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263 lines
6.4 KiB
Markdown
263 lines
6.4 KiB
Markdown
# Transforms Tutorial
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<!-- TOC -->
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## Translation
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The `translate()` command is very simple:
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```openscad
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include <BOSL2/std.scad>
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#sphere(d=20);
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translate([0,0,30]) sphere(d=20);
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```
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But at a glance, or when the formula to calculate the move is complex, it can be difficult to see
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just what axis is being moved along, and in which direction. It's also a bit verbose for such a
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frequently used command. For these reasons, BOSL2 provides you with shortcuts for each direction.
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These shortcuts are `up()`, `down()`, `fwd()`, `back()`, `left()`, and `right()`:
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```openscad
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include <BOSL2/std.scad>
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#sphere(d=20);
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up(30) sphere(d=20);
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```
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```openscad
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include <BOSL2/std.scad>
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#sphere(d=20);
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down(30) sphere(d=20);
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```
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```openscad
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include <BOSL2/std.scad>
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#sphere(d=20);
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fwd(30) sphere(d=20);
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```
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```openscad
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include <BOSL2/std.scad>
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#sphere(d=20);
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back(30) sphere(d=20);
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```
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```openscad
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include <BOSL2/std.scad>
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#sphere(d=20);
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left(30) sphere(d=20);
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```
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```openscad
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include <BOSL2/std.scad>
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#sphere(d=20);
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right(30) sphere(d=20);
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```
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There is also a more generic `move()` command that can work just like `translate()`:
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```openscad
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include <BOSL2/std.scad>
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#sphere(d=20);
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move([30,-10]) sphere(d=20);
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```
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## Scaling
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The `scale()` command is also fairly simple:
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```openscad
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include <BOSL2/std.scad>
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scale(2) cube(10, center=true);
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```
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```openscad
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include <BOSL2/std.scad>
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scale([1,2,3]) cube(10, center=true);
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```
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If you want to only change the scaling on one axis, though, BOSL2 provides clearer
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commands to do just that; `xscale()`, `yscale()`, and `zscale()`:
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```openscad
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include <BOSL2/std.scad>
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xscale(2) cube(10, center=true);
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```
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```openscad
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include <BOSL2/std.scad>
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yscale(2) cube(10, center=true);
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```
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```openscad
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include <BOSL2/std.scad>
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zscale(2) cube(10, center=true);
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```
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## Rotation
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The `rotate()` command is fairly straightforward:
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```openscad
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include <BOSL2/std.scad>
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rotate([0,30,0]) cube(20, center=true);
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```
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It is also a bit verbose, and can, at a glance, be difficult to tell just how it is rotating.
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BOSL2 provides shortcuts for rotating around each axis, for clarity; `xrot()`, `yrot()`, and `zrot()`:
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```openscad
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include <BOSL2/std.scad>
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xrot(30) cube(20, center=true);
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```
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```openscad
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include <BOSL2/std.scad>
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yrot(30) cube(20, center=true);
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```
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```openscad
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include <BOSL2/std.scad>
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zrot(30) cube(20, center=true);
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```
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The `rot()` command is a more generic rotation command, and shorter to type than `rotate()`:
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```openscad
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include <BOSL2/std.scad>
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rot([0,30,15]) cube(20, center=true);
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```
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All of the rotation shortcuts can take a `cp=` argument, that lets you specify a
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centerpoint to rotate around:
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```openscad
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include <BOSL2/std.scad>
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cp = [0,0,40];
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color("blue") move(cp) sphere(d=3);
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#cube(20, center=true);
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xrot(45, cp=cp) cube(20, center=true);
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```
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```openscad
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include <BOSL2/std.scad>
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cp = [0,0,40];
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color("blue") move(cp) sphere(d=3);
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#cube(20, center=true);
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yrot(45, cp=cp) cube(20, center=true);
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```
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```openscad
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include <BOSL2/std.scad>
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cp = [0,40,0];
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color("blue") move(cp) sphere(d=3);
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#cube(20, center=true);
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zrot(45, cp=cp) cube(20, center=true);
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```
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You can also do a new trick with it. You can rotate from pointing in one direction, towards another.
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You give these directions using vectors:
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```openscad
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include <BOSL2/std.scad>
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#cylinder(d=10, h=50);
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rot(from=[0,0,1], to=[1,0,1]) cylinder(d=10, h=50);
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```
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There are several direction vectors constants and aliases you can use for clarity:
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Constant | Value | Direction
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------------------------------ | ------------ | --------------
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`CENTER`, `CTR` | `[ 0, 0, 0]` | Centered
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`LEFT` | `[-1, 0, 0]` | Towards X-
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`RIGHT` | `[ 1, 0, 0]` | Towards X+
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`FWD`, `FORWARD`, `FRONT` | `[ 0,-1, 0]` | Towards Y-
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`BACK` | `[ 0, 1, 0]` | Towards Y+
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`DOWN`, `BOTTOM`, `BOT` | `[ 0, 0,-1]` | Towards Z-
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`UP`, `TOP` | `[ 0, 0, 1]` | Towards Z+
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This lets you rewrite the above vector rotation more clearly as:
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```openscad
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include <BOSL2/std.scad>
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#cylinder(d=10, h=50);
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rot(from=UP, to=UP+RIGHT) cylinder(d=10, h=50);
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```
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## Mirroring
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The standard `mirror()` command works like this:
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```openscad
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include <BOSL2/std.scad>
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#yrot(60) cylinder(h=50, d1=20, d2=10);
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mirror([1,0,0]) yrot(60) cylinder(h=50, d1=20, d2=10);
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```
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BOSL2 provides shortcuts for mirroring across the standard axes; `xflip()`, `yflip()`, and `zflip()`:
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```openscad
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include <BOSL2/std.scad>
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#yrot(60) cylinder(h=50, d1=20, d2=10);
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xflip() yrot(60) cylinder(h=50, d1=20, d2=10);
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```
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```openscad
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include <BOSL2/std.scad>
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#xrot(60) cylinder(h=50, d1=20, d2=10);
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yflip() xrot(60) cylinder(h=50, d1=20, d2=10);
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```
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```openscad
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include <BOSL2/std.scad>
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#cylinder(h=50, d1=20, d2=10);
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zflip() cylinder(h=50, d1=20, d2=10);
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```
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All of the flip commands can offset where the mirroring is performed:
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```openscad
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include <BOSL2/std.scad>
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#zrot(30) cube(20, center=true);
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xflip(x=-20) zrot(30) cube(20, center=true);
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color("blue",0.25) left(20) cube([0.1,50,50], center=true);
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```
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```openscad
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include <BOSL2/std.scad>
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#zrot(30) cube(20, center=true);
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yflip(y=20) zrot(30) cube(20, center=true);
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color("blue",0.25) back(20) cube([40,0.1,40], center=true);
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```
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```openscad
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include <BOSL2/std.scad>
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#xrot(30) cube(20, center=true);
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zflip(z=-20) xrot(30) cube(20, center=true);
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color("blue",0.25) down(20) cube([40,40,0.1], center=true);
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```
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## Skewing / Shearing
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One transform that OpenSCAD does not perform natively is skewing, also
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known as shearing.
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BOSL2 provides the `skew()` command for that. You give it multipliers
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for the skews you want to perform. The arguments used all start with `s`,
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followed by the axis you want to skew along, followed by the axis that
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the skewing will increase along. For example, to skew along the X axis as
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you get farther along the Y axis, use the `sxy=` argument. If you give it
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a multiplier of `0.5`, then for each unit further along the Y axis you get,
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you will add `0.5` units of skew to the X axis. Giving a negative multiplier
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reverses the direction it skews:
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```openscad
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include <BOSL2/std.scad>
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skew(sxy=0.5) cube(10,center=false);
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```
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```openscad
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include <BOSL2/std.scad>
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skew(sxz=-0.5) cube(10,center=false);
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```
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```openscad
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include <BOSL2/std.scad>
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skew(syx=-0.5) cube(10,center=false);
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```
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```openscad
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include <BOSL2/std.scad>
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skew(syz=0.5) cube(10,center=false);
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```
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```openscad
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include <BOSL2/std.scad>
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skew(szx=-0.5) cube(10,center=false);
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```
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```openscad
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include <BOSL2/std.scad>
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skew(szy=0.5) cube(10,center=false);
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```
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