light.typ

// adapted from https://github.com/cetz-package/cetz/blob/a082e02a/gallery/waves.typ
#import "@preview/cetz:0.3.1": canvas, draw, vector, matrix

#set page(width: auto, height: auto, margin: .5cm)

#canvas({
  import draw: set-transform, scale, content, line, grid, group, rotate

  // Set up the transformation matrix
  set-transform(matrix.transform-rotate-dir((1, 1, -1.3), (0, 1, .4)))
  scale(x: 1.5, z: -1)
  let arrow-style = (mark: (end: "stealth", fill: black, scale: 0.5))
  // Coordinate axes labels and arrows
  draw.line((0, -2, 0), (0, 2.5, 0), ..arrow-style)
  draw.line((-0.5, 0, 0), (8.5, 0, 0), ..arrow-style)
  draw.line((0, 0, -1.5), (0, 0, 2), ..arrow-style)
  content((0, 0, 2.3), [$arrow(E)$])
  content((0, 3, 0), [$arrow(B)$])
  content((8.7, 0, 0), [$arrow(v)$])

  grid((0, -2), (8, 2), stroke: gray + .5pt)

  // Draw a sine wave on the xy plane
  let wave(amplitude: 1, fill: none, phases: 2, scale: 8, samples: 100) = {
    line(
      ..(
        for x in range(0, samples + 1) {
          let x = x / samples
          let p = (2 * phases * calc.pi) * x
          ((x * scale, calc.sin(p) * amplitude),)
        }
      ),
      fill: fill,
    )

    let subdivs = 8
    for phase in range(0, phases) {
      let x = phase / phases
      for div in range(1, subdivs + 1) {
        let p = 2 * calc.pi * (div / subdivs)
        let y = calc.sin(p) * amplitude
        let x = x * scale + div / subdivs * scale / phases
        line((x, 0), (x, y), stroke: rgb(0, 0, 0, 150) + .5pt)
      }
    }
  }

  // Draw waves
  group({
    rotate(x: 90deg)
    wave(amplitude: 1.6, fill: rgb(0, 0, 255, 50))
  })
  wave(amplitude: 1, fill: rgb(255, 0, 0, 50))
})