a value or list of values in a vector, string or more complex list-of-list construct.

#### Search Usage

search( match_value , string_or_vector [, num_returns_per_match [, index_col_num ] ] );

#### Search Arguments

• match_value
• Can be a single value or vector of values.
• Strings are treated as vectors-of-characters to iterate over; the search function does not search for substrings.
• Note: If match_value is a vector of strings, search will look for exact string matches.
• See Example 9 below.
• string_or_vector
• The string or vector to search for matches.
• num_returns_per_match (default: 1)
• By default, search only looks for one match per element of match_value to return as a list of indices
• If num_returns_per_match > 1, search returns a list of lists of up to num_returns_per_match index values for each element of match_value.
• See Example 8 below.
• If num_returns_per_match = 0, search returns a list of lists of all matching index values for each element of match_value.
• See Example 6 below.
• index_col_num (default: 0)
• When string_or_vector is a vector-of-vectors, multidimensional table or more complex list-of-lists construct, the match_value may not be found in the first (index_col_num=0) column.
• See Example 5 below for a simple usage example.

#### Search Usage Examples

##### Index values return as list
Example Code Result

1

search("a","abcdabcd");

[0]

2

search("e","abcdabcd");

[]

3

search("a","abcdabcd",0);

[[0,4]]

4

data=[ ["a",1],["b",2],["c",3],["d",4],["a",5],["b",6],["c",7],["d",8],["e",9] ];

search("a", data, num_returns_per_match=0);

##### Search on different column; return Index values

Example 5:

 data= [ ["a",1],["b",2],["c",3],["d",4],["a",5],["b",6],["c",7],["d",8],["e",3] ];
search(3, data, num_returns_per_match=0, index_col_num=1);


Returns:

   [2,8]

##### Search on list of values

Example 6: Return all matches per search vector element.

 data= [ ["a",1],["b",2],["c",3],["d",4],["a",5],["b",6],["c",7],["d",8],["e",9] ];
search("abc", data, num_returns_per_match=0);


Returns:

   [[0,4],[1,5],[2,6]]


Example 7: Return first match per search vector element; special case return vector.

 data= [ ["a",1],["b",2],["c",3],["d",4],["a",5],["b",6],["c",7],["d",8],["e",9] ];
search("abc", data, num_returns_per_match=1);


Returns:

   [0,1,2]


Example 8: Return first two matches per search vector element; vector of vectors.

 data= [ ["a",1],["b",2],["c",3],["d",4],["a",5],["b",6],["c",7],["d",8],["e",9] ];
search("abce", data, num_returns_per_match=2);


Returns:

 [[0,4],[1,5],[2,6],[8]]

##### Search on list of strings

Example 9:

 lTable2=[ ["cat",1],["b",2],["c",3],["dog",4],["a",5],["b",6],["c",7],["d",8],["e",9],["apple",10],["a",11] ];
lSearch2=["b","zzz","a","c","apple","dog"];
l2=search(lSearch2,lTable2);
echo(str("Default list string search (",lSearch2,"): ",l2));


Returns

 ECHO: "Default list string search (["b", "zzz", "a", "c", "apple", "dog"]): [1, [], 4, 2, 9, 3]"

##### Getting the right results
// workout which vectors get the results
v=[ ["O",2],["p",3],["e",9],["n",4],["S",5],["C",6],["A",7],["D",8] ];
//
echo(v[0]);                                     // -> ["O",2]
echo(v[1]);                                     // -> ["p",3]
echo(v[1][0],v[1][1]);                          // -> "p",3
echo(search("p",v));                            // find "p" -> [1]
echo(search("p",v)[0]);                         // -> 1
echo(search(9,v,0,1));                          // find  9  -> [2]
echo(v[search(9,v,0,1)[0]]);                    // -> ["e",9]
echo(v[search(9,v,0,1)[0]][0]);                 // -> "e"
echo(v[search(9,v,0,1)[0]][1]);                 // -> 9
echo(v[search("p",v,1,0)[0]][1]);               // -> 3
echo(v[search("p",v,1,0)[0]][0]);               // -> "p"
echo(v[search("D",v,1,0)[0]][1]);               // -> 8


version() and version_num() will return OpenSCAD version number.

• The version() function will return the OpenSCAD version as a vector, e.g. [2011, 09, 23]
• The version_num() function will return the OpenSCAD version as a number, e.g. 20110923

### parent_module(n) and $parent_modules$parent_module 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"


# Chapter 7 -- User-Defined Functions and Modules

### 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.

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.

### Functions

Functions operate on values to calculate and return new values.

function definition
function name ( parameters ) = value ;

name
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
n==0 ?
sum :

// 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]){
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 $children < 2 } } aim(30,20)arrow(); aim(35,270)cannon(); aim(15){cannon();base();}   module RotaryCluster(radius=30,number=8) for (azimuth =[0:360/number:359]) rotate([0,0,azimuth]) translate([radius,0,0]) { children(); translate([40,0,30]) text(str(azimuth)); } RotaryCluster(200,7) color("lightgreen") aim(15){cannon();base();} rotate([0,0,110]) RotaryCluster(100,4.5) aim(35)cannon(); color("LightBlue")aim(55,30){cannon();base();}  #### Recursive Modules Like functions, modules may contain recursive calls. However, there is no tail-recursion elimination for recursive modules. The code below generates a crude model of a tree. Each tree branch is itself a modified version of the tree and produced by recursion. Be careful to keep the recursion depth (branching) n below 7 as the number of primitives and the preview time grow exponentially. A simple tree created with a recursive OpenSCAD module  module simple_tree(size, dna, n) { if (n > 0) { // trunk cylinder(r1=size/10, r2=size/12, h=size,$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

# Chapter 8 -- Debugging aids

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, $fn=100); // first object that will subtracted rotate ([90,0,0]) cylinder (h = 15, r=1, center = true,$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.

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

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!"


# Chapter 9 -- External libraries and code files

## Use and Include

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.

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.

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.

A library file for generating rings might look like this (defining a function and providing an example):

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
module a() {
ring();
}


but this will result in an syntax error:

 //a.scad
module a() {
ring();
}


Default variables in an include can be overridden, for example

i=1;
k=3;
module x() {
echo("hello world");
echo("i=",i,"j=",j,"k=",k);
}


j=4;
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


#### 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.

## import

Imports a file for use in the current OpenSCAD model. OpenSCAD currently supports import of DXF, OFF and STL (both ASCII and Binary) files.

NOTE: The file extension is used to determine which type.

   OpenSCAD can export files as  STL, OFF, AMF, DXF, SVG, CSG OR PNG(Image).

These file types created by OpenSCAD, or others, can be imported as follows:

STL, OFF and DXF are imported using import().
CSG can be imported using include<> or loaded like an SCAD file
PNG can be imported using surface()
There are open pull requests for SVG and AMF, which require a bit more work/testing.
The file suffix is used to determine type.


Parameters

<file>
A string containing the path to the STL, OFF or DXF file.
<convexity>
An 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.
import("example012.stl", convexity=3);
import("D:\\Documents and Settings\\User\\My Documents\\Gear.stl", convexity=3);
(Windows users must "escape" the backslashes by writing them doubled.)


#### Convexity

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.

#### Notes

In the latest version of OpenSCAD, import() is now used for importing both 2D (DXF for extrusion) and 3D (STL) files.

If you want to render the imported STL file later, you have to make sure that the STL file is "clean". This means that the mesh has to be manifold and should not contain holes nor self-intersections. If the STL is not clean, you might get errors like:

 CGAL error in CGAL_Build_PolySet: CGAL ERROR: assertion violation!
Expr: check_protocoll == 0
Line: 199


or

 CGAL error in CGAL_Nef_polyhedron3(): CGAL ERROR: assertion violation!
Expr: pe_prev->is_border() || !internal::Plane_constructor<Plane>::get_plane(pe_prev->facet(),pe_prev->facet()->plane()).is_degenerate()
Line: 253


In order to clean the STL file, you have the following options:

- use http://wiki.netfabb.com/Semi-Automatic_Repair_Options . This will repair the holes but not the self-intersections.

- use netfabb basic. This free software doesnt have the option to close holes nor can it fix the self-intersections

- use MeshLab, This free software can fix all the issues

Using MeshLab, you can do:

- Render - Show non Manif Edges

- Render - Show non Manif Vertices

- if found, use Filters - Selection - Select non Manifold Edges or Select non Manifold Vertices - Apply - Close. Then click button 'Delete the current set of selected vertices...' or check http://www.youtube.com/watch?v=oDx0Tgy0UHo for an instruction video. The screen should show "0 non manifold edges", "0 non manifold vertices"

Next, you can click the icon 'Fill Hole', select all the holes and click Fill and then Accept. You might have to redo this action a few times.

Use File - Export Mesh to save the STL.

## import_dxf

DEPRECATED: Will be removed in future releases. Use import() instead.

Read a DXF file and create a 2D shape.

linear_extrude(height = 5, center = true, convexity = 10)
import_dxf(file = "example009.dxf", layer = "plate");


## import_stl

DEPRECATED: Will be removed in future releases. Use import() instead.

Imports an STL file for use in the current OpenSCAD model

import_stl("example012.stl", convexity = 5);


## Surface

Surface reads Heightmap information from text or image files. Surface can read PNG files.

Parameters

file
String. The path to the file containing the heightmap data.
center
Boolean. This determines the positioning of the generated object. If true, object is centered in X- and Y-axis. Otherwise, the object is placed in the positive quadrant. Defaults to false.
invert
Boolean. Inverts how the color values of imported images are translated into height values. This has no effect when importing text data files. Defaults to false. [Note: Requires version 2015.03]
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 final rendering.

#### Text file format

The format for text based heightmaps is a matrix of numbers that represent the height for a specific point. Rows are mapped to the Y-axis, columns to the X axis. The numbers must be separated by spaces or tabs. Empty lines and lines starting with a # character are ignored.

#### Images

[Note: Requires version 2015.03]

Currently only PNG images are supported. Alpha channel information of the image is ignored and the height for the pixel is determined by converting the color value to Grayscale using the linear luminance for the sRGB color space (Y = 0.2126R + 0.7152G + 0.0722B). The gray scale values are scaled to be in the range 0 to 100.

#### Examples

Example 1:

//surface.scad
surface(file = "surface.dat", center = true, convexity = 5);
%translate([0,0,5])cube([10,10,10], center =true);

#surface.dat
10 9 8 7 6 5 5 5 5 5
9 8 7 6 6 4 3 2 1 0
8 7 6 6 4 3 2 1 0 0
7 6 6 4 3 2 1 0 0 0
6 6 4 3 2 1 1 0 0 0
6 6 3 2 1 1 1 0 0 0
6 6 2 1 1 1 1 0 0 0
6 6 1 0 0 0 0 0 0 0
3 1 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0


Result:

Example 2

 // example010.dat generated using octave:
// d = (sin(1:0.2:10)' * cos(1:0.2:10)) * 10;
// save("example010.dat", "d");
intersection() {
surface(file = "example010.dat", center = true, convexity = 5);
rotate(45, [0, 0, 1]) surface(file = "example010.dat", center = true, convexity = 5);
}


Example 3:

[Note: Requires version 2015.03]

// Example 3a
scale([1, 1, 0.1])
surface(file = "smiley.png", center = true);

// Example 3b
scale([1, 1, 0.1])
surface(file = "smiley.png", center = true, invert = true);

Input image
Example 3a: surface(invert = false)
Example 3b: surface(invert = true)
Example 3: Using surface() with a PNG image as heightmap input.