# User:LABoyd2/contents from The OpenSCAD Language 151106

## 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. Objects end in a semicolon ';'.

Actions

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

Operators

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

 Examples

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


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

// This is a comment

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

/*
can span multiple lines.
*/


### Values and Data Types

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

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

#### Numbers

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

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

• PI

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

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

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

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


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

#### Boolean Values

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

• false
• 0 and -0
• ""
• []
• undef

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

#### Strings

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

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

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

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

 Example:

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

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

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


#### Ranges

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

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

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

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


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

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

#### The Undefined Value

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

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

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

### Variables

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

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


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

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

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

Before version 2015.03

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

Since version 2015.03

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

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


#### Undefined variable

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

 Example

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


#### Scope of variables

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

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

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

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

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


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

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

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

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


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

#### Special Variables

Special variables provide an alternate means of passing arguments to modules and functions. All variables starting with a '$' are special variables, similar to special variables in lisp. As such they are more dynamic than regular variables. (for more details see Other Language Features) ### Vectors A vector is a sequence of zero or more OpenSCAD values. Vectors are a collection (or list or table) of numeric or boolean values, variables, vectors, strings or any combination thereof. They can also be expressions which evaluate to one of these. Vectors handle the role of arrays found in many imperative languages. The information here also applies to lists and tables which use vectors for their data. A vector has square brackets, [] enclosing zero or more items (elements or members), separated by commas. A vector can contain vectors, which contain vectors, etc. examples  [1,2,3] [a,5,b] [] [5.643] ["a","b","string"] [[1,r],[x,y,z,4,5]] [3, 5, [6,7], [[8,9],[10,[11,12],13], c, "string"] [4/3, 6*1.5, cos(60)]  use in OpenSCAD:  cube( [width,depth,height] ); // optional spaces shown for clarity translate( [x,y,z] ) polygon( [ [x0,y0], [x1,y1], [x2,y2] ] );  creation Vectors are created by writing the list of elements, separated by commas, and enclosed in square brackets. Variables are replaced by their values.  cube([10,15,20]); a1 = [1,2,3]; a2 = [4,5]; a3 = [6,7,8,9]; b = [a1,a2,a3]; // [ [1,2,3], [4,5], [6,7,8,9] ] note increased nesting depth  elements within vectors Elements within vectors are numbered from 0 to n-1 where n is the length returned by len(). Address elements within vectors with the following notation: e[5] // element no 5 (sixth) at 1st nesting level e[5][2] // element 2 of element 5 2nd nesting level e[5][2][0] // element 0 of 2 of 5 3rd nesting level e[5][2][0][1] // element 1 of 0 of 2 of 5 4th nesting level  example elements with lengths from len() e = [ [1], [], [3,4,5], "string", "x", [[10,11],[12,13,14],[[15,16],[17]]] ]; // length 6 address length element e[0] 1 [1] e[1] 0 [] e[5] 3 [ [10,11], [12,13,14], [[15,16],[17]] ] e[5][1] 3 [ 12, 13, 14 ] e[5][2] 2 [ [15,16], [17] ] e[5][2][0] 2 [ 15, 16 ] e[5][2][0][1] undef 16 e[3] 6 "string" e[3 ][2] 1 "r" s = [2,0,5]; a = 2; s[a] undef 5 e[s[a]] 3 [ [10,11], [12,13,14], [[15,16],[17]] ]  alternate dot notation The first three elements of a vector can be accessed with an alternate dot notation: e.x //equivalent to e[0] e.y //equivalent to e[1] e.z //equivalent to e[2]  ##### vector operators ###### concat [Note: Requires version 2015.03] concat() combines the elements of 2 or more vectors into a single vector. No change in nesting level is made.  vector1 = [1,2,3]; vector2 = [4]; vector3 = [5,6]; new_vector = concat(vector1, vector2, vector3); // [1,2,3,4,5,6] string_vector = concat("abc","def"); // ["abc", "def"] one_string = str(string_vector[0],string_vector[1]); // "abcdef"  ###### len len() is a function which returns the length of vectors or strings. Indices of elements are from [0] to [length-1]. vector Returns the number of elements at this level. Single values, which are not vectors, return undef. string Returns the number of characters in string.  a = [1,2,3]; echo(len(a)); // 3  ##### Matrix A matrix is a vector of vectors. Example which defines a 2D rotation matrix mr = [ [cos(angle), -sin(angle)], [sin(angle), cos(angle)] ];  ### Getting input Now we have variables, it would be nice to be able to get input into them instead of setting the values from code. There are a few functions to read data from DXF files, or you can set a variable with the -D switch on the command line. Getting a point from a drawing Getting a point is useful for reading an origin point in a 2D view in a technical drawing. The function dxf_cross will read the intersection of two lines on a layer you specify and return the intersection point. This means that the point must be given with two lines in the DXF file, and not a point entity. OriginPoint = dxf_cross(file="drawing.dxf", layer="SCAD.Origin", origin=[0, 0], scale=1);  Getting a dimension value You can read dimensions from a technical drawing. This can be useful to read a rotation angle, an extrusion height, or spacing between parts. In the drawing, create a dimension that does not show the dimension value, but an identifier. To read the value, you specify this identifier from your program: TotalWidth = dxf_dim(file="drawing.dxf", name="TotalWidth", layer="SCAD.Origin", origin=[0, 0], scale=1);  For a nice example of both functions, see Example009 and the image on the homepage of OpenSCAD. ## 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.
$fa Fragment angle in degrees$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, $fs=0.1);  ### Cylinder Creates a cylinder or cone centered about the z axis. When center is true, it is also centered vertically along the z axis. Parameter names are optional if given in the order shown here. If a parameter is named, all following parameters must also be named. NOTE: If r, d, d1 or d2 are used they must be named. cylinder(h = height, r1 = BottomRadius, r2 = TopRadius, center = true/false);  Parameters h : height of the cylinder or cone r : radius of cylinder. r1 = r2 = r. r1 : radius, bottom of cone. r2 : radius, top of cone. d : diameter of cylinder. r1 = r2 = d / 2. [Note: Requires version 2014.03] d1 : diameter, bottom of cone. r1 = d1 / 2. [Note: Requires version 2014.03] d2 : diameter, top of cone. r2 = d2 / 2. [Note: Requires version 2014.03] center false (default), z ranges from 0 to h true, z ranges from -h/2 to +h/2$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: triangles will be removed in future releases. Use faces parameter instead] 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 [Note: Requires version 2014.03] Vector of faces which collectively enclose the solid. Each face is a vector containing the indices (0 based) of 3 or more points from the points vector. Faces may be defined in any order. Define enough faces to fully enclose the solid, with no overlap. Points which describe a single face must all be on the same plane. convexity Integer. The convexity parameter specifies the maximum number of faces a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode. It has no effect on the polyhedron rendering. For display problems, setting it to 10 should work fine for most cases.  default values: polyhedron(); yields: polyhedron(points = undef, faces = undef, convexity = 1);  All faces must have points ordered in the same direction . OpenSCAD prefers clockwise when looking at each face from outside inwards. The back is viewed from the back, the bottom from the bottom, etc.. Example 1 Using polyhedron to generate cube( [ 10, 7, 5 ] ); point numbers for cube unfolded cube faces CubePoints = [ [ 0, 0, 0 ], //0 [ 10, 0, 0 ], //1 [ 10, 7, 0 ], //2 [ 0, 7, 0 ], //3 [ 0, 0, 5 ], //4 [ 10, 0, 5 ], //5 [ 10, 7, 5 ], //6 [ 0, 7, 5 ]]; //7 CubeFaces = [ [0,1,2,3], // bottom [4,5,1,0], // front [7,6,5,4], // top [5,6,2,1], // right [6,7,3,2], // back [7,4,0,3]]; // left polyhedron( CubePoints, CubeFaces );  equivalent descriptions of the bottom face [0,1,2,3], [0,1,2,3,0], [1,2,3,0], [2,3,0,1], [3,0,1,2], [0,1,2],[2,3,0], // 2 triangles with no overlap [1,2,3],[3,0,1], [1,2,3],[0,1,3],  Example 2 A square base pyramid: A simple polyhedron, square base pyramid polyhedron( points=[ [10,10,0],[10,-10,0],[-10,-10,0],[-10,10,0], // the four points at base [0,0,10] ], // the apex point faces=[ [0,1,4],[1,2,4],[2,3,4],[3,0,4], // each triangle side [1,0,3],[2,1,3] ] // two triangles for square base );  Example 3 A triangular prism: A polyhedron triangular prism  module prism(l, w, h){ polyhedron( points=[[0,0,0], [l,0,0], [l,w,0], [0,w,0], [0,w,h], [l,w,h]], faces=[[0,1,2,3],[5,4,3,2],[0,4,5,1],[0,3,4],[5,2,1]] ); // preview unfolded (do not include in your function z = 0.08; separation = 2; border = .2; translate([0,w+separation,0]) cube([l,w,z]); translate([0,w+separation+w+border,0]) cube([l,h,z]); translate([0,w+separation+w+border+h+border,0]) cube([l,sqrt(w*w+h*h),z]); translate([l+border,w+separation+w+border+h+border,0]) polyhedron( points=[[0,0,0],[h,0,0],[0,sqrt(w*w+h*h),0], [0,0,z],[h,0,z],[0,sqrt(w*w+h*h),z]], faces=[[0,1,2], [3,5,4], [0,3,4,1], [1,4,5,2], [2,5,3,0]] ); translate([0-border,w+separation+w+border+h+border,0]) polyhedron( points=[[0,0,0],[0-h,0,0],[0,sqrt(w*w+h*h),0], [0,0,z],[0-h,0,z],[0,sqrt(w*w+h*h),z]], faces=[[1,0,2],[5,3,4],[0,1,4,3],[1,2,5,4],[2,0,3,5]] ); } prism(10, 5, 3);  #### Debugging polyhedra Mistakes in defining polyhedra include not having all faces with the same order, overlap of faces and missing faces or portions of faces. As a general rule, the polyhedron faces should also satisfy (manifold conditions): • exactly two faces should meet at any polyhedron edge. • if two faces have a vertex in common, they should be in the same cycle face-edge around the vertex. The first rule eliminates polyhedron like two cubes with a common edge and not watertight models; the second excludes polyhedron like two cubes with a common vertex. When viewed from the outside, the points describing each face must be in the same order . OpenSCAD prefers CW, and provides a mechanism for detecting CCW. When the thrown together view (F12) is used with F5, CCW faces are shown in pink. Reorder the points for incorrect faces. Rotate the object to view all faces. The pink view can be turned off with F10. OpenSCAD allows, temporarily, commenting out part of the face descriptions so that only the remaining faces are displayed. Use // to comment out the rest of the line. Use /* and */ to start and end a comment block. This can be part of a line or extend over several lines. Viewing only part of the faces can be helpful in determining the right points for an individual face. Note that a solid is not shown, only the faces. If using F12, all faces have one pink side. Commenting some faces helps also to show any internal face. example 1 showing only 2 faces CubeFaces = [ /* [0,1,2,3], // bottom [4,5,1,0], // front */ [7,6,5,4], // top /* [5,6,2,1], // right [6,7,3,2], // back */ [7,4,0,3]]; // left  After defining a polyhedron, its preview may seem correct. The polyhedron alone may even render fine. However to be sure it is a valid manifold and that it will generate a valid STL file, union it with any cube and render it (F6). If the polyhedron disappears, it means that it is not correct. Revise the winding order of all faces and the two rules stated above. #### Mis-ordered faces Example 4 a more complex polyhedron with mis-ordered faces When you select 'Thrown together' from the view menu and compile the design (not compile and render!) you will see a preview with the mis-oriented polygons highlighted. Unfortunately this highlighting is not possible in the OpenCSG preview mode because it would interfere with the way the OpenCSG preview mode is implemented.) Below you can see the code and the picture of such a problematic polyhedron, the bad polygons (faces or compositions of faces) are in pink. // Bad polyhedron polyhedron (points = [ [0, -10, 60], [0, 10, 60], [0, 10, 0], [0, -10, 0], [60, -10, 60], [60, 10, 60], [10, -10, 50], [10, 10, 50], [10, 10, 30], [10, -10, 30], [30, -10, 50], [30, 10, 50] ], faces = [ [0,2,3], [0,1,2], [0,4,5], [0,5,1], [5,4,2], [2,4,3], [6,8,9], [6,7,8], [6,10,11], [6,11,7], [10,8,11], [10,9,8], [0,3,9], [9,0,6], [10,6, 0], [0,4,10], [3,9,10], [3,10,4], [1,7,11], [1,11,5], [1,7,8], [1,8,2], [2,8,11], [2,11,5] ] );  Polyhedron with badly oriented polygons A correct polyhedron would be the following: polyhedron (points = [ [0, -10, 60], [0, 10, 60], [0, 10, 0], [0, -10, 0], [60, -10, 60], [60, 10, 60], [10, -10, 50], [10, 10, 50], [10, 10, 30], [10, -10, 30], [30, -10, 50], [30, 10, 50] ], faces = [ [0,3,2], [0,2,1], [4,0,5], [5,0,1], [5,2,4], [4,2,3], [6,8,9], [6,7,8], [6,10,11],[6,11,7], [10,8,11], [10,9,8], [3,0,9], [9,0,6], [10,6, 0],[0,4,10], [3,9,10], [3,10,4], [1,7,11], [1,11,5], [1,8,7], [2,8,1], [8,2,11], [5,11,2] ] );  Beginner's tip: If you don't really understand "orientation", try to identify the mis-oriented pink faces and then invert the sequence of the references to the points vectors until you get it right. E.g. in the above example, the third triangle ([0,4,5]) was wrong and we fixed it as [4,0,5]. Remember that a face list is a circular list. In addition, you may select "Show Edges" from the "View Menu", print a screen capture and number both the points and the faces. In our example, the points are annotated in black and the faces in blue. Turn the object around and make a second copy from the back if needed. This way you can keep track. Clockwise Technique: Orientation is determined by clockwise circular indexing. This means that if you're looking at the triangle (in this case [4,0,5]) from the outside you'll see that the path is clockwise around the center of the face. The winding order [4,0,5] is clockwise and therefore good. The winding order [0,4,5] is counter-clockwise and therefore bad. Likewise, any other clockwise order of [4,0,5] works: [5,4,0] & [0,5,4] are good too. If you use the clockwise technique, you'll always have your faces outside (outside of OpenSCAD, other programs do use counter-clockwise as the outside though). Think of it as a Left Hand Rule: If you place your left hand on the face with your fingers curled in the direction of the order of the points, your thumb should point outwards. If your thumb points inward, you need to reverse the winding order. Polyhedron with badly oriented polygons Succinct description of a 'Polyhedron' * Points define all of the points/vertices in the shape. * Faces is a list of flat polygons that connect up the points/vertices.  Each point, in the point list, is defined with a 3-tuple x,y,z position specification. Points in the point list are automatically enumerated starting from zero for use in the faces list (0,1,2,3,... etc). Each face, in the faces list, is defined by selecting 3 or more of the points (using the point order number) out of the point list. e.g. faces=[ [0,1,2] ] defines a triangle from the first point (points are zero referenced) to the second point and then to the third point. When looking at any face from the outside, the face must list all points in a clockwise order. #### Point repetitions in a polyhedron point list The point list of the polyhedron definition may have repetitions. When two or more points have the same coordinates they are considered the same polyhedron vertex. So, the following polyhedron: points = [[ 0, 0, 0], [10, 0, 0], [ 0,10, 0], [ 0, 0, 0], [10, 0, 0], [ 0,10, 0], [ 0,10, 0], [10, 0, 0], [ 0, 0,10], [ 0, 0, 0], [ 0, 0,10], [10, 0, 0], [ 0, 0, 0], [ 0,10, 0], [ 0, 0,10]]; polyhedron(points, [[0,1,2], [3,4,5], [6,7,8], [9,10,11], [12,13,14]]);  define the same tetrahedron as: points = [[0,0,0], [0,10,0], [10,0,0], [0,0,10]]; polyhedron(points, [[0,2,1], [0,1,3], [1,2,3], [0,3,2]]);  ## 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 examples:  for (a =[3:5])echo(a); // 3 4 5 for (a =[3:0]){echo(a);} // 0 1 2 3 start > end is invalid, deprecated by 2015.3 for (a =[3:0.5:5])echo(a); // 3 3.5 4 4.5 5 for (a =[0:2:5])echo(a); // 0 2 4 a never equals end for (a =[3:-2:-1])echo(a); // 3 1 -1 negative increment requires 2015.3 be sure end < start  As a vector The Action is evaluated for each element of the vector  for (a =[3,4,1,5])echo(a); // 3 4 1 5 for (a =[0.3,PI,1,99]){echo(a);} // 0.3 3.14159 1 99 x1=2; x2=8; x3=5.5; for (a =[x1,x2,x3]){echo(a);} // 2 8 5.5 for (a =[[1,2],6,"s",[[3,4],[5,6]]])echo(a); // [1,2] 6 "s" [[3,4],[5,6]]  for() is an Operator. Operators require braces {} if more than one Action is within it scope. Actions end in semicolons, Operators do not. for() is not an exception to the rule about variables having only one value within a scope. Each evaluation is given its own scope, allowing any variables to have unique values. No, you still can't do a=a+1; Remember this is not an iterative language, the for() does not loop in the programmatic sense, it builds a tree of objects one branch for each item in the range/vector, inside each branch the 'variable' is a specific and separate instantiation or scope. Hence: for (i=[0:3]) translate([i*10,0,0]) cube(i+1);  Produces: [See Design/Display-CSG-Tree menu]  group() { group() { multmatrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) { cube(size = [1, 1, 1], center = false); } multmatrix([[1, 0, 0, 10], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) { cube(size = [2, 2, 2], center = false); } multmatrix([[1, 0, 0, 20], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) { cube(size = [3, 3, 3], center = false); } multmatrix([[1, 0, 0, 30], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]) { cube(size = [4, 4, 4], center = false); } } }  All instances of the for() exist at the same time, they do not iterate sequentially. Nested for() While it is reasonable to nest multiple for() statements such as: for(z=[-180:45:+180]) for(x=[10:5:50]) rotate([0,0,z]) translate([x,0,0]) cube(1);  instead, all ranges/vectors can be include in the same for() operator. for ( variable1 = <range or vector> , variable2 = <range or vector> ) <do something using both variables>  for() loops nested 3 deep  example for() nested 3 deep color_vec = ["black","red","blue","green","pink","purple"]; for (x = [-20:10:20] ) for (y = [0:4] )color(color_vec[y]) for (z = [0,4,10] ) {translate([x,y*5-10,z])cube();} shorthand nesting for same result color_vec = ["black","red","blue","green","pink","purple"]; for (x = [-20:10:20], y = [0:4], z = [0,4,10] ) translate([x,y*5-10,z]){color(color_vec[y])cube();}  Examples using vector of vectors example 1 for() loop vector of vectors (rotation) example 1 - iteration over a vector of vectors (rotation) for(i = [ [ 0, 0, 0], [ 10, 20, 300], [200, 40, 57], [ 20, 88, 57] ]) { rotate(i) cube([100, 20, 20], center = true); }  example 2 for() loop vector of vectors (translation) example 2 - iteration over a vector of vectors (translation) for(i = [ [ 0, 0, 0], [10, 12, 10], [20, 24, 20], [30, 36, 30], [20, 48, 40], [10, 60, 50] ]) { translate(i) cube([50, 15, 10], center = true); }  example 3 for() loop vector of vectors example 3 - iteration over a vector of vectors for(i = [ [[ 0, 0, 0], 20], [[10, 12, 10], 50], [[20, 24, 20], 70], [[30, 36, 30], 10], [[20, 48, 40], 30], [[10, 60, 50], 40] ]) { translate([i[0][0], 2*i[0][1], 0]) cube([10, 15, i[1]]); }  ### Intersection For Loop Iterate over the values in a range or vector and create the intersection of objects created by each pass. Besides creating separate instances for each pass, the standard for() also groups all these instances creating an implicit union. intersection_for() is a work around because the implicit union prevents getting the expected results using a combination of the standard for() and intersection() statements. intersection_for() uses the same parameters, and works the same as a For Loop, other than eliminating the implicit union.  example 1 - loop over a range: intersection_for(n = [1 : 6]) { rotate([0, 0, n * 60]) { translate([5,0,0]) sphere(r=12); } }  intersection_for() either intersection() for() or for() intersection()  example 2 - rotation :  intersection_for(i = [ [ 0, 0, 0], [ 10, 20, 300], [200, 40, 57], [ 20, 88, 57] ]) { rotate(i) cube([100, 20, 20], center = true); }  intersection_for() intersection() for() In ### If Statement Performs a test to determine if the actions in a sub scope should be performed or not. if (test) scope1 if (test){scope1} if (test) scope1 else scope2 if (test){scope1} else {scope2}  Parameters test: Usually a boolean expression, but can be any value or variable. See here for true or false state of values. See here for boolean and logical operators Do not confuse the assignment operator '=' with the equal operator '==' scope1: one or more actions to take when test is true. scope2: one or more actions to take when test is false. if (b==a) cube(4); if (b<a) {cube(4); cylinder(6);} if (b&&a) {cube(4); cylinder(6);} if (b!=a) cube(4); else cylinder(3); if (b) {cube(4); cylinder(6);} else {cylinder(10,5,5);} if (!true){cube(4); cylinder(6);} else cylinder(10,5,5); if (x>y) cube(1, center=false); else {cube(size = 2, center = true);} if (a==4) {} else echo("a is not 4"); if ((b<5)&&(a>8)) {cube(4); else cylinder(3);} if (b<5&&a>8) cube(4); else cylinder(3);  Since 2015.03 variables can now be assigned in any scope. Note that assignments are only valid within the scope in which they are defined - you are still not allowed to leak values to an outer scope. See Scope of variables for more details. Nested if The scopes of both the if() portion and the else portion, can in turn contain if() statements. This nesting can be to many depths.  if (test1) { scope1 if (test2) {scope2.1} else {scope2.2} } else { scope2 if (test3) {scope3.1} else {scope3.2} }  When scope1 and scope2 contain only the if() statement, the outer sets of braces can be removed.  if (test1) if (test2) {scope2.1} else {scope2.2} else if (test3) {scope3.1} else {scope3.2}  One evolution is this: #### else if  if(test1) {scope1} else if(test2) {scope2} else if(test3) {scope3} else if(test4) {scope4} else {scope5}  Note that else and if are two separate words. When working down the chain of tests, the first true will use its scope. All further tests will be skipped. example if((k<8)&&(m>1)) cube(10); else if(y==6) {sphere(6);cube(10);} else if(y==7) color("blue")sphere(5); else if(k+m!=8) {cylinder(15,5,0);sphere(8);} else color("green"){cylinder(12,5,0);sphere(8);}  ### Conditional ? : A function which uses a test to determine which of 2 values to return.  a = test ? TrueValue : FalseValue ; echo( test ? TrueValue : FalseValue );  Parameters test: Usually a boolean expression, but can be any value or variable. See here for true or false state of values. See here for boolean and logical operators Do not confuse assignment '=' with equal '==' TrueValue: the value to return when test is true. FalseValue: the value to return when test is false. A value in OpenSCAD is either a Number (like 42), a Boolean (like true), a String (like "foo"), a Vector (like [1,2,3]), or the Undefined value (undef). Values can be stored in variables, passed as function arguments, and returned as function results. This works like the ?: operator from the family of C-like programming languages. Examples  a=1; b=2; c= a==b ? 4 : 5 ; // 5 a=1; b=2; c= a==b ? "a==b" : "a!=b" ; // "a!=b" TrueValue = true; FalseValue = false; a=5; test = a==1; echo( test ? TrueValue : FalseValue ); // false L = 75; R = 2; test = (L/R)>25; TrueValue = [test,L,R,L/R,cos(30)]; FalseValue = [test,L,R,sin(15)]; a1 = test ? TrueValue : FalseValue ; // [true, 75, 2, 37.5, 0.866025]  #### Recursive function calls Recursive function calls are supported. Using the Conditional "... ? ... : ... " it's possible to ensure the recursion is terminated. Note: There is a built-in recursion limit to prevent an application crash. If the limit is hit, the function returns undef. example  // recursion - find the sum of the values in a vector (array) by calling itself // from the start (or s'th element) to the i'th element - remember elements are zero based function sumv(v,i,s=0) = (i==s ? v[i] : v[i] + sumv(v,i-1,s)); vec=[ 10, 20, 30, 40 ]; echo("sum vec=", sumv(vec,2,1)); // calculates 20+30=50  Some forms of tail-recursion elimination are supported. ### Assign Statement [Deprecated: assign() will be removed in future releases. Variables can now be assigned anywhere. If you prefer this way of setting values, the new Let Statement can be used instead.] Set variables to a new value for a sub-tree. 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 2019.05] 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 or equal == equal != not equal >= greater or 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. In an inequality comparison between a Boolean and a number true is treated as 1 and false is treated as 0. Other inequality tests involving Booleans return false. If both operands are vectors, an equality test returns true when the vectors are identical and false otherwise. Inequality tests involving one or two vectors always return false, so for example [1] < [2] is false. Dissimilar types always test as unequal with '==' and '!='. Inequality comparisons between dissimilar types, except for Boolean and numbers as noted above, always result in false. Note that [1] and 1 are different types so [1] == 1 is false. undef doesn't equal anything but undef. Inequality comparisons involving undef result in false. nan doesn't equal anything (not even itself) and inequality tests all produce false. 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. Returns the next highest integer value by rounding up value if necessary. See: Ceil Function echo(ceil(4.4),ceil(-4.4)); // produces ECHO: 5, -4  ### concat [Note: Requires version 2015.03] Return a vector containing the arguments. Where an argument is a vector the elements of the vector are individually added to the result vector. Strings are distinct from vectors in this case. Usage examples: echo(concat("a","b","c","d","e","f")); // produces ECHO: ["a", "b", "c", "d", "e", "f"] echo(concat(["a","b","c"],["d","e","f"])); // produces ECHO: ["a", "b", "c", "d", "e", "f"] echo(concat(1,2,3,4,5,6)); // produces ECHO: [1, 2, 3, 4, 5, 6]  Vector of vectors echo(concat([ [1],[2] ], [ [3] ])); // produces ECHO: [[1], [2], [3]]  Contrast with strings echo(concat([1,2,3],[4,5,6])); // produces ECHO: [1, 2, 3, 4, 5, 6] echo(concat("abc","def")); // produces ECHO: ["abc", "def"] echo(str("abc","def")); // produces ECHO: "abcdef"  ### cross Calculates the cross product of two vectors in 3D space. The result is a vector that is perpendicular to both of the input vectors. Using invalid input parameters (e.g. vectors with a length different from 3 or other types) will produce an undefined result. Usage examples: echo(cross([2, 3, 4], [5, 6, 7])); // produces ECHO: [-3, 6, -3] echo(cross([2, 1, -3], [0, 4, 5])); // produces ECHO: [17, -10, 8] echo(cross([2, 3, 4], "5")); // produces ECHO: undef  ### exp Mathematical exp function. Returns the base-e exponential function of x, which is the number e raised to the power x. See: Exponent echo(exp(1),exp(ln(3)*4)); // produces ECHO: 2.71828, 81  ### floor Mathematical floor function. floor(x) = is the largest integer not greater than x See: Floor Function echo(floor(4.4),floor(-4.4)); // produces ECHO: 4, -5  ### ln Mathematical natural logarithm. See: Natural logarithm ### len Mathematical length function. Returns the length of an array, a vector or a string parameter. Usage examples: str1="abcdef"; len_str1=len(str1); echo(str1,len_str1); a=6; len_a=len(a); echo(a,len_a); array1=[1,2,3,4,5,6,7,8]; len_array1=len(array1); echo(array1,len_array1); array2=[[0,0],[0,1],[1,0],[1,1]]; len_array2=len(array2); echo(array2,len_array2); len_array2_2=len(array2[2]); echo(array2[2],len_array2_2);  Results: ECHO: "abcdef", 6 ECHO: 6, undef ECHO: [1, 2, 3, 4, 5, 6, 7, 8], 8 ECHO: [[0, 0], [0, 1], [1, 0], [1, 1]], 4 ECHO: [1, 0], 2  This function allows (e.g.) the parsing of an array, a vector or a string. Usage examples: str2="4711"; for (i=[0:len(str2)-1]) echo(str("digit ",i+1," : ",str2[i]));  Results: ECHO: "digit 1 : 4" ECHO: "digit 2 : 7" ECHO: "digit 3 : 1" ECHO: "digit 4 : 1"  Note that the len() function is not defined when a simple variable is passed as the parameter. This is useful when handling parameters to a module, similar to how shapes can be defined as a single number, or as an [x,y,z] vector; i.e. cube(5) or cube([5,5,5]) For example module doIt(size) { if (len(size) == undef) { // size is a number, use it for x,y & z. (or could be undef) do([size,size,size]); } else { // size is a vector, (could be a string but that would be stupid) do(size); } } doIt(5); // equivalent to [5,5,5] doIt([5,5,5]); // similar to cube(5) v's cube([5,5,5])  ### let [Note: Requires version 2015.03] Sequential assignment of variables inside an expression. The following expression is evaluated in context of the let assignments and can use the variables. This is mainly useful to make complicated expressions more readable by assigning interim results to variables. Parameters let (var1 = value1, var2 = f(var1), var3 = g(var1, var2)) expression  Usage Example: echo(let(a = 135, s = sin(a), c = cos(a)) [ s, c ]); // ECHO: [0.707107, -0.707107]  ### log Mathematical logarithm to the base 10. Example: log(1000) = 3. See: Logarithm ### lookup Look up value in table, and linearly interpolate if there's no exact match. The first argument is the value to look up. The second is the lookup table -- a vector of key-value pairs. Parameters key A lookup key <key,value> array keys and values Notes There is a bug where out-of-range keys will return the first value in the list. Newer versions of Openscad should use the top or bottom end of the table as appropriate instead.  Usage example: Will create a sort of 3D chart made out of cylinders of different height.  function get_cylinder_h(p) = lookup(p, [ [ -200, 5 ], [ -50, 20 ], [ -20, 18 ], [ +80, 25 ], [ +150, 2 ] ]); for (i = [-100:5:+100]) { // echo(i, get_cylinder_h(i)); translate([ i, 0, -30 ]) cylinder(r1 = 6, r2 = 2, h = get_cylinder_h(i)*3); }  OpenSCAD Lookup Function ### max Returns the maximum of the parameters. If a single vector is given as parameter, returns the maximum element of that vector. Parameters max(n,n{,n}...) max(vector)  <n> Two or more decimals <vector> Single vector of decimals [Note: Requires version 2014.06]. 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 [Note: Requires version 2014.06]. Usage Example: min(3.0,5.0) min(8.0,3.0,4.0,5.0) min([8,3,4,5])  Results: 3 3 3  Looking for mod - it's not a function, see modulo operator (%) ### norm Returns the euclidean norm of a vector. Note this returns the actual numeric length while len returns the number of elements in the vector or array. Usage examples: a=[1,2,3,4]; b="abcd"; c=[]; d=""; e=[[1,2,3,4],[1,2,3],[1,2],[1]]; echo(norm(a)); //5.47723 echo(norm(b)); //undef echo(norm(c)); //0 echo(norm(d)); //undef echo(norm(e[0])); //5.47723 echo(norm(e[1])); //3.74166 echo(norm(e[2])); //2.23607 echo(norm(e[3])); //1  Results: ECHO: 5.47723 ECHO: undef ECHO: 0 ECHO: undef ECHO: 5.47723 ECHO: 3.74166 ECHO: 2.23607 ECHO: 1  ### pow Mathematical power function. Parameters <base> Decimal. Base. <exponent> Decimal. Exponent. Usage examples: for (i = [0:5]) { translate([i*25,0,0]) { cylinder(h = pow(2,i)*5, r=10); echo (i, pow(2,i)); } }  echo(pow(10,2)); // means 10^2 or 10*10 // result: ECHO: 100 echo(pow(10,3)); // means 10^3 or 10*10*10 // result: ECHO: 1000 echo(pow(125,1/3)); // means 125^(0.333...) which equals calculating the cube root of 125 // result: ECHO: 5  ### rands Random number generator. Generates a constant vector of pseudo random numbers, much like an array. The numbers are doubles not integers. When generating only one number, you still call it with variable[0] Parameters min_value Minimum value of random number range max_value Maximum value of random number range value_count Number of random numbers to return as a vector seed_value (optional) Seed value for random number generator for repeatable results. On versions before late 2015, seed_value gets rounded to the nearest integer Usage Examples: // get a single number single_rand = rands(0,10,1)[0]; echo(single_rand);  // get a vector of 4 numbers seed=42; random_vect=rands(5,15,4,seed); echo( "Random Vector: ",random_vect); sphere(r=5); for(i=[0:3]) { rotate(360*i/4) { translate([10+random_vect[i],0,0]) sphere(r=random_vect[i]/2); } } // ECHO: "Random Vector: ", [8.7454, 12.9654, 14.5071, 6.83435]  ### round The "round" operator returns the greatest or least integer part, respectively, if the numeric input is positive or negative. Some examples: round(x.5) = x+1. round(x.49) = x. round(-(x.5)) = -(x+1). round(-(x.49)) = -x. round(5.4); //-> 5 round(5.5); //-> 6 round(5.6); //-> 6  ### sign Mathematical signum function. Returns a unit value that extracts the sign of a value see: Signum function Parameters <x> Decimal. Value to find the sign of. Usage examples: sign(-5.0); sign(0); sign(8.0);  Results: -1.0 0.0 1.0  ### sqrt Mathematical square root function. Usage Examples: translate([sqrt(100),0,0])sphere(100);  ## Infinities and NaNs How does OpenSCAD deal with inputs like (1/0)? Basically, the behavior is inherited from the language OpenSCAD was written in, the C++ language, and its floating point number types and the associated C math library. This system allows representation of both positive and negative infinity by the special values "Inf" or "-Inf". It also allow representation of creatures like sqrt(-1) or 0/0 as "NaN", an abbreviation for "Not A Number". Some very nice explanations can be found on the web, for example the Open Group's site on math.h or Wikipedia's page on the IEEE 754 number format. However OpenSCAD is it's own language so it may not exactly match everything that happens in C. For example, OpenSCAD uses degrees instead of radians for trigonometric functions. Another example is that sin() does not throw a "domain error" when the input is 1/0, although it does return NaN. Here are some examples of infinite input to OpenSCAD math functions and the resulting output, taken from OpenSCAD's regression test system in late 2015.  0/0: nan sin(1/0): nan asin(1/0): nan ln(1/0): inf round(1/0): inf -0/0: nan cos(1/0): nan acos(1/0): nan ln(-1/0): nan round(-1/0): -inf 0/-0: nan tan(1/0): nan atan(1/0): 90 log(1/0): inf sign(1/0): 1 1/0: inf ceil(-1/0): -inf atan(-1/0): -90 log(-1/0): nan sign(-1/0): -1 1/-0: -inf ceil(1/0): inf atan2(1/0, -1/0): 135 max(-1/0, 1/0): inf sqrt(1/0): inf -1/0: -inf floor(-1/0): -inf exp(1/0): inf min(-1/0, 1/0): -inf sqrt(-1/0): nan -1/-0: inf floor(1/0): inf exp(-1/0): 0 pow(2, 1/0): inf pow(2, -1/0): 0 ## 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. ### ord [Note: Requires version 2019.05] Convert a character to a number representing the Unicode code point. If the parameter is not a string, the ord() will return undef. Parameters ord(String) Convert the first character of the given string to a Unicode code point. Examples echo(ord("a")); // ECHO: 97 echo(ord("BCD")); // ECHO: 66 echo([for (c = "Hello! 🙂") ord(c)]); // ECHO: [72, 101, 108, 108, 111, 33, 32, 128578]  ### Also See search() search() for text searching. ## Transformations ### Basic concept Transformation affect the child nodes and as the name implies transforms them in various ways such as moving/rotating or scaling the child. Cascading transformations are used to apply a variety of transforms to a final child. Cascading is achieved by nesting statements i.e. rotate([45,45,45]) translate([10,20,30]) cube(10);  Transformations can be applied to a group of child nodes by using '{' and '}' to enclose the subtree e.g. translate([0,0,-5]) { cube(10); cylinder(r=5,h=10); }  Transformations are written before the object they affect. Imagine commands like translate, mirror and scale as verbs. Commands like color are like adjectives that describe the object. Notice that there is no semicolon following transformation command. ### Advanced concept As OpenSCAD uses different libraries to implement capabilities this can introduce some inconsistencies to the F5 preview behaviour of transformations. Traditional transforms (translate, rotate, scale, mirror & multimatrix) are performed using OpenGL in preview, while other more advanced transforms, such as resize, perform a CGAL operation, behaving like a CSG operation affecting the underlying object, not just transforming it. In particular this can affect the display of modifier characters, specifically "#" and "%", where the highlight may not display intuitively, such as highlighting the pre-resized object, but highlighting the post-scaled object. ### scale Scales its child elements using the specified vector. The argument name is optional. Usage Example: scale(v = [x, y, z]) { ... }  cube(10); translate([15,0,0]) scale([0.5,1,2]) cube(10);  Note: Do not use negative scale values. Negative scale values appear to work for previews, but they lead to unpredictable errors when rendering through CGAL. Use the mirror() function instead. ### resize Modifies the size of the child object to match the given x,y, and z. resize() is a CGAL operation, and like others such as render() operates with full geometry, so even in preview will take time to process. Usage Example: // resize the sphere to extend 30 in x, 60 in y, and 10 in the z directions. resize(newsize=[30,60,10]) sphere(r=10);  If x,y, or z is 0 then that dimension is left as-is. // resize the 1x1x1 cube to 2x2x1 resize([2,2,0]) cube();  If the 'auto' parameter is set to true, it will auto-scale any 0-dimensions to match. For example. // resize the 1x2x0.5 cube to 7x14x3.5 resize([7,0,0], auto=true) cube([1,2,0.5]);  The 'auto' parameter can also be used if you only wish to auto-scale a single dimension, and leave the other as-is. // resize to 10x8x1. Note that the z dimension is left alone. resize([10,0,0], auto=[true,true,false]) cube([5,4,1]);  ### rotate Rotates its child 'a' degrees about the axis of the coordinate system or around an arbitrary axis. The argument names are optional if the arguments are given in the same order as specified. //Usage: rotate(a = deg_a, v = [x, y, z]) { ... } // or rotate(deg_a, [x, y, z]) { ... } rotate(a = [deg_x, deg_y, deg_z]) { ... } rotate([deg_x, deg_y, deg_z]) { ... }  The 'a' argument (deg_a) can be an array, as expressed in the later usage above; when deg_a is an array, the 'v' argument is ignored. Where 'a' specifies multiple axes then the rotation is applied in the following order: x, y, z. That means the code: rotate(a=[ax,ay,az]) {...}  is equivalent to: rotate(a=[0,0,az]) rotate(a=[0,ay,0]) rotate(a=[ax,0,0]) {...}  The optional argument 'v' is a vector and allows you to set an arbitrary axis about which the object will be rotated. For example, to flip an object upside-down, you can rotate your object 180 degrees around the 'y' axis. rotate(a=[0,180,0]) { ... }  This is frequently simplified to rotate([0,180,0]) { ... }  When specifying a single axis the 'v' argument allows you to specify which axis is the basis for rotation. For example, the equivalent to the above, to rotate just around y rotate(a=180, v=[0,1,0]) { ... }  When specifying a single axis, 'v' is a vector defining an arbitrary axis for rotation; this is different from the multiple axis above. For example, rotate your object 45 degrees around the axis defined by the vector [1,1,0], rotate(a=45, v=[1,1,0]) { ... }  Rotate with a single scalar argument rotates around the Z axis. This is useful in 2D contexts where that is the only axis for rotation. For example: rotate(45) square(10);  ##### Rotation rule help Right-hand grip rule For the case of: rotate([a, b, c]) { ... };  "a" is a rotation about the X axis, from the +Y axis, toward the +Z axis. "b" is a rotation about the Y axis, from the +Z axis, toward the +X axis. "c" is a rotation about the Z axis, from the +X axis, toward the +Y axis. These are all cases of the Right Hand Rule. Point your right thumb along the positive axis, your fingers show the direction of rotation. Thus if "a" is fixed to zero, and "b" and "c" are manipulated appropriately, this is the spherical coordinate system. So, to construct a cylinder from the origin to some other point (x,y,z): x= 10; y = 10; z = 10; // point coordinates of end of cylinder length = norm([x,y,z]); // radial distance b = acos(z/length); // inclination angle c = atan2(y,x); // azimuthal angle rotate([0, b, c]) cylinder(h=length, r=0.5); %cube([x,y,z]); // corner of cube should coincide with end of cylinder  ### translate Translates (moves) its child elements along the specified vector. The argument name is optional. Example: translate(v = [x, y, z]) { ... }  cube(2,center = true); translate([5,0,0]) sphere(1,center = true);  ### mirror Mirrors the child element on a plane through the origin. The argument to mirror() is the normal vector of a plane intersecting the origin through which to mirror the object. #### Function signature: mirror(v= [x, y, z] ) { ... }  #### Examples The original is on the right side. Note that mirror doesn't make a copy. Like rotate and scale, it changes the object. rotate([0,0,10]) cube([3,2,1]); mirror([1,0,0]) translate([1,0,0]) rotate([0,0,10]) cube([3,2,1]);  ### multmatrix Multiplies the geometry of all child elements with the given 4x4 transformation matrix. Usage: multmatrix(m = [...]) { ... } This is a breakdown of what you can do with the independent elements in the matrix (for the first three rows):  [Scale X] [Scale X sheared along Y] [Scale X sheared along Z] [Translate X] [Scale Y sheared along X] [Scale Y] [Scale Y sheared along Z] [Translate Y] [Scale Z sheared along X] [Scale Z sheared along Y] [Scale Z] [Translate Z] the fourth row is used in 3D environments to define a view of the object. it is not used in OpenSCAD and should be [0,0,0,1] Example which rotates by 45 degrees in XY plane and translates by [10,20,30], ie the same as translate([10,20,30]) rotate([0,0,45]) would do. angle=45; multmatrix(m = [ [cos(angle), -sin(angle), 0, 10], [sin(angle), cos(angle), 0, 20], [ 0, 0, 1, 30], [ 0, 0, 0, 1] ]) union() { cylinder(r=10.0,h=10,center=false); cube(size=[10,10,10],center=false); }  Example that skews a model, something that is not possible with the other transformations. Also shows you can have the matrix in a variable. M = [ [ 1 , 0 , 0 , 0 ], [ 0 , 1 , 0.7, 0 ], // The "0.7" is the skew value; pushed along the y axis [ 0 , 0 , 1 , 0 ], [ 0 , 0 , 0 , 1 ] ] ; multmatrix(M) { union() { cylinder(r=10.0,h=10,center=false); cube(size=[10,10,10],center=false); } }  #### More? Learn more about it here: ### color Displays the child elements using the specified RGB color + alpha value. This is only used for the F5 preview as CGAL and STL (F6) do not currently support color. The alpha value will default to 1.0 (opaque) if not specified. #### Function signature: color( c = [r, g, b, a] ) { ... } color( c = [r, g, b], alpha = 1.0 ) { ... } color( "#hexvalue" ) { ... } color( "colorname", 1.0 ) { ... }  Note that the r, g, b, a values are limited to floating point values in the range [0,1] rather than the more traditional integers { 0 ... 255 }. However, nothing prevents you to using R, G, B values from {0 ... 255} with appropriate scaling: color([ R/255, G/255, B/255 ]) { ... }  [Note: Requires 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); [Note: Requires version 2019.05] Hex values can be given in 4 formats, #rgb, #rgba, #rrggbb and #rrggbbaa. If the alpha value is given in both the hex value and as sparate alpha parameter, the alpha parameter will take precedence. The available color names are taken from the World Wide Web consortium's SVG color list. A chart of the color names is as follows, (note that both spellings of grey/gray including slategrey/slategray etc are valid):  Purples Lavender Thistle Plum Violet Orchid Fuchsia Magenta MediumOrchid MediumPurple BlueViolet DarkViolet DarkOrchid DarkMagenta Purple Indigo DarkSlateBlue SlateBlue MediumSlateBlue Pinks Pink LightPink HotPink DeepPink MediumVioletRed PaleVioletRed  Blues Aqua Cyan LightCyan PaleTurquoise Aquamarine Turquoise MediumTurquoise DarkTurquoise CadetBlue SteelBlue LightSteelBlue PowderBlue LightBlue SkyBlue LightSkyBlue DeepSkyBlue DodgerBlue CornflowerBlue RoyalBlue Blue MediumBlue DarkBlue Navy MidnightBlue Reds IndianRed LightCoral Salmon DarkSalmon LightSalmon Red Crimson FireBrick DarkRed  Greens GreenYellow Chartreuse LawnGreen Lime LimeGreen PaleGreen LightGreen MediumSpringGreen SpringGreen MediumSeaGreen SeaGreen ForestGreen Green DarkGreen YellowGreen OliveDrab Olive DarkOliveGreen MediumAquamarine DarkSeaGreen LightSeaGreen DarkCyan Teal Oranges LightSalmon Coral Tomato OrangeRed DarkOrange Orange  Yellows Gold Yellow LightYellow LemonChiffon LightGoldenrodYellow PapayaWhip Moccasin PeachPuff PaleGoldenrod Khaki DarkKhaki Browns Cornsilk BlanchedAlmond Bisque NavajoWhite Wheat BurlyWood Tan RosyBrown SandyBrown Goldenrod DarkGoldenrod Peru Chocolate SaddleBrown Sienna Brown Maroon  Whites White Snow Honeydew MintCream Azure AliceBlue GhostWhite WhiteSmoke Seashell Beige OldLace FloralWhite Ivory AntiqueWhite Linen LavenderBlush MistyRose Grays Gainsboro LightGrey Silver DarkGray Gray DimGray LightSlateGray SlateGray DarkSlateGray Black #### Example A 3-D multicolor sine wave Here's a code fragment that draws a wavy multicolor object  for(i=[0:36]) { for(j=[0:36]) { color( [0.5+sin(10*i)/2, 0.5+sin(10*j)/2, 0.5+sin(10*(i+j))/2] ) translate( [i, j, 0] ) cube( size = [1, 1, 11+10*cos(10*i)*sin(10*j)] ); } }  ↗ Being that -1<=sin(x)<=1 then 0<=(1/2 + sin(x)/2)<=1 , allowing for the RGB components assigned to color to remain within the [0,1] interval. #### Example 2 In cases where you want to optionally set a color based on a parameter you can use the following trick:  module myModule(withColors=false) { c=withColors?"red":undef; color(c) circle(r=10); }  Setting the colorname to undef will keep the default colors. ### offset [Note: Requires version 2015.03] Offset allows moving 2D outlines outward or inward by a given amount. • This is useful for making thin walls, by differencing a positive-offset exterior and a negative-offset interior. • Fillet: offset(r=-3) offset(delta=+3) rounds all inside (concave) corners, and leaves flat walls unchanged. However, holes less than 2*r in diameter will vanish. • Round: offset(r=+3) offset(delta=-3) rounds all outside (convex) corners, and leaves flat walls unchanged. However, walls less than 2*r thick will vanish. Parameters r | delta Double. Amount to offset the polygon. When negative, the polygon is offset inwards. The parameter r specifies the radius that is used to generate rounded corners, using delta gives straight edges. chamfer Boolean. (default false) When using the delta parameter, this flag defines if edges should be chamfered (cut off with a straight line) or not (extended to their intersection). Positive r/delta value Negative r/delta value Result for different parameters. The black polygon is the input for the offset() operation. Examples Example 1: Result. // Example 1 linear_extrude(height = 60, twist = 90, slices = 60) { difference() { offset(r = 10) { square(20, center = true); } offset(r = 8) { square(20, center = true); } } }  // Example 2 module fillet(r) { offset(r = -r) { offset(delta = r) { children(); } } }  ### minkowski A box and a cylinder Minkowski sum of the box and cylinder Displays the minkowski sum of child nodes. Usage example: Say you have a flat box, and you want a rounded edge. There are many ways to do this, but minkowski is very elegant. Take your box, and a cylinder: $fn=50;
cube([10,10,1]);
cylinder(r=2,h=1);


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

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

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


### intersection

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

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


### render

Warning: Using render, always calculates the CSG model for this tree (even in OpenCSG preview mode). This can make previewing very slow and OpenSCAD to appear to hang/freeze.

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

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

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

## Modifier Characters

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

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

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

### Background Modifier

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

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

Usage

 % { ... }


Example

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


Example Output

Output without the modifier.

### Root Modifier

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

Usage

 ! { ... }


Example

difference() {
cube(10, center = true);
translate([0, 0, 5]) {
!rotate([90, 0, 0]) {
#cylinder(r = 2, h = 20, center = true, $fn = 40); } } }  Example Output Output without the modifier. Output with modifier added. As shown in the example output with the root modifier active, the rotate() is executed as it's part of the subtree marked with the root modifier, but the translate() has no effect. ### Disable Modifier Simply ignore this entire subtree. Usage  * { ... }  Example difference() { cube(10, center = true); translate([0, 0, 5]) { rotate([0, 90, 0]) { cylinder(r = 2, h = 20, center = true,$fn = 40);
}
*rotate([90, 0, 0]) {
#cylinder(r = 2, h = 20, center = true, $fn = 40); } } }  Example Output Output without the modifier. Output with modifier added. The disable modifier allows to comment out one or multiple subtrees. Compared to using the usual line or multi-line comments, it's aware of the hierarchical structure which makes it easier to disable even larger trees without the need to search for the end of the subtree. ### Echo Statements see also OpenSCAD User Manual/Other Language Features#Echo Statements This function prints the contents to the compilation window (aka Console). Useful for debugging code. Also see the String function str(). Numeric values are rounded to 5 significant digits. The OpenSCAD console supports a subset of HTML markup language. See here for details. It can be handy to use 'variable=variable' as the expression to easily label the variables, see the example below. Usage examples: my_h=50; my_r=100; echo("This is a cylinder with h=", my_h, " and r=", my_r); echo(my_h=my_h,my_r=my_r); // shortcut cylinder(h=my_h, r=my_r); // echo("<b>Hello</b> <i>Qt!</i>");  Shows in the Console as ECHO: "This is a cylinder with h=", 50, " and r=", 100 ECHO: my_h = 50, my_r = 100 ECHO: "Hello Qt!"  ## Modules and Functions ### Introduction Users can extend the language by defining their own modules and functions. This allows grouping portions of script for easy reuse with different values. Well chosen names also help document your script. OpenSCAD provides: functions which return values. modules which perform actions, but do not return values. OpenSCAD calculates the value of variables at compile-time, not run-time. The last variable assignment within a scope will apply everywhere in that scope. It also applies to any inner scopes, or children, thereof. See Scope of variables for more details. It may be helpful to think of them as override-able constants rather than as variables. For functions and modules OpenSCAD makes copies of pertinent portions of the script for each use. Each copy has its own scope, which contains fixed values for variables and expressions unique to that instance. The name of functions and modules is case sensitive, therefore test() and TEST() refer to different functions/modules. ### Scope Modules and functions can be defined within a module definition, where they will only be visible in the scope of that module. For example function parabola(f,x) = ( 1/(4*f) ) * x*x; module plotParabola(f,wide,steps=1) { function y(x) = parabola(f,x); module plot(x,y) { translate([x,y]) circle(1,$fn=12);
}
xAxis=[-wide/2:steps:wide/2];
for (x=xAxis)
plot(x,y(x));
}
color("red")  plotParabola(10,100,5);
color("blue") plotParabola(4,60,2);


The function y() and module plot() cannot be called in the global scope.

### 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]){
translate([0.5,0.5,1]) sphere(r=0.5,$fn=20); cube(); } } } house(); translate([2,0,0]) house("pitched"); translate([4,0,0]) house("domical",[0,1,0]); translate([6,0,0]) house(roof="pitched",paint=[0,0,1]); translate([0,3,0]) house(paint=[0,0,0],roof="pitched"); translate([2,3,0]) house(roof="domical"); translate([4,3,0]) house(paint=[0,0.5,0.5]);  //example 3 element_data = [[0,"","",0], // must be in order [1,"Hydrogen","H",1.008], // indexed via atomic number [2,"Helium", "He",4.003] // redundant atomic number to preserve your sanity later ]; Hydrogen = 1; Helium = 2; module coaster(atomic_number){ element = element_data[atomic_number][1]; symbol = element_data[atomic_number][2]; atomic_mass = element_data[atomic_number][3]; //rest of script }  #### Operator Modules Use of children() allows modules to act as operators applied to any or all of the objects within this module instantiation. In use, operator modules do not end with a semi-colon. name ( parameter values ){scope of operator}  #### Children Objects are indexed via integers from 0 to$children-1. OpenSCAD sets $children to the total number of objects within the scope. Objects grouped into a sub scope are treated as one child. See example of separate children below and Scope of variables. Note that children(), echo() and empty block statements (including ifs) count as $children objects, even if no geometry is present (as of v2017.12.23).

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


Deprecated child() module

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

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

Examples

//Use all children

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

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

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

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

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

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

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

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

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

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


#### Further Module Examples

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

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

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

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

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

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

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


#### Recursive Modules

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

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

A simple tree created with a recursive OpenSCAD module
    module simple_tree(size, dna, n) {
if (n > 0) {
// trunk
cylinder(r1=size/10, r2=size/12, h=size, $fn=24); // branches translate([0,0,size]) for(bd = dna) { angx = bd[0]; angz = bd[1]; scal = bd[2]; rotate([angx,0,angz]) simple_tree(scal*size, dna, n-1); } } else // leaves color("green") scale([1,1,3]) translate([0,0,size/6]) rotate([90,0,0]) cylinder(r=size/6,h=size/10); } // dna is a list of branching data bd of the tree: // bd[0] - inclination of the branch // bd[1] - Z rotation angle of the branch // bd[2] - relative scale of the branch dna = [ [12, 80, 0.85], [55, 0, 0.6], [62, 125, 0.6], [57, -125, 0.6] ]; simple_tree(50, dna, 5);  Another example of recursive module may be found in Tips and Tricks ### Overwriting built-in modules It is possible to overwrite the built-in modules. A simple, but pointless example would be: module sphere(){ square(); } sphere();  Note that the built-in sphere module can not be called when over written. A more sensible way to use this language feature is to overwrite the 3D primitives with extruded 2D-primitives. This allows additional to customize the default parameters and to add additional parameters. ### Overwriting built-in functions It is possible to overwrite the built-in functions. Source Code Console output echo (sin(1)); function sin() = true; echo (sin(1)); Compiling design (CSG Tree generation)... ECHO: true ECHO: true Compiling design (CSG Products generation)... ## Importing Geometry Importing is achieved by the import() command. [Note: Requires version 2015.03-2] The File >> Open command may be used to insert this command. The file type filter of the Open File dialog may only show OpenSCAD files, but file name can be replaced with a wildcard (e.g. *.stl) to browse to additional file types. ## 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. 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.:If the give path is not absolute, it is resolved relative to the importing script. Note that when using include<> with a script that uses import(), this is relative to the script doing the include<>. <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. Optional. <layer> For DXF import only, specify a specific layer to import. Optional. 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, or replace the backslashes with forward slashes.)  Read a layer of a 2D DXF file and create a 3D shape. linear_extrude(height = 5, center = true, convexity = 10) import_dxf(file = "example009.dxf", layer = "plate");  #### 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 File: /home/don/openscad_deps/mxe/usr/i686-pc-mingw32/include/CGAL/Polyhedron_incremental_builder_3.h 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() File: /home/don/openscad_deps/mxe/usr/i686-pc-mingw32/include/CGAL/Nef_3/polyhedron_3_to_nef_3.h 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 doesn't 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. If Meshlab can't fill the last hole then Blender might help: 1. Start Blender 2. X, 1 to remove the default object 3. File, Import, Stl 4. Tab to edit the mesh 5. A to de-select all vertices 6. Alt+Ctrl+Shift+M to select all non-manifold vertices 7. MMB to rotate, Shift+MMB to pan, wheel to zoom 8. C for "circle" select, Esc to finish 9. Alt+M, 1 to merge or Space and search for "merge" as alternative 10. Merging vertices is a useful way of filling holes where the vertices are so closely packed that the slight change in geometry is unimportant compared to the precision of a typical 3D printer ## import_dxf [Deprecated: import_dxf() will be removed in future releases. Use import() instead.] Read a DXF file and create a 3D shape. linear_extrude(height = 5, center = true, convexity = 10) import_dxf(file = "example009.dxf", layer = "plate");  ## import_stl [Deprecated: import_stl() will be removed in future releases. Use import() instead.] Imports an STL file for use in the current OpenSCAD model import_stl("body.stl", convexity = 5);  ## surface surface() reads Heightmap information from text or image files. It 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. ## Include Statement For including code from external files in OpenSCAD, there are two commands available: • include <filename> acts as if the contents of the included file were written in the including file, and • use <filename> imports modules and functions, but does not execute any commands other than those definitions. Library files are searched for in the same folder as the design was open from, or in the library folder of the OpenSCAD installation. You can use a relative path specification to either. If they lie elsewhere you must give the complete path. Newer versions have predefined user libraries, see the OpenSCAD_User_Manual/Libraries page, which also documents a number of library files included in OpenSCAD. Wildcards (*, for e.g. include <MCAD/*.scad>) can not be used to include multiple files. #### Directory separators Windows and Linux/Mac use different separators for directories. Windows uses \, e.g. directory\file.ext, while the others use /, e.g. directory/file.ext. This could lead to cross platform issues. However OpenSCAD on Windows correctly handles the use of /, so using / in all include or use statements will work on all platforms. To access the parent directory ../ can be used under Linux. #### Variables ##### Scope of variables Using include <filename> allows default variables to be specified in the library. These defaults can be overridden in the main code. An OpenSCAD variable only has one value during the life of the program. When there are multiple assignments it takes the last value, but assigns when the variable is first created. This has an effect when assigning in a library, as any variables which you later use to change the default, must be assigned before the include statement. See the second example below. ##### Overwriting variables Default variables in an include can be overridden, for example lib.scad i=1; k=3; module x() { echo("hello world"); echo("i=",i,"j=",j,"k=",k); }  hello.scad j=4; include <lib.scad>; x(); i=5; x(); k=j; x();  Produces the following ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", 4 ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", 4 ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", 4  However, placing j=4; after the include fails, producing ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", undef ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", undef ECHO: "hello world" ECHO: "i=", 5, "j=", 4, "k=", undef  #### Example "Ring-Library" A library file for generating rings might look like this (defining a function and providing an example): ring.scad: module ring(r1, r2, h) { difference() { cylinder(r = r1, h = h); translate([ 0, 0, -1 ]) cylinder(r = r2, h = h+2); } } ring(5, 4, 10);  Including the library using include <ring.scad>; rotate([90, 0, 0]) ring(10, 1, 1);  would result in the example ring being shown in addition to the rotated ring, but use <ring.scad>; rotate([90, 0, 0]) ring(10, 1, 1);  only shows the rotated ring. If using the use function, make sure to place the use statements at top of the file, or at least not within a module! This will work fine:  // a.scad use <ring.scad>; module a() { ring(); }  but this will result in an syntax error:  //a.scad module a() { use <ring.scad>; ring(); }  #### Nested Include and Use OpenSCAD will execute nested calls to include and use. There is one caveat to this, that use only brings functions and modules into the local file context. As a result, nested calls to use will have no effect on the environment of the base file; the child use call will work in the parent use context, but the modules and functions so imported will fall out of context before they are seen by the base context. ## 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 an 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 $fs are used to determine the number of fragments for a circle, then OpenSCAD will never use fewer than 5 fragments. This is the C code that calculates the number of fragments in a circle:  int get_fragments_from_r(double r, double fn, double fs, double fa) { if (r < GRID_FINE) return 3; if (fn > 0.0) return (int)(fn >= 3 ? fn : 3); return (int)ceil(fmax(fmin(360.0 / fa, r*2*M_PI / fs), 5)); }  Or you can embed this OpenSCAD version in your code to work out what's going on, you need to set r= to your size  echo(n=($fn>0?($fn>=3?$fn:3):ceil(max(min(360/$fa,r*2*PI/$fs),5))),a_based=360/$fa,s_based=r*2*PI/$fs);


Spheres are first sliced into as many slices as the number of fragments being used to render a circle of the sphere's radius, and then every slice is rendered into as many fragments as are needed for the slice radius. You might have recognized already that the pole of a sphere is usually a pentagon. This is why.

The number of fragments for a cylinder is determined using the greater of the two radii.

The method is also used when rendering circles and arcs from DXF files. The variables have no effect when importing STL files.

You can generate high resolution spheres by resetting the $fX values in the instantiating module: $fs = 0.01;
sphere(2);


or simply by passing the special variable as parameter:

      sphere(2, $fs = 0.01);  You can even scale the special variable instead of resetting it:  sphere(2,$fs = $fs * 0.01);  ####$t

The $t variable is used for animation. If you enable the animation frame with view->animate and give a value for "FPS" and "Steps", the "Time" field shows the current value of$t. With this information in mind, you can animate your design. The design is recompiled every 1/"FPS" seconds with $t incremented by 1/"Steps" for "Steps" times, ending at either$t=1 or $t=1-1/steps. If "Dump Pictures" is checked, then images will be created in the same directory as the .scad file, using the following$t values, and saved in the following files:

• $t=0/Steps filename="frame00001.png" •$t=1/Steps filename="frame00002.png
• $t=2/Steps filename="frame00003.png" • . . . •$t=1-3/Steps filename="frame<Steps-2>.png"
• $t=1-2/Steps filename="frame<Steps-1>.png" •$t=1-1/Steps filename="frame00000.png"

Or, for other values of Steps, it follows this pattern:

• $t=0/Steps filename="frame00001.png" •$t=1/Steps filename="frame00002.png
• $t=2/Steps filename="frame00003.png" • . . . •$t=1-3/Steps filename="frame<Steps-2>.png"
• $t=1-2/Steps filename="frame<Steps-1>.png" •$t=1-1/Steps filename="frame<Steps-0>.png"
• $t=1-0/Steps filename="frame00000.png" Which pattern it chooses appears to be an unpredictable, but consistent, function of Steps. For example, when Steps=4, it follows the first pattern, and outputs a total of 4 files. When Steps=3, it follows the second pattern, and also outputs 4 files. It will always output either Steps or Steps+1 files, though it may not be predictable which. When finished, it will wrap around and recreate each of the files, looping through and recreating them forever. ####$vpr, $vpt and$vpd

These contain the current viewport rotation and translation and camera distance - at the time of doing the rendering. Moving the viewport does not update them. During an animation they are updated for each frame.

• $vpr shows rotation •$vpt shows translation (i.e. won't be affected by rotate and zoom)
• $vpd shows the camera distance [Note: Requires version 2015.03] Example  cube([10, 10,$vpr[0] / 10]);


which makes the cube change size based on the view angle, if an animation loop is active (which does not need to use the $t variable) You can also make bits of a complex model vanish as you change the view. All three variables are writable but only assignments at the top-level of the main file will have an effect on the viewport. [Note: Requires version 2015.03] Example $vpr = [0, 0, $t * 360];  which allows a simple 360 degree rotation around the Z axis in animation mode. The menu command Edit - Paste Viewport Rotation/Translation copies the current value of the viewport, but not the current$vpr or $vpt. ####$preview

[Note: Requires version 2019.05]

$preview is true, when in OpenCSG preview (F5).$preview is false, when in render (F6).

This can, for example, be used to reduce detail during preview to save time, without losing detail in the final rendered result:

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


Note that the render module does not affect $preview: render(){$fn = $preview ? 12 : 72; sphere(r = 1); }  Another use could be to make the preview show an assembly view and the render generate just the printed parts laid out for printing. If printed parts need extra features that are removed post printing, for example support for suspended holes, then the preview can omit these to show the finished part after post processing. When OpenSCAD is run from the command line$preview is only true when generating a PNG image with OpenCSG. It is false when generating STL, DXF and SVG files with CGAL. It is also false when generating CSG and ECHO files. This may or may not be what you want, but you can always override it on the command line like any other variable with the -D option.

### 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

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("Hello Qt!");


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!"


#### Rounding examples

An example for the rounding:

a=1.0;
b=1.000002;
echo(a);
echo(b);

if(a==b){ //while echoed the same, the values are still distinct
echo ("a==b");
}else if(a>b){
echo ("a>b");
}else if(a<b){
echo ("a<b");
}else{
echo ("???");
}


#### Small and large Numbers

c=1000002;
d=0.000002;
echo(c); //1e+06
echo(d); //2e-06


#### HTML

Working HTML examples:

echo("<h1>Heading</h1>");
echo("<b>Bold</b> <i>italic</i> <big>big</big>");
echo("i<sub>1</sub><sup>2<sup>");
echo("<font color='red'>red</font> <font color='green'>green</font> <font color='blue'>blue</font>");


not really working examples:

echo("<img src='http://www.openscad.org/assets/img/logo.png'></img>");
echo("<a href='http://en.wikibooks.org/'>wikibooks</a>");


Note: the Output can be copy and pasted into OpenOffice, where both the image and the link work fine.

### Echo Function

[Note: Requires version 2019.05]

Echo can be used in expression context to print information while the function/expression is evaluated. The output is generated before the expression evaluation to allow debugging of recursive functions.

Example

 a = 3; b = 5;

// echo() prints values before evaluating the expression
r1 = echo(a, b) a * b; // ECHO: 3, 5

// using let it's still easy to output the result
r2 = let(r = 2 * a * b) echo(r) r; // ECHO: 30

// use echo statement for showing results
echo(r1, r2); // ECHO: 15, 30


A more complex example shows how echo() can be used in both descending and ascending path of a recursive function. The result() helper function is a simple way to output the value of an expression after evaluation.

Example printing both input values and result of recursive sum()

 v = [4, 7, 9, 12];
function result(x) = echo(result = x) x;
function sum(x, i = 0) = echo(str("x[", i, "]=", x[i])) result(len(x) > i ? x[i] + sum(x, i + 1) : 0);
echo("sum(v) = ", sum(v));

// ECHO: "x[0]=4"
// ECHO: "x[1]=7"
// ECHO: "x[2]=9"
// ECHO: "x[3]=12"
// ECHO: "x[4]=undef"
// ECHO: result = 0
// ECHO: result = 12
// ECHO: result = 21
// ECHO: result = 28
// ECHO: result = 32
// ECHO: "sum(v) = ", 32


### 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.

Example 4:

[Note: Requires version 2015.03]

// Example 4
surface(file = "BRGY-Grey.png", center = true, invert = false);


### 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 string value. Search will loop over the characters in the string and search for each one in the second argument. The second argument must be a string or a list of lists (this second case is not recommended). The search function does not search for substrings.
• Can be a single numerical value.
• Can be a list of values. The search function will search for each item on the list.
• To search for a list or a full string give the list or string as a single element list such as ["abc"] to search for the string "abc" (See Example 9) or [[6,7,8]] to search for the list [6,7,8]. Without the extra brackets search will look separately for each item in the list.
• If match_value is boolean then search returns undef.
• string_or_vector
• The string or vector to search for matches.
• If match_value is a string then this should be a string and the string is searched for individual character matches to the characters in match_value
• If this is a list of lists, v=[[a0,a1,a2...],[b0,b1,b2,...],[c0,c1,c2,...],...] then search looks only at one index position of the sublists. By default this is position 0, so the search will look only at a0, b0, c0, etc. The index_col_num parameter changes which index is searched.
• If match_value is a string and this parameter is a list of lists then the characters of the string are tested against the appropriate index entry in the list of lists. However, if any characters fail to find a match a warning message is printed and that return value is excluded from the output (if num_returns_per_match is 1). This means that the length of the output is unpredictable.
• 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)
• As noted above, when searching a list of lists, search looks only at one index position of each sublist. That index position is specified by index_col_num.
• 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] ];
echo(search(3, data));    // Searches index 0, so it doesn't find anything
echo(search(3, data, num_returns_per_match=0, index_col_num=1));


Outputs:

 ECHO: []
ECHO: [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_modules contains the number of modules in the instantiation stack. parent_module(i) returns the name of the module i levels above the current module in the instantiation stack. The stack is independent of where the modules are defined. It's where they're instantiated that counts. This can be used to e.g. build BOMs.

Example:

 module top() {
children();
}
module middle() {
children();
}
top() middle() echo(parent_module(0)); // prints "middle"
top() middle() echo(parent_module(1)); // prints "top"


### assert

[Note: Requires version 2019.05]

Assert evaluates a logical expression. If the expression evaluates to false, the generation of the preview/render is stopped with an error. A string representation of the expression and, if given, the message is output to the console.

Parameters

condition
Expression. The expression to be evaluated as check for the assertion.
message
String. Optional message to be output in case the assertion failed.

#### Example

The simplest example is a simple assert(false);, e.g. in a file named assert_example1.scad.

cube();
assert(false);
sphere();

// ERROR: Assertion 'false' failed in file assert_example1.scad, line 2


This example has little use, but the simple assert(false); can be used in code sections that should be unreachable.

#### Checking parameters

A useful example is checking the validity of input parameters:

module row(cnt = 3){
// Count has to be a positive integer greater 0
assert(cnt > 0);
for (i = [1 : cnt]) {
translate([i * 2, 0, 0]) sphere();
}
}

row(0);

// ERROR: Assertion '(cnt > 0)' failed in file assert_example2.scad, line 3


When writing a library, it could be useful to output additional information to the user in case of an failed assertion.

module row(cnt = 3){
assert(cnt > 0, "Count has to be a positive integer greater 0");
for(i = [1 : cnt]) {
translate([i * 2, 0, 0]) sphere();
}
}

row(0);

// ERROR: Assertion '(cnt > 0)': "Count has to be a positive integer greater 0" failed in file assert_example3.scad, line 2


#### Using assertions in function

Assert returns its children, so when using it in a function you can write

function f(a, b) =
assert(a < 0, "wrong a") // assert input
assert(b > 0, "wrong b") // assert input
let (c = a + b) // derive a new value from input
assert(c != 0, "wrong c") // assert derived value
a * b; // calculate