OpenSCAD User Manual/The OpenSCAD Language
Contents
 1 Chapter 1  General
 2 Chapter 2  3D Objects
 3 Chapter 3  2D Objects
 4 Chapter 4  Transform
 5 Chapter 5  Boolean combination
 6 Chapter 6  Other Functions and Operators
 6.1 Conditional and Iterator Functions
 6.2 Mathematical Operators
 6.3 Mathematical Functions
 6.4 Trigonometric Functions
 6.5 Other Mathematical Functions
 6.6 Infinities and NaNs
 6.7 String Functions
 6.8 List Comprehensions
 6.9 Other Language Features
 7 Chapter 7  UserDefined Functions and Modules
 8 Chapter 8  Debugging aids
 9 Chapter 9  External libraries and code files
Chapter 1  General[edit]
OpenSCAD User Manual/The OpenSCAD Language
The text in its current form is incomplete. 
Introduction[edit]
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[edit]
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 selfevident code.
OpenSCAD uses C++style comments:
// This is a comment myvar = 10; // The rest of the line is a comment /* Multiline comments can span multiple lines. */
Values and Data Types[edit]
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[edit]
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 nonzero 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[edit]
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[edit]
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
Note: This behavior is new since OpenSCAD2011.04. You can upgrade old files using the following sed command: sed 's/\\/\\\\/' nonescaped.scad > escaped.scad
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[edit]
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[edit]
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' (notanumber) 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[edit]
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 compiletime, not runtime. This behavior is due to the need to supply variable input on the command line, via the use of D variable=value option. OpenSCAD currently places that assignment at the end of the source code, and thus must allow a variables value to be changed for this purpose.
The variable retains its last assigned value at compile time, in line with Functional programming languages. Unlike Imperative languages, such as C, OpenSCAD is not an iterative language, as such the concept of x = x + 1 is not valid, get to understand this concept and you will understand the beauty of OpenSCAD.
 Before version 2015.03
It was not possible to do assignments at any place except the file toplevel and module toplevel. 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[edit]
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[edit]
When operators such as translate() and color() need to encompass more than one action ( actions end in ; ), braces {} are needed to to group the actions, creating a new, inner scope. When there is only one semicolon, braces are usually optional.
Each pair of braces creates a new scope inside the scope where they were used. Since 2015.03, new variables can be created within this new scope. New values can be given to variables which were created in an outer scope . These variables and their values are also available to further inner scopes created within this scope, but are not available to any thing outside this scope. Variables still have only the last value assigned within a scope.
// scope 1 a = 6; // create a echo(a,b); // 6, undef translate([5,0,0]){ // scope 1.1 a= 10; b= 16; // create b echo(a,b); // 100, 16 a=10; was overridden by later a=100; color("blue") { // scope 1.1.1 echo(a,b); // 100, 20 cube(); b=20; } // back to 1,1 echo(a,b); // 100, 16 a=100; // override a in 1.1 } // back to 1 echo(a,b); // 6, undef color("red"){ // scope 1.2 cube(); echo(a,b); // 6, undef } // back to 1 echo(a,b); // 6, undef //In this example, scopes 1 and 1.1 are outer scopes to 1.1.1 but 1.2 is not.
 Anonymous scopes are not considered scopes:
{ angle = 45; } rotate(angle) square(10);
For() loops are not an exception to the rule about variables having only one value within a scope. A copy of loop contents is created for each pass. Each pass is given its own scope, allowing any variables to have unique values for that pass. No, you still can't do a=a+1;
Variables are set at compiletime, not runtime[edit]
Because OpenSCAD calculates its variable values at compiletime, not runtime, 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 overrideable 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 counterintuitive, 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 'redefine' or override those constants by simply assigning a new value to them.
Special Variables[edit]
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[edit]
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( [ [x_{0},y_{0}], [x_{1},y_{1}], [x_{2},y_{2}] ] );
 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 n1 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
e = [ [1], [], [3,4,5], "string", "x", [[10,11],[12,13,14],[[15,16],[17]]] ]; // length 6 address length element e[0] 1 [1] e[1] 0 [] e[5] 3 [ [10,11], [12,13,14], [[15,16],[17]] ] e[5][1] 3 [ 12, 13, 14 ] e[5][2] 2 [ [15,16], [17] ] e[5][2][0] 2 [ 15, 16 ] e[5][2][0][1] undef 16 e[3] 6 "string" e[3 ][2] 1 "r" s = [2,0,5]; a = 2; s[a] undef 5 e[s[a]] 3 [ [10,11], [12,13,14], [[15,16],[17]] ]
vector operators[edit]
concat[edit]
[Note: Requires version 2015.03 or later]
concat() combines the elements of 2 or more vectors into a single vector. No change in nesting level is made.
vector1 = [1,2,3]; vector2 = [4]; vector3 = [5,6]; new_vector = concat(vector1, vector2, vector3); // [1,2,3,4,5,6] string_vector = concat("abc","def"); // ["abc", "def"] one_string = str(string_vector[0],string_vector[1]); // "abcdef"
len[edit]
len() is a function which returns the length of vectors or strings. Indices of elements are from [0] to [length1].
 vector
 Returns the number of elements at this level.
 Single values, which are not vectors, return undef.
 string
 Returns the number of characters in string.
a = [1,2,3]; echo(len(a)); // 3
See example elements with lengths
Matrix[edit]
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[edit]
Now we have variables, it would be nice to be able to get input into them instead of setting the values from code. There are a few functions to read data from DXF files, or you can set a variable with the D switch on the command line.
Getting a point from a drawing
Getting a point is useful for reading an origin point in a 2D view in a technical drawing. The function dxf_cross will read the intersection of two lines on a layer you specify and return the intersection point. This means that the point must be given with two lines in the DXF file, and not a point entity.
OriginPoint = dxf_cross(file="drawing.dxf", layer="SCAD.Origin",
origin=[0, 0], scale=1);
Getting a dimension value
You can read dimensions from a technical drawing. This can be useful to read a rotation angle, an extrusion height, or spacing between parts. In the drawing, create a dimension that does not show the dimension value, but an identifier. To read the value, you specify this identifier from your program:
TotalWidth = dxf_dim(file="drawing.dxf", name="TotalWidth",
layer="SCAD.Origin", origin=[0, 0], scale=1);
For a nice example of both functions, see Example009 and the image on the homepage of OpenSCAD.
Chapter 2  3D Objects[edit]
OpenSCAD User Manual/The OpenSCAD Language
Primitive Solids [edit]
cube[edit]
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)
 size
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[edit]
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
 r
 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
 d
 Diameter. This is the diameter of the sphere.
(NOTE: d is only available in versions later than 2014.03. Debian is currently known to be behind this)
 $fa
 Fragment angle in degrees
 $fs
 Fragment size in mm
 $fn
 Resolution
default values: sphere(); yields: sphere($fn = 0, $fa = 12, $fs = 2, r = 1);
} Usage Examples
sphere(r = 1); sphere(r = 5); sphere(r = 10); sphere(d = 2); sphere(d = 10); sphere(d = 20);
// this will create a high resolution sphere with a 2mm radius sphere(2, $fn=100);
// will also create a 2mm high resolution sphere but this one // does not have as many small triangles on the poles of the sphere sphere(2, $fa=5, $fs=0.1);
cylinder[edit]
Creates a cylinder or cone centered about the z axis. When center is true, it is also centered vertically along the z axis.
Parameter names are optional if given in the order shown here. If a parameter is named, all following parameters must also be named.
NOTE: If r, d, d1 or d2 are used they must be named.
cylinder(h = height, r1 = BottomRadius, r2 = TopRadius, center = true/false);
 Parameters

 h : height of the cylinder or cone
 r : radius of cylinder. r1 = r2 = r.
 r1 : radius, bottom of cone.
 r2 : radius, top of cone.
 d : diameter of cylinder. r1 = r2 = d /2.
 d1 : diameter, bottom of cone. r1 = d1 /2
 d2 : diameter, top of cone. r2 = d2 /2
 (NOTE: d,d1,d2 require 2014.03 or later. Debian is currently known to be behind this)
 center
 false (default), z ranges from 0 to h
 true, z ranges from h/2 to +h/2
 $fa : minimum angle (in degrees) of each fragment.
 $fs : minimum circumferential length of each fragment.
 $fn : fixed number of fragments in 360 degrees. Values of 3 or more override $fa and $fs
 $fa, $fs and $fn must be named. click here for more details,.
defaults: cylinder(); yields: cylinder($fn = 0, $fa = 12, $fs = 2, h = 1, r1 = 1, r2 = 1, center = false);
equivalent scripts cylinder(h=15, r1=9.5, r2=19.5, center=false); cylinder( 15, 9.5, 19.5, false); cylinder( 15, 9.5, 19.5); cylinder( 15, 9.5, d2=39 ); cylinder( 15, d1=19, d2=39 ); cylinder( 15, d1=19, r2=19.5);
equivalent scripts cylinder(h=15, r1=10, r2=0, center=true); cylinder( 15, 10, 0, true); cylinder(h=15, d1=20, d2=0, center=true);
equivalent scripts cylinder(h=20, r=10, center=true); cylinder( 20, 10, 10,true); cylinder( 20, d=20, center=true); cylinder( 20,r1=10, d2=20, center=true); cylinder( 20,r1=10, d2=2*10, center=true);
 use of $fn
Larger values of $fn create smoother, more circular, surfaces at the cost of longer rendering time. Some use medium values during development for the faster rendering, then change to a larger value for the final F6 rendering.
However, use of small values can produce some interesting non circular objects. A few examples are show here:
scripts for these examples cylinder(20,20,20,$fn=3); cylinder(20,20,00,$fn=4); cylinder(20,20,10,$fn=4);
 undersized holes
When using cylinder() with difference() to place holes in objects, the holes will be undersized. This is because circular paths are approximated with polygons inscribed within in a circle. The points of the polygon are on the circle, but straight lines between are inside. To have all of the hole larger than the true circle, the polygon must lie wholly outside of the circle (circumscribed). Modules for circumscribed holes
Notes on accuracy Circle objects are approximated. The algorithm for doing this matters when you want 3d printed holes to be the right size. Current behavior is illustrated in a diagram . Discussion regarding optionally changing this behavior happening in a Pull Request
polyhedron[edit]
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 = [ [X_{0}, Y_{0}, Z_{0}], [X_{1}, Y_{1}, Z_{1}], ... ], triangles = [ [P_{0}, P_{1}, P_{2}], ... ], convexity = N); // before 2014.03 polyhedron( points = [ [X_{0}, Y_{0}, Z_{0}], [X_{1}, Y_{1}, Z_{1}], ... ], faces = [ [P_{0}, P_{1}, P_{2}, P_{3}, ...], ... ], 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 N1.
 points

 triangles (deprecated in version 2014.03, use faces)
 Vector of faces which collectively enclose the solid. Each face is a vector containing the indices (0 based) of 3 points from the points vector.
 triangles (deprecated in version 2014.03, use faces)

 faces (introduced in version 2014.03)
 Vector of faces which collectively enclose the solid. Each face is a vector containing the indices (0 based) of 3 or more points from the points vector.
 Faces may be defined in any order. Define enough faces to fully enclose the solid, with no overlap.
 Points which describe a single face must all be on the same plane.
 faces (introduced in version 2014.03)

 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.
 convexity
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 ] );
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:
polyhedron( points=[ [10,10,0],[10,10,0],[10,10,0],[10,10,0], // the four points at base [0,0,10] ], // the apex point faces=[ [0,1,4],[1,2,4],[2,3,4],[3,0,4], // each triangle side [1,0,3],[2,1,3] ] // two triangles for square base );
 Example 3 A rectangular prism:
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([0border,w+separation+w+border+h+border,0]) polyhedron( points=[[0,0,0],[0h,0,0],[0,sqrt(w*w+h*h),0], [0,0,z],[0h,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[edit]
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 faceedge around the vertex.
The first rule eliminates polyhedron like two cubes with a common edge and 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.
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
Misordered faces[edit]
 Example 4 a more complex polyhedron with misordered 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 misoriented 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]
]
);
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 misoriented pink faces and then permute the references to the points vectors until you get it right. E.g. in the above example, the third triangle ([0,4,5]) was wrong and we fixed it as [4,0,5]. In addition, you may select "Show Edges" from the "View Menu", print a screen capture and number both the points and the faces. In our example, the points are annotated in black and the faces in blue. Turn the object around and make a second copy from the back if needed. This way you can keep track.
Clockwise Technique:
Orientation is determined by clockwise indexing. This means that if you're looking at the triangle (in this case [4,0,5]) from the outside you'll see that the path is clockwise around the center of the face. The winding order [4,0,5] is clockwise and therefore good. The winding order [0,4,5] is counterclockwise 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 counterclockwise as the outside though).
Think of it as a Left Hand Rule:
If you hold the face and the fingers of your hand curls is the same order as the points, then your thumb points outwards.
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 3tuple x,y,z position specification. Points in the point list are automatically given an identifier starting at zero for use in the faces list (0,1,2,3,... etc).
Each face, in the faces list, is defined by selecting 3 or more of the points (using the point identifier) out of the point list.
e.g. faces=[ [0,1,2] ] defines a triangle from the first point (points are zero referenced) to the second point and then to the third point.
When looking at any face from the outside, the face must list all points in a clockwise order.
Alternate Face Descriptions[edit]
Before 2014.03, faces could only be described via triangles. Since 2014.03, a face description can have any number of points. The points, all in the same plane, must be listed in the proper order. Since version ???, the face vertices may not be planar: OpenSCAD will do its best to internally subdivide the face in triangles. Note that this may lead to different results depending on the chosen face triangulation. If a specific result is needed, the non planar face should be broken in triangular pieces by the user.
An alternate (correct) face definition for example 4:
faces = [ [0,3,2,1], [0,1,5,4], [2,3,4,5], // outside [6,7,8,9], [7,6,10,11], [11,10,9,8], // inside [0,4,3,0,6,9,10,6], // front [1,2,5,1,7,11,8,7] // back ]
3D to 2D Projection[edit]
Using the projection()
function, you can create 2d drawings from 3d models, and export them to the dxf format. It works by projecting a 3D model to the (x,y) plane, with z at 0. If cut=true
, only points with z=0 will be considered (effectively cutting the object), with cut=false
(the default), points above and below the plane will be considered as well (creating a proper projection).
Example: Consider example002.scad, that comes with OpenSCAD.
Then you can do a 'cut' projection, which gives you the 'slice' of the xy plane with z=0.
projection(cut = true) example002();
You can also do an 'ordinary' projection, which gives a sort of 'shadow' of the object onto the xy plane.
projection(cut = false) example002();
Another Example
You can also use projection to get a 'side view' of an object. Let's take example002, and move it up, out of the XY plane, and rotate it:
translate([0,0,25]) rotate([90,0,0]) example002();
Now we can get a side view with projection()
projection() translate([0,0,25]) rotate([90,0,0]) example002();
Links:
 example021.scad from Clifford Wolf's site.
 More complicated example from Giles Bathgate's blog
Chapter 3  2D Objects[edit]
OpenSCAD User Manual/The OpenSCAD Language
All 2D primitives can be transformed with 3D transformations. Usually used as part of a 3D extrusion. Although infinitely thin, they are rendered with a 1 thickness.
square[edit]
Creates a square or rectangle in the first quadrant. When center is true the square is centered on the origin. Argument names are optional if given in the order shown here.
square(size = [x, y], center = true/false); square(size = x , center = true/false);
 parameters:

 size
 single value, square with both sides this length
 2 value array [x,y], rectangle with dimensions x and y
 center
 false (default), 1st (positive) quadrant, one corner at (0,0)
 true, square is centered at (0,0)
 size
default values: square(); yields: square(size = [1, 1], center = false);
 examples:
equivalent scripts for this example square(size = 10); square(10); square([10,10]); . square(10,false); square([10,10],false); square([10,10],center=false); square(size = [10, 10], center = false); square(center = false,size = [10, 10] );
equivalent scripts for this example square([20,10],true); a=[20,10];square(a,true);
circle[edit]
Creates a circle at the origin. All parameters, except r, must be named.
circle(r=radius  d=diameter);
 Parameters
 r : circle radius. r name is the only one optional with circle.
 circle resolution is based on size, using $fa or $fs.
 r : circle radius. r name is the only one optional with circle.


 For a small, high resolution circle you can make a large circle, then scale it down, or you could set $fn or other special variables. Note: These examples exceed the resolution of a 3d printer as well as of the display screen.

scale([1/100, 1/100, 1/100]) circle(200); // create a high resolution circle with a radius of 2. circle(2, $fn=50); // Another way.

 d : circle diameter (only available in versions later than 2014.03).
 $fa : minimum angle (in degrees) of each fragment.
 $fs : minimum circumferential length of each fragment.
 $fn : fixed number of fragments in 360 degrees. Values of 3 or more override $fa and $fs
 $fa, $fs and $fa must be named. click here for more details,.
defaults: circle(); yields: circle($fn = 0, $fa = 12, $fs = 2, r = 1);
equivalent scripts for this example circle(10); circle(r=10); circle(d=20); circle(d=2+9*2);
ellipse[edit]
An ellipse can be created from a circle by using either scale() or resize() to make the x and y dimensions unequal. See OpenSCAD User Manual/Transformations
equivalent scripts for this example resize([30,10])circle(d=20); scale([1.5,.5])circle(d=20);
regular polygon[edit]
A regular polygon of 3 or more sides can be created by using circle() with $fn set to the number of sides. The polygon is inscribed within the circle with all sides (and angles) equal. One corner points to the positive x direction. For irregular shapes see the polygon primitive below.
script for these examples translate([42, 0]){circle(20,$fn=3);%circle(20,$fn=90);} translate([ 0, 0]) circle(20,$fn=4); translate([ 42, 0]) circle(20,$fn=5); translate([42,42]) circle(20,$fn=6); translate([ 0,42]) circle(20,$fn=8); translate([ 42,42]) circle(20,$fn=12);
color("black"){ translate([42, 0,1])text("3",7,,center); translate([ 0, 0,1])text("4",7,,center); translate([ 42, 0,1])text("5",7,,center); translate([42,42,1])text("6",7,,center); translate([ 0,42,1])text("8",7,,center); translate([ 42,42,1])text("12",7,,center); }
polygon[edit]
Creates a multiple sided shape from a list of x,y coordinates. A polygon is the most powerful 2D object. It can create anything that circle and squares can, as well as much more. This includes irregular shapes with both concave and convex edges. In addition it can place holes within that shape.
polygon(points = [ [x, y], ... ], paths = [ [p1, p2, p3..], ...], convexity = N);
Parameters
 points
 The list of x,y points of the polygon. : A vector of 2 element vectors.
 Note: points are indexed from 0 to n1.
 paths
 default
 If no path is specified, all points are used in the order listed.
 single vector
 The order to traverse the points. Uses indices from 0 to n1. May be in a different order and use all or part, of the points listed.
 multiple vectors
 Creates primary and secondary shapes. Secondary shapes are subtracted from the primary shape (like difference). Secondary shapes may be wholly or partially within the primary shape.
 default

 A closed shape is created by returning from the last point specified to the first.
 convexity
 Integer number of "inward" curves, ie. expected path crossings of an arbitrary line through the polygon. See below.
defaults: polygon(); yields: polygon(points = undef, paths = undef, convexity = 1);
Example no holes
equivalent scripts for this example polygon(points=[[0,0],[100,0],[130,50],[30,50]]); polygon([[0,0],[100,0],[130,50],[30,50]], paths=[[0,1,2,3]]); polygon([[0,0],[100,0],[130,50],[30,50]],[[3,2,1,0]]); polygon([[0,0],[100,0],[130,50],[30,50]],[[1,0,3,2]]); a=[[0,0],[100,0],[130,50],[30,50]]; b=[[3,0,1,2]]; polygon(a); polygon(a,b); polygon(a,[[2,3,0,1,2]]);
Example one hole
equivalent scripts for this example polygon(points=[[0,0],[100,0],[0,100],[10,10],[80,10],[10,80]], paths=[[0,1,2],[3,4,5]],convexity=10); triangle_points =[[0,0],[100,0],[0,100],[10,10],[80,10],[10,80]]; triangle_paths =[[0,1,2],[3,4,5]]; polygon(triangle_points,triangle_paths,10);
The 1st path vector, [0,1,2], selects the points, [0,0],[100,0],[0,100], for the primary shape. The 2nd path vector, [3,4,5], selects the points, [10,10],[80,10],[10,80], for the secondary shape. The secondary shape is subtracted from the primary ( think difference() ). Since the secondary is wholly within the primary, it leaves a shape with a hole.
Example multi hole
NOTE: concat() requires 2015.03 or later
//example polygon with multiple holes a0 = [[0,0],[100,0],[130,50],[30,50]]; // main b0 = [1,0,3,2]; a1 = [[20,20],[40,20],[30,30]]; // hole 1 b1 = [4,5,6]; a2 = [[50,20],[60,20],[40,30]]; // hole 2 b2 = [7,8,9]; a3 = [[65,10],[80,10],[80,40],[65,40]]; // hole 3 b3 = [10,11,12,13]; a4 = [[98,10],[115,40],[85,40],[85,10]]; // hole 4 b4 = [14,15,16,17]; a = concat (a0,a1,a2,a3,a4); b = [b0,b1,b2,b3,b4]; polygon(a,b); //alternate polygon(a,[b0,b1,b2,b3,b4]);
convexity
The convexity parameter specifies the maximum number of front sides (back sides) a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode and has no effect on the polyhedron rendering.
This image shows a 2D shape with a convexity of 4, as the ray indicated in red crosses the 2D shape a maximum of 4 times. The convexity of a 3D shape would be determined in a similar way. Setting it to 10 should work fine for most cases.
import_dxf[edit]
DEPRECATED: The import_dxf() module will be removed in future releases. Use import() instead.
Read a DXF file and create a 2D shape.
Example
linear_extrude(height = 5, center = true, convexity = 10) import_dxf(file = "example009.dxf", layer = "plate");
Text[edit]
The text
module creates text as a 2D geometric object, using fonts installed on the local system or provided as separate font file.
[Note: Requires version 2015.03]
Parameters
 text
 String. The text to generate.
 size
 Decimal. The generated text will have approximately an ascent of the given value (height above the baseline). Default is 10.
Note that specific fonts will vary somewhat and may not fill the size specified exactly, usually slightly smaller.
 font
 String. The name of the font that should be used. This is not the name of the font file, but the logical font name (internally handled by the fontconfig library). This can also include a style parameter, see below. A list of installed fonts & styles can be obtained using the font list dialog (Help > Font List).
 halign
 String. The horizontal alignment for the text. Possible values are "left", "center" and "right". Default is "left".
 valign
 String. The vertical alignment for the text. Possible values are "top", "center", "baseline" and "bottom". Default is "baseline".
 spacing
 Decimal. Factor to increase/decrease the character spacing. The default value of 1 will result in the normal spacing for the font, giving a value greater than 1 will cause the letters to be spaced further apart.
 direction
 String. Direction of the text flow. Possible values are "ltr" (lefttoright), "rtl" (righttoleft), "ttb" (toptobottom) and "btt" (bottomtotop). Default is "ltr".
 language
 String. The language of the text. Default is "en".
 script
 String. The script of the text. Default is "latin".
 $fn
 used for subdividing the curved path segments provided by freetype
Example
text("OpenSCAD");
 Note
To allow specification of particular Unicode characters you can specify them in a string with the following escape codes;
\x03  single hex character (only allowed values are 01h  7fh)
\u0123  unicode char with 4 hexadecimal digits (note: Lowercase)
\U012345  unicode char with 6 hexadecimal digits (note: Uppercase)
Example
t="\u20AC10 \u263A"; // 10 euro and a smilie
Using Fonts & Styles[edit]
Fonts are specified by their logical font name; in addition a style parameter can be added to select a specific font style like "bold" or "italic", such as:
font="Liberation Sans:style=Bold Italic"
The font list dialog shows the font name and the font style for each available font. For reference, the dialog also displays the location of the font file. You can drag a font in the font list, into the editor window to use in the text() statement.
OpenSCAD includes the fonts Liberation Mono, Liberation Sans, Liberation Sans Narrow and Liberation Serif. Hence, as fonts in general differ by platform type, use of these included fonts is likely to be portable across platforms.
For common/casual text usage, the specification of one of these fonts is recommended for this reason. Liberation Sans is the default font to encourage this.
In addition to the installed fonts, it's possible to add project specific font files. Supported font file formats are TrueType Fonts (*.ttf) and OpenType Fonts (*.otf). The files need to be registered with use<>.
use <ttf/paratypeserif/PTF55F.ttf>
After the registration, the font will also be listed in the font list dialog, so in case logical name of a font is unknown, it can be looked up there are it was registered.
Example
square(10); translate([15, 15]) { text("OpenSCAD", font = "Liberation Sans"); } translate([15, 0]) { text("OpenSCAD", font = "Liberation Sans:style=Bold Italic"); }
Alignment[edit]
Vertical alignment[edit]
 top
 The text is aligned with the top of the bounding box at the given Y coordinate.
 center
 The text is aligned with the center of the bounding box at the given Y coordinate.
 baseline
 The text is aligned with the font baseline at the given Y coordinate. This is the default.
 bottom
 The text is aligned with the bottom of the bounding box at the given Y coordinate.
text = "Align"; font = "Liberation Sans"; valign = [ [ 0, "top"], [ 40, "center"], [ 75, "baseline"], [110, "bottom"] ]; for (a = valign) { translate([10, 120  a[0], 0]) { color("red") cube([135, 1, 0.1]); color("blue") cube([1, 20, 0.1]); linear_extrude(height = 0.5) { text(text = str(text,"_",a[1]), font = font, size = 20, valign = a[1]); } } }
Horizontal alignment[edit]
 left
 The text is aligned with the left side of the bounding box at the given X coordinate. This is the default.
 center
 The text is aligned with the center of the bounding box at the given X coordinate.
 right
 The text is aligned with the right of the bounding box at the given X coordinate.
text = "Align"; font = "Liberation Sans"; halign = [ [10, "left"], [50, "center"], [90, "right"] ]; for (a = halign) { translate([140, a[0], 0]) { color("red") cube([115, 2,0.1]); color("blue") cube([2, 20,0.1]); linear_extrude(height = 0.5) { text(text = str(text,"_",a[1]), font = font, size = 20, halign = a[1]); } } }
Renderable 3Dtext[edit]
It is easy only using the function linear_extrude(height);
3D to 2D Projection[edit]
Using the projection()
function, you can create 2d drawings from 3d models, and export them to the dxf format. It works by projecting a 3D model to the (x,y) plane, with z at 0. If cut=true
, only points with z=0 will be considered (effectively cutting the object), with cut=false
(the default), points above and below the plane will be considered as well (creating a proper projection).
Example: Consider example002.scad, that comes with OpenSCAD.
Then you can do a 'cut' projection, which gives you the 'slice' of the xy plane with z=0.
projection(cut = true) example002();
You can also do an 'ordinary' projection, which gives a sort of 'shadow' of the object onto the xy plane.
projection(cut = false) example002();
Another Example
You can also use projection to get a 'side view' of an object. Let's take example002, and move it up, out of the XY plane, and rotate it:
translate([0,0,25]) rotate([90,0,0]) example002();
Now we can get a side view with projection()
projection() translate([0,0,25]) rotate([90,0,0]) example002();
Links:
 example021.scad from Clifford Wolf's site.
 More complicated example from Giles Bathgate's blog
2D to 3D Extrusion[edit]
The text in its current form is incomplete. 
Extrusion is the process of creating an object with a fixed crosssectional profile. OpenSCAD provides two commands to create 3D solids from a 2D shape: linear_extrude() and rotate_extrude(). Linear extrusion is similar to pushing Playdoh through a press with a die of a specific shape.
Rotational extrusion is similar to the process of turning or "throwing" a bowl on the Potter's wheel.
Both extrusion methods work on a (possibly disjointed) 2D shape which exists on the XY plane. While transformations that operates on both 2D shapes and 3D solids can move a shape off the XY plane, when the extrusion is performed the end result is not very intuitive. What actually happens is that any information in the third coordinate (the Z coordinate) is ignored for any 2D shape, this process amounts to an implicit projection() performed on any 2D shape before the extrusion is executed. It is recommended to perform extrusion on shapes that remains strictly on the XY plane. See also 3D and 2D objects.
Linear Extrude[edit]
Linear Extrusion is a modeling operation that takes a 2D polygon as input and extends it in the third dimension. This way a 3D shape is created. Keep in mind that extrusion is always performed from XY plane to the height indicate along Z axis; so if you rotate or apply other transformations before extrusion, the extrusion is applied to the projection of the 2D polygon to the XY plane.
Usage[edit]
linear_extrude(height = fanwidth, center = true, convexity = 10, twist = fanrot, slices = 20, scale = 1.0) {...}
You must use parameter names due to a backward compatibility issue.
height
must be positive.
If the extrusion fails for a nontrivial 2D shape, try setting the convexity parameter (the default is not 10, but 10 is a "good" value to try). See explanation further down.
Twist[edit]
Twist is the number of degrees of through which the shape is extruded. Setting the parameter twist = 360 will extrude through one revolution. The twist direction follows the left hand rule.
0° of Twist
linear_extrude(height = 10, center = true, convexity = 10, twist = 0) translate([2, 0, 0]) circle(r = 1);
100° of Twist
linear_extrude(height = 10, center = true, convexity = 10, twist = 100) translate([2, 0, 0]) circle(r = 1);
100° of Twist
linear_extrude(height = 10, center = true, convexity = 10, twist = 100) translate([2, 0, 0]) circle(r = 1);
500° of Twist
linear_extrude(height = 10, center = true, convexity = 10, twist = 500) translate([2, 0, 0]) circle(r = 1);
Center[edit]
It is similar to the parameter center of cylinders. If center
is false the linear extrusion Z range is from 0 to height; if it is true, the range is from height/2 to height/2.
center = true
linear_extrude(height = 10, center = true, convexity = 10, twist = 500) translate([2, 0, 0]) circle(r = 1);
center = false
linear_extrude(height = 10, center = false, convexity = 10, twist = 500) translate([2, 0, 0]) circle(r = 1);
Mesh Refinement[edit]
The slices parameter defines the number of intermediate points along the Z axis of the extrusion. Its default increases with the value of twist. Explicitly setting slices may improve the output refinement.
linear_extrude(height = 10, center = false, convexity = 10, twist = 360, slices = 100) translate([2, 0, 0]) circle(r = 1);
The special variables $fn, $fs and $fa can also be used to improve the output. If slices is not defined, its value is taken from the defined $fn value.
linear_extrude(height = 10, center = false, convexity = 10, twist = 360, $fn = 100) translate([2, 0, 0]) circle(r = 1);
Scale[edit]
Scales the 2D shape by this value over the height of the extrusion. Scale can be a scalar or a vector:
linear_extrude(height = 10, center = true, convexity = 10, scale=3) translate([2, 0, 0]) circle(r = 1);
linear_extrude(height = 10, center = true, convexity = 10, scale=[1,5], $fn=100) translate([2, 0, 0]) circle(r = 1);
Note that if scale is a vector, the resulting side walls may be nonplanar. Use twist=0
and the slices
parameter to avoid asymmetry.
linear_extrude(height=10, scale=[1,0.1], slices=20, twist=0) polygon(points=[[0,0],[20,10],[20,10]]);
Rotate Extrude[edit]
Rotational extrusion spins a 2D shape around the Zaxis to form a solid which has rotational symmetry. One way to think of this operation is to imagine a Potter's wheel placed on the XY plane with its axis of rotation pointing up towards +Z. Then place the tobemade object on this virtual Potter's wheel (possibly extended down below the XY plane towards Z, take the crosssection of this object on the XZ plane but keep only the right half (X >= 0). That is the 2D shape that need to be fed to rotate_extrude() as the child in order to generate this solid.
Since a 2D shape is rendered by OpenSCAD on the XY plane, an alternative way to think of this operation is as follows: spins a 2D shape around the Yaxis to form a solid. The resultant solid is placed so that its axis of rotation lies along the Zaxis.
It can not be used to produce a helix or screw threads.
The 2D shape needs to lie completely on either the right (recommended) or the left side of the Yaxis. More precisely speaking, each vertex of the shape must have either x >= 0 or x <= 0. If the shape crosses the X axis a warning will be shown in the console windows and the rotate_extrude() will be ignored. For OpenSCAD versions prior to 2016.xxxx, if the shape is in the negative axis the faces will be insideout, which may cause undesired effects.
Parameters
Usage[edit]
rotate_extrude(angle = 360, convexity = 2) {...}
You must use parameter names due to a backward compatibility issue.
 convexity
 If the extrusion fails for a nontrival 2D shape, try setting the convexity parameter (the default is not 10, but 10 is a "good" value to try). See explanation further down.
 angle [Note: Requires version 2016.XX]
 Defaults to 360. Specifies the number of degrees to sweep, starting at the positive X axis. The direction of the sweep follows the Right Hand Rule, hence a negative angle will sweep clockwise.
Examples[edit]
A simple torus can be constructed using a rotational extrude.
rotate_extrude(convexity = 10) translate([2, 0, 0]) circle(r = 1);
Mesh Refinement[edit]
Increasing the number of fragments that the 2D shape is composed of will improve the quality of the mesh, but take longer to render.
rotate_extrude(convexity = 10) translate([2, 0, 0]) circle(r = 1, $fn = 100);
The number of fragments used by the extrusion can also be increased.
rotate_extrude(convexity = 10, $fn = 100) translate([2, 0, 0]) circle(r = 1, $fn = 100);
Using the parameter angle (with OpenSCAD versions 2016.xx), a hook can be modeled .
translate([0,60,0]) rotate_extrude(angle=270, convexity=10) translate([40, 0]) circle(10); rotate_extrude(angle=90, convexity=10) translate([20, 0]) circle(10); translate([20,0,0]) rotate([90,0,0]) cylinder(r=10,h=80);
Extruding a Polygon[edit]
Extrusion can also be performed on polygons with points chosen by the user.
Here is a simple polygon and its 200 step rotational extrusion. (Note it has been rotated 90 degrees to show how the rotation will look; the rotate_extrude()
needs it flat).
rotate([90,0,0]) polygon( points=[[0,0],[2,1],[1,2],[1,3],[3,4],[0,5]] );
rotate_extrude($fn=200) polygon( points=[[0,0],[2,1],[1,2],[1,3],[3,4],[0,5]] );
For more information on polygons, please see: 2D Primitives: Polygon.
Description of extrude parameters[edit]
Extrude parameters for all extrusion modes[edit]
convexity  Integer. The convexity parameter specifies the maximum number of front sides (back sides) a ray intersecting the object might penetrate.
This parameter is only needed for correctly displaying the object in OpenCSG preview mode and has no effect on the polyhedron rendering. 
This image shows a 2D shape with a convexity of 4, as the ray indicated in red crosses the 2D shape a maximum of 4 times. The convexity of a 3D shape would be determined in a similar way. Setting it to 10 should work fine for most cases.
Extrude parameters for linear extrusion only[edit]
height  The extrusion height 
center  If true the solid will be centered after extrusion 
twist  The extrusion twist in degrees 
slices  Similar to special variable $fn without being passed down to the child 2D shape. 
scale  Scales the 2D shape by this value over the height of the extrusion. 
Chapter 4  Transform[edit]
OpenSCAD User Manual/The OpenSCAD Language
Basic concept[edit]
Transformation affect the child nodes and as the name implies transforms them in various ways such as moving/rotating or scaling the child. Cascading transformations are used to apply a variety of transforms to a final child. Cascading is achieved by nesting statements i.e.
rotate([45,45,45]) translate([10,20,30]) cube(10);
Transformations can be applied to a group of child nodes by using '{' and '}' to enclose the subtree e.g.
translate([0,0,5])
{
cube(10);
cylinder(r=5,h=10);
}
Transformations are written before the object they affect.
Imagine command like translate, mirror and scale as verbs. Commands like color are like adjectives that describe the object.
Notice that there is no semicolon following transformation command.
Advanced concept[edit]
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 preresized object, but highlighting the postscaled object.
The text in its current form is incomplete. 
scale[edit]
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[edit]
resize() is available since OpenSCAD 2013.06. It modifies the size of the child object to match the given x,y, and z.
There is a bug with shrinking in the 2013.06 release, that will be fixed in the next release.
Usage Example:
// resize the sphere to extend 30 in x, 60 in y, and 10 in the z directions.
resize(newsize=[30,60,10]) sphere(r=10);
If x,y, or z is 0 then that dimension is left asis.
// resize the 1x1x1 cube to 2x2x1
resize([2,2,0]) cube();
If the 'auto' parameter is set to true, it will autoscale any 0dimensions 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 autoscale a single dimension, and leave the other asis.
// resize to 10x8x1. Note that the z dimension is left alone.
resize([10,0,0], auto=[true,true,false]) cube([5,4,1]);
rotate[edit]
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 upsidedown, 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[edit]
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[edit]
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[edit]
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:[edit]
mirror(v= [x, y, z] ) { ... }
Examples[edit]
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[edit]
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?[edit]
Learn more about it here:
color[edit]
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:[edit]
color( c = [r, g, b, a] ) { ... } color( c = [r, g, b], alpha = 1.0 ) { ... } color( "colorname", 1.0 ) { ... }
Note that the r, g, b, a
values are limited to floating point values in the range [0,1] rather than the more traditional integers { 0 ... 255 }. However, nothing prevents you to using R, G, B
values from {0 ... 255} with appropriate scaling: color([ R/255, G/255, B/255 ]) { ... }
Since version 2011.12, colors can also be defined by name (case insensitive). For example, to create a red sphere, you can write color("red") sphere(5);
. Alpha is specified as an extra parameter for named colors: color("Blue",0.5) cube(5);
The available color names are taken from the World Wide Web consortium's SVG color list. A chart of the color names is as follows,
(note that both spellings of grey/gray including slategrey/slategray etc are valid):





Example[edit]
Here's a code fragment that draws a wavy multicolor object
for(i=[0:36]) {
for(j=[0:36]) {
color( [0.5+sin(10*i)/2, 0.5+sin(10*j)/2, 0.5+sin(10*(i+j))/2] )
translate( [i, j, 0] )
cube( size = [1, 1, 11+10*cos(10*i)*sin(10*j)] );
}
}
↗ Being that 1<=sin(x)<=1 then 0<=(1/2 + sin(x)/2)<=1 , allowing for the RGB components assigned to color to remain within the [0,1] interval.
Chart based on "Web Colors" from Wikipedia
Example 2[edit]
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[edit]
[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 positiveoffset exterior and a negativeoffset 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).
Examples
// 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[edit]
Displays the minkowski sum of child nodes.
Usage example:
Say you have a flat box, and you want a rounded edge. There are many ways to do this, but minkowski is very elegant. Take your box, and a cylinder:
$fn=50;
cube([10,10,1]);
cylinder(r=2,h=1);
Then, do a minkowski sum of them (note that the outer dimensions of the box are now 10+2+2 = 14 units by 14 units by 2 units high as the heights of the objects are summed):
$fn=50;
minkowski()
{
cube([10,10,1]);
cylinder(r=2,h=1);
}
NB: The origin of the second object is used for the addition. If the second object is not centered, then the addition will be asymmetric. The following minkowski sums are different: the first expands the original cube by 0.5 units in all directions, both positive and negative. The second expands it by +1 in each positive direction, but doesn't expand in the negative directions.
minkowski() {
cube([10, 10, 1]);
cube(1, center=true);
}
minkowski() {
cube([10, 10, 1]);
cube(1);
}
hull[edit]
Displays the convex hull of child nodes.
Usage example:
hull() {
translate([15,10,0]) circle(10);
circle(10);
}
Combining transformations[edit]
When combining transformations, it is a sequential process, but going righttoleft. That is
rotate( ... ) translate ( ... ) cube(5) ;
would first move the cube, and then move in an arc (turning it the same amount) at the radius given by the translation.
translate ( ... ) rotate( ... ) cube(5) ;
would first turn the cube and place it at the offset defined by the translate.
color("red") translate([0,10,0] ) rotate([45,0,0]) cube(5); color("green") rotate([45,0,0]) translate([0,10,0] ) cube(5);
Chapter 5  Boolean combination[edit]
OpenSCAD User Manual/The OpenSCAD Language
The text in its current form is incomplete. 
boolean overview[edit]
2D examples[edit]
union() {square(10);circle(10);} // square or circle
difference() {square(10);circle(10);} // square and not circle
difference() {circle(10);square(10);} // circle and not square
intersection(){square(10);circle(10);} // square and circle
3D examples[edit]
union() {cube(12, center=true); sphere(8);} // cube or sphere
difference() {cube(12, center=true); sphere(8);} // cube and not sphere
difference() {sphere(8); cube(12, center=true);} // sphere and not cube
intersection(){cube(12, center=true); sphere(8);} // cube and sphere
union[edit]
Creates a union of all its child nodes. This is the sum of all children (logical or).
May be used with either 2D or 3D objects, but don't mix them.
//Usage example:
union() {
cylinder (h = 4, r=1, center = true, $fn=100);
rotate ([90,0,0]) cylinder (h = 4, r=0.9, center = true, $fn=100);
}
Remark: union is implicit when not used. But it is mandatory, for example, in difference to group first child nodes into one.
difference[edit]
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[edit]
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[edit]
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[edit]
Always calculate the CSG model for this tree (even in OpenCSG preview mode).
Usage example:
render(convexity = 1) { ... }
convexity  Integer. The convexity parameter specifies the maximum number of front and back sides a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode and has no effect on the polyhedron rendering. 
This image shows a 2D shape with a convexity of 4, as the ray indicated in red crosses the 2D shape a maximum of 4 times. The convexity of a 3D shape would be determined in a similar way. Setting it to 10 should work fine for most cases.
Chapter 6  Other Functions and Operators[edit]
OpenSCAD User Manual/The OpenSCAD Language
Conditional and Iterator Functions[edit]
For loop[edit]
Evaluate each value in a range or vector, applying it to the following Action.
for(variable = [start : increment : end]) for(variable = [start : end]) for(variable = [vector])
parameters
 As a range [ start : <increment : > end ] (see section on range)

 _{Note: For range, values are separated by colons rather than commas used in vectors.}
 start  initial value
 increment or step  amount to increase the value, optional, default = 1
 end  stop when next value would be past end

 As a vector
 The Action is evaluated for each element of the vector
 examples:
for (a =[3:5])echo(a); // 3 4 5 for (a =[3:0]){echo(a);} // 0 1 2 3 start < end is invalid, deprecated by 2015.3 for (a =[3:0.5:5])echo(a); // 3 3.5 4 4.5 5 for (a =[0:2:5])echo(a); // 0 2 4 a never equals end for (a =[3:2:1])echo(a); // 3 1 1 negative increment requires 2015.3 be sure end < start for (a =[3,4,1,5])echo(a); // 3 4 1 5 for (a =[0.3,PI,1,99]){echo(a);} // 0.3 3.14159 1 99 x1=2; x2=8; x3=5.5; for (a =[x1,x2,x3]){echo(a);} // 2 8 5.5 for (a =[[1,2],6,"s",[[3,4],[5,6]]])echo(a); // [1,2] 6 "s" [[3,4],[5,6]]
for() is an Operator. Operators require braces {} if more than one Action is within it scope. Actions end in semicolons, Operators do not.
for() is not an exception to the rule about variables having only one value within a scope. Each evaluation is given its own scope, allowing any variables to have unique values. No, you still can't do a=a+1;
Remember this is not an iterative language, the for() does not loop in the programmatic sense, it builds a tree of objects one branch for each item in the range/vector, inside each branch the 'variable' is a specific and separate instantiation or scope.
Hence:
for (i=[0:3]) translate([i*10,0,0]) cube(i+1);
Produces: _{[See Design/DisplayCSGTree 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>
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*510,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*510,z]){color(color_vec[y])cube();}
 Examples using vector of vectors
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  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  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[edit]
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);
}
}

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);
}

In
If Statement[edit]
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.
 test: Usually a boolean expression, but can be any value or variable.
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[edit]
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 ? :[edit]
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.

 test: Usually a boolean expression, but can be any value or variable.
This works like the ?: operator from the family of Clike 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[edit]
Recursive function calls are supported. Using the Conditional "... ? ... : ... " it's possible to ensure the recursion is terminated. Note: There is a builtin 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,i1,s)); vec=[ 10, 20, 30, 40 ]; echo("sum vec=", sumv(vec,2,1)); // calculates 20+30=50
Some forms of tailrecursion elimination are supported.
Assign Statement[edit]
Set variables to a new value for a subtree.
Since 2015.03 assign() is deprecated, as variables can now be assigned anywhere, see 2nd example below. If you prefer this way of setting values, the new Let Statement can be used instead.
 Parameters

 The variables that should be (re)assigned
 example:
for (i = [10:50])
{
assign (angle = i*360/20, distance = i*10, r = i*2)
{
rotate(angle, [1, 0, 0])
translate([0, distance, 0])
sphere(r = r);
}
}
for (i = [10:50])
{
angle = i*360/20;
distance = i*10;
r = i*2;
rotate(angle, [1, 0, 0])
translate([0, distance, 0])
sphere(r = r);
}
Let Statement[edit]
[Note: Requires version 2016.XX] (ie a development version)
Set variables to a new value for a subtree. 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[edit]
The text in its current form is incomplete. 
Scalar Arithmetical Operators[edit]
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[edit]
Relational operators produce a Boolean result from two operands.
<  less than 
<=  less equal 
==  equal 
!=  not equal 
>=  greater equal 
>  greater than 
If both operands are simple numbers, the meaning is selfevident.
If both operands are strings, alphabetical sorting determines equality and order. E.g., "ab" > "aa" > "a".
If both operands are Booleans, true > false. If one operand is Boolean, the other operand is converted to Boolean before the comparison is made.
If both operands are vectors, OpenSCAD performs an elementbyelement comparison and can only result in true if the vectors are equal in size and each and every pair of elements results in true upon the comparison. Otherwise, false is returned.
Vectors of different sizes are treated as unequal for '==' and '!=' operators, and always result in false for '>', '>=', '<' and '<=' operators. In fact the same principle applies for all comparison between dissimilar types of operand, e.g. comparing a string with a number.
Note that [1] ≠ 1.
undef doesn't equal anything but undef. undef compares ('>' etc.) anything result in false.
nan doesn't equal anything. See Numbers.
Logical Operators[edit]
All logical operators take Booleans as operands and produce a Boolean. NonBoolean 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[edit]
The ?: operator can be used to conditionally evaluate one or another expression. It works like the ?: operator from the family of Clike 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. 
VectorNumber Operators[edit]
The vectornumber 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[edit]
The vector operators take vectors as operands and produce a new vector.
+  add elementwise 
  subtract elementwise 
The "" can also be used as prefix operator to elementwise 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 DotProduct Operator[edit]
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 . If the operands' sizes don't match, the result is undef
.
Matrix Multiplication[edit]
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
.
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
.
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
.
In linear algebra, this is the product of a row vector and a matrix.
Matrix multiplication is not commutative: , .
Mathematical Functions[edit]
The text in its current form is incomplete. 
Trigonometric Functions[edit]
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[edit]
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);

sin[edit]
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);

tan[edit]
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[edit]
Mathematical arccosine, or inverse cosine, expressed in degrees. See: Inverse trigonometric functions
asin[edit]
Mathematical arcsine, or inverse sine, expressed in degrees. See: Inverse trigonometric functions
atan[edit]
Mathematical arctangent, or inverse tangent, function. Returns the principal value of the arc tangent of x, expressed in degrees. See: Inverse trigonometric functions
atan2[edit]
Mathematical twoargument 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[edit]
abs[edit]
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[edit]
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[edit]
[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[edit]
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[edit]
Mathematical exp function. Returns the basee 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[edit]
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[edit]
Mathematical natural logarithm. See: Natural logarithm
len[edit]
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[edit]
[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[edit]
Mathematical logarithm to the base 10. Example: log(1000) = 3. See: Logarithm
lookup[edit]
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 keyvalue pairs.
Parameters
 key
 A lookup key
 <key,value> array
 keys and values
Notes
There is a bug where outofrange 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:


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);
}

max[edit]
Returns the maximum of the parameters. If a single vector is given as parameter, returns the maximum element of that vector.
Parameters
max(n,n{,n}...) max(vector)
 <n>
 Two or more decimals
 <vector>
 Single vector of decimals (requires OpenSCAD version 2014.06 or later).
Usage Example:
max(3.0,5.0) max(8.0,3.0,4.0,5.0) max([8,3,4,5])
Results:
5 8 8
min[edit]
Returns the minimum of the parameters. If a single vector is given as parameter, returns the minimum element of that vector.
Parameters
min(n,n{,n}...) min(vector)
 <n>
 Two or more decimals
 <vector>
 Single vector of decimals (requires OpenSCAD version 2014.06 or later).
Usage Example:
min(3.0,5.0) min(8.0,3.0,4.0,5.0) min([8,3,4,5])
Results:
3 3 3
Looking for mod  it's not a function, see modulo operator (%)
norm[edit]
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[edit]
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[edit]
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[edit]
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[edit]
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[edit]
Mathematical square root function.
Usage Examples:
translate([sqrt(100),0,0])sphere(100);
Infinities and NaNs[edit]
How does OpenSCAD deal with inputs like (1/0)? Basically, the behavior is inherited from the language OpenSCAD was written in, the C++ language and it's floating point number types and the associated C math library. This system allows representation of both positive and negative infinity by the special values "Inf" or "Inf". It also allow representation of creatures like sqrt(1) or 0/0 as "NaN", an abbreviation for "Not A Number". Some very nice explanations can be found on the web, for example the Open Group's site on math.h or Wikipedia's page on the IEEE 754 number format. However OpenSCAD is it's own language so it may not exactly match everything that happens in C. For example, OpenSCAD uses degrees instead of radians for trigonometric functions. Another example is that sin() does not throw a "domain error" when the input is 1/0, although it does return NaN.
Here are some examples of infinite input to OpenSCAD math functions and the resulting output, taken from OpenSCAD's regression test system in late 2015.
0/0: nan  sin(1/0): nan  asin(1/0): nan  ln(1/0): inf  round(1/0): inf 
0/0: nan  cos(1/0): nan  acos(1/0): nan  ln(1/0): nan  round(1/0): inf 
0/0: nan  tan(1/0): nan  atan(1/0): 90  log(1/0): inf  sign(1/0): 1 
1/0: inf  ceil(1/0): inf  atan(1/0): 90  log(1/0): nan  sign(1/0): 1 
1/0: inf  ceil(1/0): inf  atan2(1/0, 1/0): 135  max(1/0, 1/0): inf  sqrt(1/0): inf 
1/0: inf  floor(1/0): inf  exp(1/0): inf  min(1/0, 1/0): inf  sqrt(1/0): nan 
1/0: inf  floor(1/0): inf  exp(1/0): 0  pow(2, 1/0): inf  pow(2, 1/0): 0 
String Functions[edit]
The text in its current form is incomplete. 
str[edit]
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[edit]
[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 UTF8 encoding) if the code point is valid.
 chr(Vector)
 Convert all code points given in the argument vector to a string.
 chr(Range)
 Convert all code points produced by the range argument to a string.
Examples
echo(chr(65), chr(97)); // ECHO: "A", "a"
echo(chr(65, 97)); // ECHO: "Aa"
echo(chr([66, 98])); // ECHO: "Bb"
echo(chr([97 : 2 : 102])); // ECHO: "ace"
echo(chr(3)); // ECHO: ""
echo(chr(9786), chr(9788)); // ECHO: "☺", "☼"
echo(len(chr(9788))); // ECHO: 1
Note: When used with echo() the output to the console for character codes greater than 127 is platform dependent.
Also See search()[edit]
search() for text searching.
List Comprehensions[edit]
The text in its current form is incomplete. 
[Note: Requires version 2015.03]
Basic Syntax[edit]
The list comprehensions provide a flexible way to generate lists using the general syntax
[ listdefinition expression ]
The following elements are supported to construct the list definition
 for (i = sequence)
 Iteration over a range or an existing list
 if (condition)
 Selection criteria, when true the expression will be calculated and added to the result list
 let (x = value)
 Local variable assignment
for[edit]
The for element defines the input values for the list generation, the syntax is the same as used by the for iterator.
 [ for (i = [start : step : end]) i ]
 Generate output based on a range definition, this version is mainly useful to calculate list values or access existing lists using the range value as index.
Examples
// generate a list with all values defined by a range
list1 = [ for (i = [0 : 2 : 10]) i ];
echo(list1); // ECHO: [0, 2, 4, 6, 8, 10]
// extract every second character of a string
str = "SomeText";
list2 = [ for (i = [0 : 2 : len(str)  1]) str[i] ];
echo(list2); // ECHO: ["S", "m", "T", "x"]
// indexed list access, using function to map input values to output values
function func(x) = x < 1 ? 0 : x + func(x  1);
input = [1, 3, 5, 8];
output = [for (a = [ 0 : len(input)  1 ]) func(input[a]) ];
echo(output); // ECHO: [1, 6, 15, 36]
 [ for (i = [a, b, c, ...]) i ]
 Use list parameter as input, this version can be used to map input values to calculated output values.
Examples
// map input list to output list
list = [ for (i = [2, 3, 5, 7, 11]) i * i ];
echo(list); // ECHO: [4, 9, 25, 49, 121]
// calculate Fibonacci numbers
function func(x) = x < 3 ? 1 : func(x  1) + func(x  2);
input = [7, 10, 12];
output = [for (a = input) func(a) ];
echo(output); // ECHO: [13, 55, 144]
if[edit]
The if element allows selection if the expression should be allocated and added to the result list or not. In the simplest case this allows filtering of an list.
 [ for (i = list) if (condition(i)) i ]
 When the evaluation of the condition returns true, the expression i is added to the result list.
Example
list = [ for (a = [ 1 : 8 ]) if (a % 2 == 0) a ];
echo(list); // ECHO: [2, 4, 6, 8]
Note that the if element cannot be inside an expression, it should be at the top.
Example
// from the input list include all positive odd numbers
// and also all even number divided by 2
list = [10:5];
echo([for(n=list) if(n%2==0  n>=0) n%2==0 ? n/2 : n ]);
// ECHO: [5, 4, 3, 2, 1, 0, 1, 1, 3, 2, 5]
// echo([for(n=list) n%2==0 ? n/2 : if(n>=0) n ]); // this would generate a syntactical error
let[edit]
The let element allows sequential assignment of variables inside a list comprehension definition.
 [ for (i = list) let (assignments) a ]
Example
list = [ for (a = [ 1 : 4 ]) let (b = a*a, c = 2 * b) [ a, b, c ] ];
echo(list); // ECHO: [[1, 1, 2], [2, 4, 8], [3, 9, 18], [4, 16, 32]]
Nested loops[edit]
There are different ways to define nested loops. Defining multiple loop variables inside one for element and multiple for elements produce both flat result lists. To generate nested result lists an additional [ ] markup is required.
// nested loop using multiple variables
flat_result1 = [ for (a = [ 0 : 2 ], b = [ 0 : 2 ]) a == b ? 1 : 0 ];
echo(flat_result1); // ECHO: [1, 0, 0, 0, 1, 0, 0, 0, 1]
// nested loop using multiple for elements
flat_result2 = [ for (a = [ 0 : 2 ]) for (b = [0 : 2]) a == b ? 1 : 0 ];
echo(flat_result2); // ECHO: [1, 0, 0, 0, 1, 0, 0, 0, 1]
// nested loop to generate a bidimensional matrix
identity_matrix = [ for (a = [ 0 : 2 ]) [ for (b = [ 0 : 2 ]) a == b ? 1 : 0 ] ];
echo(identity_matrix); // ECHO: [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
Advanced Examples[edit]
This chapter lists some advanced examples, useful idioms and usecases for the list comprehension syntax.
Generating vertices for a polygon[edit]
Using list comprehension, a parametric equation can be calculated at a number of points to approximate many curves, such as the following example for an ellipse (using polygon()):
sma = 20; // semiminor axis
smb = 30; // semimajor axis
polygon(
[ for (a = [0 : 5 : 359]) [ sma * sin(a), smb * cos(a) ] ]
);
Flattening a nested vector[edit]
List comprehension can be used in a userdefined function to perform tasks on or for vectors. Here is a userdefined function that flattens a nested vector.
// input : nested list
// output : list with the outer level nesting removed
function flatten(l) = [ for (a = l) for (b = a) b ] ;
nested_list = [ [ 1, 2, 3 ], [ 4, 5, 6 ] ];
echo(flatten(nested_list)); // ECHO: [1, 2, 3, 4, 5, 6]
Sorting a vector[edit]
Even a complicated algorithm Quicksort becomes doable with for(), if(), let() and recursion:
// input : list of numbers
// output : sorted list of numbers
function quicksort(arr) = !(len(arr)>0) ? [] : let(
pivot = arr[floor(len(arr)/2)],
lesser = [ for (y = arr) if (y < pivot) y ],
equal = [ for (y = arr) if (y == pivot) y ],
greater = [ for (y = arr) if (y > pivot) y ]
) concat(
quicksort(lesser), equal, quicksort(greater)
);
// use seed in rands() to get reproducible results
unsorted = [for (a = rands(0, 10, 6, 3)) ceil(a)];
echo(unsorted); // ECHO: [6, 1, 8, 9, 3, 2]
echo(quicksort(unsorted)); // ECHO: [1, 2, 3, 6, 8, 9]
Selecting elements of a vector[edit]
select() performs selection and reordering of elements into a new vector.
function select(vector,indices) = [ for (index = indices) vector[index] ];
vector1 = [[0,0],[1,1],[2,2],[3,3],[4,4]];
selector1 = [4,0,3];
vector2 = select(vector1,selector1); // [[4, 4], [0, 0], [3, 3]]
vector3 = select(vector1,[0,2,4,4,2,0]);// [[0, 0], [2, 2], [4, 4],[4, 4], [2, 2], [0, 0]]
// range also works as indices
vector4 = select(vector1, [4:1:0]); // [[4, 4], [3, 3], [2, 2], [1, 1], [0, 0]]
Concatenating two vectors[edit]
Using indices:
function cat(L1, L2) = [for (i=[0:len(L1)+len(L2)1])
i < len(L1)? L1[i] : L2[ilen(L1)]] ;
echo(cat([1,2,3],[4,5])); //concatenates two OpenSCAD lists [1,2,3] and [4,5], giving [1, 2, 3, 4, 5]
Without using indices:
function cat(L1, L2) = [for(L=[L1, L2], a=L) a];
echo(cat([1,2,3],[4,5])); //concatenates two OpenSCAD lists [1,2,3] and [4,5], giving [1, 2, 3, 4, 5]
Other Language Features[edit]
The text in its current form is incomplete. 
Special variables[edit]
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.
Several special variables are already defined by OpenSCAD.
$fa, $fs and $fn[edit]
The $fa, $fs and $fn special variables control the number of facets used to generate an arc:
$fa is the minimum angle for a fragment. Even a huge circle does not have more fragments than 360 divided by this number. The default value is 12 (i.e. 30 fragments for a full circle). The minimum allowed value is 0.01. Any attempt to set a lower value will cause a warning.
$fs is the minimum size of a fragment. Because of this variable very small circles have a smaller number of fragments than specified using $fa. The default value is 2. The minimum allowed value is 0.01. Any attempt to set a lower value will cause a warning.
$fn is usually 0. When this variable has a value greater than zero, the other two variables are ignored and full circle is rendered using this number of fragments. The default value is 0.
The higher the number of fragments, the more memory and CPU consumed, large values will bring many systems to their knees. Depending on the design, $fn values, and the corresponding results of $fa & $fs, should be kept small, at least until the design is finalised when it can be increased for the final result. A $fn over 100 is not recommended or only for specific circumstances, and below 50 would be advisable for performance.
TIP: If you want to create a circle/cylinder/sphere which has a axis aligned integer bounding box (i.e. a bounding box that has integral dimensions, and an integral position) use a value of $fn that is divisible by 4.
When $fa and $fs are used to determine the number of fragments for a circle, then OpenSCAD will never use fewer than 5 fragments.
This is the C code that calculates the number of fragments in a circle:
int get_fragments_from_r(double r, double fn, double fs, double fa) { if (r < GRID_FINE) return 3; if (fn > 0.0) return (int)(fn >= 3 ? fn : 3); return (int)ceil(fmax(fmin(360.0 / fa, r*2*M_PI / fs), 5)); }
Spheres are first sliced into as many slices as the number of fragments being used to render a circle of the sphere's radius, and then every slice is rendered into as many fragments as are needed for the slice radius. You might have recognized already that the pole of a sphere is usually a pentagon. This is why.
The number of fragments for a cylinder is determined using the greater of the two radii.
The method is also used when rendering circles and arcs from DXF files. The variables have no effect when importing STL files.
You can generate high resolution spheres by resetting the $fX values in the instantiating module:
$fs = 0.01; sphere(2);
or simply by passing the special variable as parameter:
sphere(2, $fs = 0.01);
You can even scale the special variable instead of resetting it:
sphere(2, $fs = $fs * 0.01);
$t[edit]
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=11/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=13/Steps filename="frame<Steps2>.png"
 $t=12/Steps filename="frame<Steps1>.png"
 $t=11/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=13/Steps filename="frame<Steps2>.png"
 $t=12/Steps filename="frame<Steps1>.png"
 $t=11/Steps filename="frame<Steps0>.png"
 $t=10/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[edit]
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 toplevel of the main file will have an effect on the viewport. [Note: Requires version 2015.03]
Example
$vpr = [0, 0, $t * 360];
which allows a simple 360 degree rotation around the Z axis in animation mode.
The menu command Edit  Paste Viewport Rotation/Translation copies the current value of the viewport, but not the current $vpr or $vpt.
Echo Statements[edit]
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[edit]
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!"
Rounding examples[edit]
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[edit]
c=1000002;
d=0.000002;
echo(c); //1e+06
echo(d); //2e06
HTML[edit]
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.
Render[edit]
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[edit]
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 Yaxis. 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[edit]
The format for text based heightmaps is a matrix of numbers that represent the height for a specific point. Rows are mapped to the Yaxis, 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[edit]
[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[edit]
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);
Example 4:
[Note: Requires version 2015.03]
// Example 4 surface(file = "BRGYGrey.png", center = true, invert = false);
Search[edit]
The search() function is a generalpurpose function to find one or more (or all) occurrences of a value or list of values in a vector, string or more complex listoflist construct.
Search Usage[edit]
 search( match_value , string_or_vector [, num_returns_per_match [, index_col_num ] ] );
Search Arguments[edit]
 match_value

 Can be a single value or vector of values.
 Strings are treated as vectorsofcharacters to iterate over; the search function does not search for substrings.
 Note: If match_value is a vector of strings, search will look for exact string matches.

 See Example 9 below.
 string_or_vector

 The string or vector to search for matches.
 num_returns_per_match (default: 1)

 By default, search only looks for one match per element of match_value to return as a list of indices
 If num_returns_per_match > 1, search returns a list of lists of up to num_returns_per_match index values for each element of match_value.

 See Example 8 below.
 If num_returns_per_match = 0, search returns a list of lists of all matching index values for each element of match_value.

 See Example 6 below.
 index_col_num (default: 0)

 When string_or_vector is a vectorofvectors, multidimensional table or more complex listoflists construct, the match_value may not be found in the first (index_col_num=0) column.
 See Example 5 below for a simple usage example.
Search Usage Examples[edit]
 See example023.scad included with OpenSCAD for a renderable example.
Index values return as list[edit]
Example  Code  Result 

1 

[0] 
2 

[] 
3 

[[0,4]] 
4 

[[0,4]] (see also Example 6 below) 
Search on different column; return Index values[edit]
Example 5:
data= [ ["a",1],["b",2],["c",3],["d",4],["a",5],["b",6],["c",7],["d",8],["e",3] ]; search(3, data, num_returns_per_match=0, index_col_num=1);
Returns:
[2,8]
Search on list of values[edit]
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[edit]
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[edit]
// 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]][0]); // "d" not found > undef echo(v[search("D",v,1,0)[0]][1]); // > 8
OpenSCAD Version[edit]
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[edit]
$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[edit]
[Note: Requires version 2017.01 Experimental Build]
see also Assertion (software development)
Assert evaluates a logical expression. If the logical expression evaluates to false, the generation of the preview/render is stopped with an error.
Assertion can be used for e.g. in modules to make sure, that the parameters are valid.
Currently (2017.01 Experimental Build), OpenSCAD does not output the file name in which the assertion failed. This can be an issue when writing libraries. (see Issue #1910)
failing example[edit]
The simplest example is a simple assert(false);
.
Source Code  Console output 

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

Compiling design (CSG Tree generation)...
ERROR: Assertion 'false' failed, line 2
Compiling design (CSG Products generation)...
Geometries in cache: 0
Geometry cache size in bytes: 0
CGAL Polyhedrons in cache: 0
CGAL cache size in bytes: 0
Compiling design (CSG Products normalization)...
Normalized CSG tree has 0 elements
Compile and preview finished.
Total rendering time: 0 hours, 0 minutes, 0 seconds

This example has little use, but the simple assert(false);
has.
assert(false);
can be used in code sections that should be unreachable.
checking parameters[edit]
A useful example is checking the validity of input parameters:
module row(cnt=1){
assert(cnt>0); //Error: Count has to be a positive integer greater 0
for(i = [1 : cnt]){
translate([i*2,0,0])sphere();
}
}
row(2);
combining assert with echo[edit]
If you write a library containing modules, it could be useful to output additional information to the user in case of an failed assertion. This can be done by using echo.
module row(cnt=1){
if(cnt<=0){
echo("<font color='red'>Error: Count has to be a positive integer greater 0</font>");
assert(false);
}
for(i = [1 : cnt]){
translate([i*2,0,0])sphere();
}
}
cube();
row(0);
assert vs. echo[edit]
The benefit of using assert over echo are:
 assert stops the execution, forcing the user to resolve the issue
Benefit of echo over assert:
 with echo, you (for e.g. as library creator) can output a meaning full error message
Chapter 7  UserDefined Functions and Modules[edit]
OpenSCAD User Manual/The OpenSCAD Language
Introduction[edit]
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 compiletime, not runtime. 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 overrideable constants rather than as variables.
For functions and modules OpenSCAD makes copies of pertinent portions of the script for each use. Each copy has its own scope, which contains fixed values for variables and expressions unique to that instance.
The name of functions and modules is case sensitive, therefore test() and TEST() refer to different functions/modules.
Functions[edit]
Functions operate on values to calculate and return new values.
 function definition
function name ( parameters ) = value ;

 name
 Your name for this function. A meaningful name is helpful later.
 parameters
 Zero or more arguments. Parameters can be assigned default values, to use in case they are omitted in the call. Parameter names are local and do not conflict with external variables of the same name.
 value
 an expression which calculates a value. This value can be a vector.
 name
 function use

 When used, functions are treated as values, and do not themselves end with a semicolon ';'.

//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:(endstart)/(no_steps1):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 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[edit]
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(n1) );
There is a builtin 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 tailrecursive 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 tailrecursion elimination:
// tailrecursion elimination example: add all integers up to n
function add_up_to(n, sum=0) =
n==0 ?
sum :
add_up_to(n1, sum+n);
echo(sum=add_up_to(100000));
// ECHO: sum = 5.00005e+009
Tailrecursion elimination allows much higher recursion limits.
Modules[edit]
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.
 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.
 actions
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[edit]
Object modules use one or more primitives, with associated operators, to define new objects.
In use, object modules are actions ending with a semicolon ';'.
name ( parameter values );
//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[range1][0];
color( ColorBreak[range][1] )
translate([10*period,0,RangeLo])
if (value > RangeHi) cube([5,2,RangeHiRangeLo]);
else if (value > RangeLo) cube([5,2,valueRangeLo]);
}
module ShowColorBars(values){
for (month = [0:len(values)1], range = [1:len(ColorBreak)1])
ColorBar(values[month],month,range);
}
//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[edit]
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 semicolon.
name ( parameter values ){scope of operator}
Children[edit]
Objects are indexed via integers from 0 to $children1. OpenSCAD sets $children to the total number of objects within the scope. Objects grouped into a sub scope are treated as one child. See example of separate children below and Scope of variables.
children(); all children children(index); value or variable to select one child children([start : step : end]); select from start to end incremented by step children([start : end]); step defaults to 1 or 1 children([vector]); selection of several children
Deprecated child() module
Up to release 2013.06 the now deprecated child()
module was used instead. This can be translated to the new children() according to the table:
up to 2013.06  2014.03 and later 

child()  children(0) 
child(x)  children(x) 
for (a = [0:$children1]) child(a)  children([0:$children1]) 
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
module lineup(num, space) {
for (i = [0 : num1])
translate([ space*i, 0, 0 ]) children(0);
}
lineup(5, 65){ sphere(30);cube(35);}
//Separate action for each child
module SeparateChildren(space){
for ( i= [0:1:$children1]) // step needed in case $children < 2
translate([i*space,0,0]) {children(i);text(str(i));}
}
SeparateChildren(20){
cube(5); // 0
sphere(5); // 1
translate([0,20,0]){ // 2
cube(5);
sphere(5);
}
cylinder(15); // 3
cube(8,true); // 4
}
translate([0,40,0])color("lightblue")
SeparateChildren(20){cube(3,true);}
//Multiple ranges
module MultiRange(){
color("lightblue") children([0:1]);
color("lightgreen")children([2:$children2]);
color("lightpink") children($children1);
}
MultiRange()
{
cube(5); // 0
sphere(5); // 1
translate([0,20,0]){ // 2
cube(5);
sphere(5);
}
cylinder(15); // 3
cube(8,true); // 4
}
Further Module Examples[edit]
 Objects
module arrow(){
cylinder(10);
cube([4,.5,3],true);
cube([.5,4,3],true);
translate([0,0,10]) cylinder(4,2,0,true);
}
module cannon(){
difference(){union()
{sphere(10);cylinder(40,10,8);} cylinder(41,4,4);
} }
module base(){
difference(){
cube([40,30,20],true);
translate([0,0,5]) cube([50,20,15],true);
} }
 Operators
module aim(elevation,azimuth=0)
{ rotate([0,0,azimuth])
{ rotate([0,90elevation,0]) children(0);
children([1:1:$children1]); // step needed in case $children < 2
} }
aim(30,20)arrow();
aim(35,270)cannon();
aim(15){cannon();base();}
module RotaryCluster(radius=30,number=8)
for (azimuth =[0:360/number:359])
rotate([0,0,azimuth])
translate([radius,0,0]) { children();
translate([40,0,30]) text(str(azimuth)); }
RotaryCluster(200,7) color("lightgreen") aim(15){cannon();base();}
rotate([0,0,110]) RotaryCluster(100,4.5) aim(35)cannon();
color("LightBlue")aim(55,30){cannon();base();}
Recursive Modules[edit]
Like functions, modules may contain recursive calls. However, there is no tailrecursion 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.
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, n1);
}
}
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 builtin modules[edit]
It is possible to overwrite the builtin modules.
A simple, but pointless example would be:
module sphere(){
square();
}
sphere();
Note that the builtin 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 2Dprimitives. This allows additional to customize the default parameters and to add additional parameters.
Overwriting builtin functions[edit]
It is possible to overwrite the builtin 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)...

Chapter 8  Debugging aids[edit]
OpenSCAD User Manual/The OpenSCAD Language
The text in its current form is incomplete. 
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.
Advanced concept[edit]
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 preresized object, but highlighting the postscaled 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[edit]
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
Debug Modifier[edit]
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
Root Modifier[edit]
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
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[edit]
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
The disable modifier allows to comment out one or multiple subtrees. Compared to using the usual line or multiline 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[edit]
This function prints the contents to the compilation window (aka Console). Useful for debugging code. Also see the String function str().
Numeric values are rounded to 5 significant digits.
The OpenSCAD console supports a subset of HTML markup language. See here for details.
It can be handy to use 'variable=variable' as the expression to easily label the variables, see the example below.
Usage examples:
my_h=50; my_r=100; echo("This is a cylinder with h=", my_h, " and r=", my_r); echo(my_h=my_h,my_r=my_r); // shortcut cylinder(h=my_h, r=my_r); // echo("<b>Hello</b> <i>Qt!</i>");
Shows in the Console as
ECHO: "This is a cylinder with h=", 50, " and r=", 100 ECHO: my_h = 50, my_r = 100 ECHO: "Hello Qt!"
Chapter 9  External libraries and code files[edit]
OpenSCAD User Manual/The OpenSCAD Language
Use and Include[edit]
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, anduse <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[edit]
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[edit]
Scope of variables[edit]
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[edit]
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 "RingLibrary"[edit]
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[edit]
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.
The text in its current form is incomplete. 
import[edit]
Imports a file for use in the current OpenSCAD model. OpenSCAD currently supports import of DXF, OFF and STL (both ASCII and Binary) files.
NOTE: The file extension is used to determine which type.
OpenSCAD can export files as STL, OFF, AMF, DXF, SVG, CSG OR PNG(Image). These file types created by OpenSCAD, or others, can be imported as follows: STL, OFF and DXF are imported using import(). CSG can be imported using include<> or loaded like an SCAD file PNG can be imported using surface() There are open pull requests for SVG and AMF, which require a bit more work/testing. The file suffix is used to determine type.
Parameters
 <file>
 A string containing the path to the STL, OFF or DXF file.
 <convexity>
 An Integer. The convexity parameter specifies the maximum number of front sides (back sides) a ray intersecting the object might penetrate. This parameter is only needed for correctly displaying the object in OpenCSG preview mode and has no effect on the polyhedron rendering.
import("example012.stl", convexity=3); import("D:\\Documents and Settings\\User\\My Documents\\Gear.stl", convexity=3); (Windows users must "escape" the backslashes by writing them doubled.)
Convexity[edit]
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[edit]
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 selfintersections. 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/i686pcmingw32/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/i686pcmingw32/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/SemiAutomatic_Repair_Options . This will repair the holes but not the selfintersections.
 use netfabb basic. This free software doesnt have the option to close holes nor can it fix the selfintersections
 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:
 Start Blender
 `X, 1` to remove the default object
 File, Import, Stl
 `Tab` to edit the mesh
 `A` to deselect all vertices
 `Alt+Ctrl+Shift+M` to select all nonmanifold vertices
 `MMB` to rotate, `Shift+MMB` to pan, `wheel` to zoom
 `C` for "circle" select, `Esc` to finish
 `Alt+M, 1` to merge or `Space` and search for "merge" as alternative
 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[edit]
DEPRECATED: Will be removed in future releases. Use import() instead.
Read a DXF file and create a 2D shape.
linear_extrude(height = 5, center = true, convexity = 10) import_dxf(file = "example009.dxf", layer = "plate");
import_stl[edit]
DEPRECATED: 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[edit]
Surface reads Heightmap information from text or image files. Surface can read PNG files.
Parameters
 file
 String. The path to the file containing the heightmap data.
 center
 Boolean. This determines the positioning of the generated object. If true, object is centered in X and Yaxis. 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[edit]
The format for text based heightmaps is a matrix of numbers that represent the height for a specific point. Rows are mapped to the Yaxis, 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[edit]
[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[edit]
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);