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Tutorial Transforms

Adrian Mariano edited this page Aug 26, 2026 · 1 revision

Transforms Tutorial

Translation

The translate() command is very simple:

include <BOSL2/std.scad>
#sphere(d=20);
translate([0,0,30]) sphere(d=20);

Figure 1

But at a glance, or when the formula to calculate the move is complex, it can be difficult to see just what axis is being moved along, and in which direction. It's also a bit verbose for such a frequently used command. For these reasons, BOSL2 provides you with shortcuts for each direction. These shortcuts are up(), down(), fwd(), back(), left(), and right():

include <BOSL2/std.scad>
#sphere(d=20);
up(30) sphere(d=20);

Figure 2

include <BOSL2/std.scad>
#sphere(d=20);
down(30) sphere(d=20);

Figure 3

include <BOSL2/std.scad>
#sphere(d=20);
fwd(30) sphere(d=20);

Figure 4

include <BOSL2/std.scad>
#sphere(d=20);
back(30) sphere(d=20);

Figure 5

include <BOSL2/std.scad>
#sphere(d=20);
left(30) sphere(d=20);

Figure 6

include <BOSL2/std.scad>
#sphere(d=20);
right(30) sphere(d=20);

Figure 7

There is also a more generic move() command that can work just like translate():

include <BOSL2/std.scad>
#sphere(d=20);
move([30,-10]) sphere(d=20);

Figure 8

Scaling

The scale() command is also fairly simple:

include <BOSL2/std.scad>
scale(2) cube(10, center=true);

Figure 9

include <BOSL2/std.scad>
scale([1,2,3]) cube(10, center=true);

Figure 10

If you want to only change the scaling on one axis, though, BOSL2 provides clearer commands to do just that; xscale(), yscale(), and zscale():

include <BOSL2/std.scad>
xscale(2) cube(10, center=true);

Figure 11

include <BOSL2/std.scad>
yscale(2) cube(10, center=true);

Figure 12

include <BOSL2/std.scad>
zscale(2) cube(10, center=true);

Figure 13

Rotation

The rotate() command is fairly straightforward:

include <BOSL2/std.scad>
rotate([0,30,0]) cube(20, center=true);

Figure 14

It is also a bit verbose, and can, at a glance, be difficult to tell just how it is rotating. BOSL2 provides shortcuts for rotating around each axis, for clarity; xrot(), yrot(), and zrot():

include <BOSL2/std.scad>
xrot(30) cube(20, center=true);

Figure 15

include <BOSL2/std.scad>
yrot(30) cube(20, center=true);

Figure 16

include <BOSL2/std.scad>
zrot(30) cube(20, center=true);

Figure 17

The rot() command is a more generic rotation command, and shorter to type than rotate():

include <BOSL2/std.scad>
rot([0,30,15]) cube(20, center=true);

Figure 18

All of the rotation shortcuts can take a cp= argument, that lets you specify a centerpoint to rotate around:

include <BOSL2/std.scad>
cp = [0,0,40];
color("blue") move(cp) sphere(d=3);
#cube(20, center=true);
xrot(45, cp=cp) cube(20, center=true);

Figure 19

include <BOSL2/std.scad>
cp = [0,0,40];
color("blue") move(cp) sphere(d=3);
#cube(20, center=true);
yrot(45, cp=cp) cube(20, center=true);

Figure 20

include <BOSL2/std.scad>
cp = [0,40,0];
color("blue") move(cp) sphere(d=3);
#cube(20, center=true);
zrot(45, cp=cp) cube(20, center=true);

Figure 21

You can also do a new trick with it. You can rotate from pointing in one direction, towards another. You give these directions using vectors:

include <BOSL2/std.scad>
#cylinder(d=10, h=50);
rot(from=[0,0,1], to=[1,0,1]) cylinder(d=10, h=50);

Figure 22

There are several direction vectors constants and aliases you can use for clarity:

Constant Value Direction
CENTER, CTR [ 0, 0, 0] Centered
LEFT [-1, 0, 0] Towards X-
RIGHT [ 1, 0, 0] Towards X+
FWD, FORWARD, FRONT [ 0,-1, 0] Towards Y-
BACK [ 0, 1, 0] Towards Y+
DOWN, BOTTOM, BOT [ 0, 0,-1] Towards Z-
UP, TOP [ 0, 0, 1] Towards Z+

This lets you rewrite the above vector rotation more clearly as:

include <BOSL2/std.scad>
#cylinder(d=10, h=50);
rot(from=UP, to=UP+RIGHT) cylinder(d=10, h=50);

Figure 23

Mirroring

The standard mirror() command works like this:

include <BOSL2/std.scad>
#yrot(60) cylinder(h=50, d1=20, d2=10);
mirror([1,0,0]) yrot(60) cylinder(h=50, d1=20, d2=10);

Figure 24

BOSL2 provides shortcuts for mirroring across the standard axes; xflip(), yflip(), and zflip():

include <BOSL2/std.scad>
#yrot(60) cylinder(h=50, d1=20, d2=10);
xflip() yrot(60) cylinder(h=50, d1=20, d2=10);

Figure 25

include <BOSL2/std.scad>
#xrot(60) cylinder(h=50, d1=20, d2=10);
yflip() xrot(60) cylinder(h=50, d1=20, d2=10);

Figure 26

include <BOSL2/std.scad>
#cylinder(h=50, d1=20, d2=10);
zflip() cylinder(h=50, d1=20, d2=10);

Figure 27

All of the flip commands can offset where the mirroring is performed:

include <BOSL2/std.scad>
#zrot(30) cube(20, center=true);
xflip(x=-20) zrot(30) cube(20, center=true);
color("blue",0.25) left(20) cube([0.1,50,50], center=true);

Figure 28

include <BOSL2/std.scad>
#zrot(30) cube(20, center=true);
yflip(y=20) zrot(30) cube(20, center=true);
color("blue",0.25) back(20) cube([40,0.1,40], center=true);

Figure 29

include <BOSL2/std.scad>
#xrot(30) cube(20, center=true);
zflip(z=-20) xrot(30) cube(20, center=true);
color("blue",0.25) down(20) cube([40,40,0.1], center=true);

Figure 30

Skewing / Shearing

One transform that OpenSCAD does not perform natively is skewing, also known as shearing.
BOSL2 provides the skew() command for that. You give it multipliers for the skews you want to perform. The arguments used all start with s, followed by the axis you want to skew along, followed by the axis that the skewing will increase along. For example, to skew along the X axis as you get farther along the Y axis, use the sxy= argument. If you give it a multiplier of 0.5, then for each unit further along the Y axis you get, you will add 0.5 units of skew to the X axis. Giving a negative multiplier reverses the direction it skews:

include <BOSL2/std.scad>
skew(sxy=0.5) cube(10,center=false);

Figure 31

include <BOSL2/std.scad>
skew(sxz=-0.5) cube(10,center=false);

Figure 32

include <BOSL2/std.scad>
skew(syx=-0.5) cube(10,center=false);

Figure 33

include <BOSL2/std.scad>
skew(syz=0.5) cube(10,center=false);

Figure 34

include <BOSL2/std.scad>
skew(szx=-0.5) cube(10,center=false);

Figure 35

include <BOSL2/std.scad>
skew(szy=0.5) cube(10,center=false);

Figure 36

Indices

Table of Contents
Function Index
Topics Index
Cheat Sheet
Tutorials

List of Files:

Basic Modeling:

Advanced Modeling:

Math:

Data Management:

Threaded Parts:

Parts:

Footnotes:

STD = Included in std.scad

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