projection: Add orthographic projection utilities

[johannes-wolf]

This PR adds some helper functions for setting up orthographic projection.

Three functions for drawing on different planes got added: on-xy, on-xz and on-yz.
These allow elements which do not allow to be used with different z-coordinates to be drawn in 3D space without having to use rotations etc.

The new ortho function sets-up an isometric projection by default:

There is no z-sorting (yet?).

Code

#import "src/lib.typ" as cetz
#set page(width: auto, height: auto)

#cetz.canvas({
import cetz.draw: *

let cube() = {
  set-style(
    line: (mark: (end: ">", scale: .3)))

  scale(3)
  line((-1,0,0), (1,0,0))
  line((0,-1,0), (0,1,0))
  line((0,0,-1), (0,0,1))

  set-style(
    stroke: (paint: black, thickness: 1pt, join: "round"),
    fill: rgb(0,0,255,50))

  scale(.35)
  on-xy(z: -1, rect((-1,-1), (1,1)))
  on-xy(z: +1, rect((-1,-1), (1,1)))
  on-xz(y: -1, rect((-1,-1), (1,1)))
  on-xz(y: +1, rect((-1,-1), (1,1)))
  on-yz(x: -1, rect((-1,-1), (1,1)))
  on-yz(x: +1, rect((-1,-1), (1,1)))
}

ortho(name: "ortho", {
  cube()
})

set-origin("ortho.east")
group(name: "ortho", anchor: "west", ortho(x: 20deg, {
  cube()
}))

set-origin("ortho.east")
group(name: "ortho", anchor: "west", ortho(y: 20deg, {
  cube()
}))
})

#cetz.canvas({
import cetz.draw: *

ortho({
  scale(2)
  on-xy(z: -1.1, {
    rect((-1,-1), (1,1))
    translate((-.9, -.9))
    cetz.plot.plot(size: (1.8, 1.8), x-tick-step: none, y-tick-step: none, x-label: none, y-label: none, {
      cetz.plot.add(domain: (-2, 2), x => x * x * x)
      cetz.plot.add-contour(
        (x, y) => 2 - (x - 1) * (y - 1),
        fill: true,
        x-domain: (-2, 2),
        y-domain: (-10, 11))
    })
  })
  on-xz(y: -1.1, {
    rect((-1,-1), (1,1))
    grid((-.9, -.9), (.9, .9), step: .2)
  })
  group(name: "g3", {
    on-yz(x: -1.1, {
      rect((-1,-1), (1,1))
      for r in range(1, 10) {
        circle((0,0), radius: .1 * r)
      }
    })
  })
}, name: "gO")
})

[KronosTheLate]

That looks neat! Would it be possible to allow helper-functions/krwargs to make ticks and axis-labels? E.g. ortho(content, axis-labels=true) for default label style and position, and ortho(content, axis-labels=(x, y, z)), with x y z being either strongs or content. And similarly a kwarg tick-spacing which is a number applied to all axis, or a vector of number for finer control.

This looks nice though. Easy to use and rotate round any axis. However, would this be much different from defining your object, and rhen rotating the entire thing? I am not sure what ortho adds that is not east enough already.

[johannes-wolf]

That looks neat! Would it be possible to allow helper-functions/krwargs to make ticks and axis-labels? E.g. ortho(content, axis-labels=true) for default label style and position, and ortho(content, axis-labels=(x, y, z)), with x y z being either strongs or content. And similarly a kwarg tick-spacing which is a number applied to all axis, or a vector of number for finer control.

Adding axes with ticks should be a separate Element.

This looks nice though. Easy to use and rotate round any axis. However, would this be much different from defining your object, and rhen rotating the entire thing? I am not sure what ortho adds that is not east enough already.

• It gives an environment for 3D, we could even sort by camera z-order insides ortho.
• I do not really like the default z-shearing transformation, we could remove it
• Ortho outputs "flat" coordinates with no z-value (outsides the environment), which is useful with anchors and other elements.

[KronosTheLate]

Alright, I can see how on-xy and friends, plus ortho would be useful. I am unable to really check the pros and cons of this implementation in my mind, but like it, and do not immediately have any reservations about it ^_^ I would also say that tagging breaking releases in quick succession due to trying things out if not a big problem as I see it, given the maturity of both Typst and all its packages. So I feel like it makes sense to give this a go, and to not be afraid to change it if usage reveals issues.

[fenjalien]

This is really cool.

Standard extra stuff, manual, changelog, tests are still needed

[fenjalien]

Update changelog first

[johannes-wolf]

@fenjalien Do we want to add this to 0.2.2? This is a non-breaking change.

[fenjalien]

I don't see why not :)