OpenSCAD User Manual/Transformations
Contents
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 commands like translate, mirror and scale as verbs. Commands like color are like adjectives that describe the object.
Notice that there is no semicolon following transformation command.
Advanced concept[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.
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]
Modifies the size of the child object to match the given x,y, and z.
resize() is a CGAL operation, and like others such as render() operates with full geometry, so even in preview will take time to process.
Usage Example:
// resize the sphere to extend 30 in x, 60 in y, and 10 in the z directions.
resize(newsize=[30,60,10]) sphere(r=10);
If x,y, or z is 0 then that dimension is left 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 or 4x3 affine transformation matrix, where the matrix is a vector of 3 row vectors with 4 elements each.
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]  [Shear X along Y]  [Shear X along Z]  [Translate X] 
[Shear Y along X]  [Scale Y]  [Shear Y along Z]  [Translate Y] 
[Shear Z along X]  [Shear Z along Y]  [Scale Z]  [Translate Z] 
the fourth row is an implicit [0,0,0,1] and can be omitted unless you are combining matrices before passing to multmatrix, as it is not processed in OpenSCAD. Each matrix operates on the points of the given geometry as if each vertex is a 4 element vector consisting of a 3D vector with an implicit 1 as its 4th element, such as v=[x, y, z, 1]. The role of the implicit fourth row of m is to preserve the implicit 1 in the 4th element of the vectors, permitting the translations to work. The operation of multmatrix therefore performs m*v for each vertex v. Any elements (other than the 4th row) not specified in m are treated as zeros.
This example rotates by 45 degrees in the XY plane and translates by [10,20,30], i.e. 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);
}
The following example demonstrates combining affine transformation matrices by matrix multiplication, producing in the final version a transformation equivalent to rotate([0, 35, 0]) translate([40, 0, 0]) Obj();. Note that the signs on the sin function appear to be in a different order than the above example, because the positive one must be ordered as x into y, y into z, z into x for the rotation angles to correspond to rotation about the other axis in a righthanded coordinate system.
ang=35;
mrot_y = [ [ cos(y_ang), 0, sin(y_ang), 0],
[ 0, 1, 0, 0],
[sin(y_ang), 0, cos(y_ang), 0],
[ 0, 0, 0, 1]
];
mtrans_x = [ [1, 0, 0, 40],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]
];
module Obj() {
cylinder(r=10.0,h=10,center=false);
cube(size=[10,10,10],center=false);
}
echo(mrot_y*mtrans_x);
Obj();
multmatrix(mtrans_x) Obj();
multmatrix(mrot_y * mtrans_x) Obj();
This example skews a model, which is not possible with the other transformations.
M = [ [ 1 , 0 , 0 , 0 ],
[ 0 , 1 , 0.7, 0 ], // The "0.7" is the skew value; pushed along the y axis as z changes.
[ 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( "#hexvalue" ) { ... } color( "colorname", 1.0 ) { ... }
Note that the r, g, b, a
values are limited to floating point values in the range [0,1] rather than the more traditional integers { 0 ... 255 }. However, nothing prevents you to using R, G, B
values from {0 ... 255} with appropriate scaling: color([ R/255, G/255, B/255 ]) { ... }
[Note: Requires version 2011.12]
Colors can also be defined by name (case insensitive). For example, to create a red sphere, you can write color("red") sphere(5);
. Alpha is specified as an extra parameter for named colors: color("Blue",0.5) cube(5);
[Note: Requires version 2019.05]
Hex values can be given in 4 formats, #rgb
, #rgba
, #rrggbb
and #rrggbbaa
. If the alpha value is given in both the hex value and as sparate alpha parameter, the alpha parameter will take precedence.
The available color names are taken from the World Wide Web consortium's SVG color list. A chart of the color names is as follows,
(note that both spellings of grey/gray including slategrey/slategray etc are valid):





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 multiple ways to do this (for example, see hull below), but minkowski is 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]);
cylinder(1, center=true);
}
minkowski() {
cube([10, 10, 1]);
cylinder(1);
}
hull[edit]
Displays the convex hull of child nodes.
Usage example:
hull() {
translate([15,10,0]) circle(10);
circle(10);
}
Hull with 2D arguments can only produce a 2D result; translating the constituent 2D parts in the Z direction has no effect.
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);