Torus Fundamental Domain

#import "@preview/cetz:0.5.2": canvas, draw
#import draw: arc, content, line, rect

#set page(width: auto, height: auto, margin: 1pt, fill: none)

#let (xmin, xmax) = (-1, 1)
#let (ymin, ymax) = (-0.5, 2.4)

// Set global styles
#let arrow-style = (
  mark: (end: "stealth", fill: black, scale: 0.2),
  stroke: (thickness: 0.4pt),
)
#set text(size: 12pt)

// TODO this figure needs revisiting to get the gray-shaded areas right without overlaying opaque fills once CetZ implements path clipping
// https://github.com/cetz-package/cetz/discussions/813#discussioncomment-12218646
#canvas({
  draw.set-style(stroke: (thickness: 0.4pt))
  draw.set-viewport((0, 0), (20, 20), bounds: (12, 12))

  // Light gray vertical strip
  rect(
    (-0.5, 0),
    (0.5, ymax),
    fill: rgb(128, 128, 128).lighten(80%),
    stroke: none,
  )
  // Draw semicircle B and B' (dark red)
  arc(
    (0, 0),
    radius: 1,
    start: 0deg,
    stop: 180deg,
    stroke: (paint: red),
    fill: gray.transparentize(30%),
    name: "B-arc",
    anchor: "origin",
  )
  for (start, name, arc-anchor, label-anchor, label-pos, label) in (
    (0deg, "C-arc", "start", "north-east", "C-arc.20%", $C$),
    (90deg, "C-prime-arc", "arc-end", "north-west", "C-prime-arc.25%", $C'$),
  ) {
    arc(
      (0, 0),
      radius: 1,
      start: start,
      stop: start + 90deg,
      mode: "PIE",
      stroke: (paint: green),
      fill: rgb("#cdd3da"),
      name: name,
      anchor: arc-anchor,
    )
    content(label-pos, label, fill: green, anchor: label-anchor, padding: 2pt)
  }
  // Draw semicircle B and B' (dark red)
  arc(
    (0, 0),
    radius: 1,
    start: 0deg,
    stop: 180deg,
    stroke: (paint: red),
    name: "B-arc",
    anchor: "origin",
  )

  line((xmin, 0), (xmax, 0), ..arrow-style, name: "x-axis")
  line((0, ymin), (0, ymax), ..arrow-style, name: "y-axis")

  for (x, name, label) in ((-0.5, "x-minus-tick", $-1 \/ 2$), (0.5, "x-plus-tick", $1 \/ 2$)) {
    line((x, -0.02), (x, 0.02), name: name)
    content((rel: (0, -0.08), to: name + ".mid"), label, anchor: "north")
  }

  line((-0.02, 1), (0.02, 1), name: "i-tick", stroke: (thickness: 0.6pt))
  content("i-tick", $i$, anchor: "north-west", padding: 1pt)

  content("B-arc.60%", $B$, fill: red, anchor: "south", padding: (0, 0, 3pt))
  content("B-arc.40%", $B'$, fill: red, anchor: "south", padding: (0, 0, 3pt))

  for (x, name, label, anchor, padding) in (
    (-0.5, "A-line", $A$, "east", (0, 4pt, 0, 0)),
    (0.5, "A-prime-line", $A'$, "west", (0, 0, 0, 4pt)),
  ) {
    line(
      (x, 0),
      (x, ymax),
      stroke: (paint: blue),
      mark: (end: "stealth", fill: blue, scale: 0.2),
      name: name,
    )
    content(name + ".80%", label, fill: blue, anchor: anchor, padding: padding)
  }

  content("y-axis.80%", $F_0$, anchor: "west", padding: (0, 0, 0, 2pt))
  content((rel: (-0.2, -0.2), to: "B-arc.50%"), $F_0'$)
})