Precisely position elements on wavy circle

[janosh]

wondering if there's a cleaner way to draw this diagram, especially how to best position the arrows, dot and crossed circle on exactly 3, 6, 9 and 12 of the wavy loop.

#import "@preview/cetz:0.3.2": canvas, draw, decorations
#import draw: line, content, circle

#set page(width: auto, height: auto, margin: 8pt)

#let equation = $partial_t (diff V) / (diff chi) =$
#let rad = 0.8
#canvas({
  // Define styles
  let arrow-style = (
    stroke: (paint: black, thickness: 0.5pt),
  )

  // Draw the loop using wave decoration
  let loop = circle((1, 0), radius: rad, stroke: none)
  decorations.wave(
    loop,
    amplitude: 0.1,
    segments: 16,
    close: true,
    stroke: (paint: black, thickness: 0.5pt),
    name: "loop",
    mark: (end: "stealth"),
  )

  // Add vertices
  circle("loop.23%", radius: 0.075, fill: black, name: "dot")
  content(
    "loop.74.5%",
    text(size: 10pt)[$times.circle$],
    name: "regulator",
    fill: white,
    frame: "circle",
    stroke: none,
    padding: -1.7pt,
  )


  // Draw input line
  line((rel: (-1, 0), to: "dot"), "dot", name: "input", ..arrow-style)


  content(
    "input.start",
    $ partial_t (diff V) / (diff chi) = $,
    anchor: "east",
    padding: (0, 5pt, 0),
  )

  // Add momentum label
  content((rad, rad * 1.4), $q$, name: "momentum")
  content((rad, rad * -1.4), $q$, name: "momentum")
})

[johannes-wolf]

Yes, you can use intersections(<name>, <element 1>, <element ...>) to find intersections between paths. You can pass element name and use hide(...) to calculate the intersection with a hidden line.

#import "@preview/cetz:0.3.2": canvas, draw, decorations
#import draw: line, content, circle, intersections, group, hide

#set page(width: auto, height: auto, margin: 8pt)

#let equation = $partial_t (diff V) / (diff chi) =$
#let rad = 0.8
#canvas({
  // Define styles
  let arrow-style = (
    stroke: (paint: black, thickness: 0.5pt),
  )

  // Draw the loop using wave decoration
  decorations.wave(
    circle((1, 0), radius: rad),
    amplitude: .1,
    segments: 16,
    close: true,
    stroke: (paint: black, thickness: 0.5pt),
    name: "loop",
    mark: (end: "stealth"),
  )

  // Find left and right position on the loop
  intersections("loop-points", "loop",
    hide(line((rel: (-2 * rad, 0), to: "loop.centroid"),
              (rel: (+2 * rad, 0), to: "loop.centroid"))),
    hide(line((rel: (0, +2 * rad), to: "loop.centroid"),
              (rel: (0, -2 * rad), to: "loop.centroid"))))
  
  // Add vertices
  circle("loop-points.0", radius: 0.075, fill: black, name: "dot")
  content(
    "loop-points.1",
    text(size: 10pt)[$times.circle$],
    name: "regulator",
    fill: white,
    frame: "circle",
    stroke: none,
    padding: -1.7pt,
  )

  // Draw input line
  line((rel: (-1, 0), to: "dot"), "dot", name: "input", ..arrow-style)

  content(
    "input.start",
    $ partial_t (diff V) / (diff chi) = $,
    anchor: "east",
    padding: (0, 5pt, 0),
  )

  // Add momentum label
  content((rad, rad * 1.4), $q$, name: "momentum")
  content((rad, rad * -1.4), $q$, name: "momentum")

  // Draw arrows
  set-style(mark: (scale: 1.25, fill: black))
  mark("loop-points.2", (rel: (1, 0)), symbol: "<", anchor: "center")
  mark("loop-points.3", (rel: (1, 0)), symbol: ">", anchor: "center")
})

[johannes-wolf]

It's this:

// Find left and right position on the loop
  intersections("loop-points", "loop",
    hide(line((rel: (-2 * rad, 0), to: "loop.centroid"),
              (rel: (+2 * rad, 0), to: "loop.centroid"))))

[janosh]

at the risk of asking something that's already documented, i would appreciate any advice on how to fill the gray regions in this diagram

#import "@preview/cetz:0.3.2": canvas, draw
#import draw: line, content, arc, rect, set-style, set-viewport

#set page(width: auto, height: auto, margin: 1pt)

// Constants
#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: 8pt)

#canvas({
  set-style(stroke: (thickness: 0.4pt))
  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 axes
  line((xmin, 0), (xmax, 0), ..arrow-style, name: "x-axis")
  line((0, ymin), (0, ymax), ..arrow-style, name: "y-axis")

  // Draw tick marks with labels
  line((-0.5, -0.02), (-0.5, 0.02), name: "x-tick")
  content((-0.5, -0.1), $-1 / 2$, anchor: "north")

  line((0.5, -0.02), (0.5, 0.02), name: "x-tick")
  content((0.5, -0.1), $1 / 2$, 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)

  // Draw semicircle B and B' (dark red)
  arc(
    (0, 0),
    radius: 1,
    start: 0deg,
    stop: 180deg,
    stroke: (paint: red),
    name: "B-arc",
    anchor: "origin",
  )
  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))

  // Draw vertical lines A and A' (dark blue)
  line(
    (-0.5, 0),
    (-0.5, ymax),
    stroke: (paint: blue),
    mark: (end: "stealth", fill: blue, scale: 0.2),
    name: "A-line",
  )
  content("A-line.80%", $A$, fill: blue, anchor: "east", padding: (0, 4pt, 0, 0))

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

  // Add F₀ labels
  content("y-axis.80%", $F_0$, anchor: "west", padding: (0, 0, 0, 2pt))
  content((rel: (-0.2, -0.2), to: "B-arc.50%"), $F_0'$)

  // Draw the extended green arcs (C and C') first
  arc(
    (0, 0),
    radius: 1,
    start: 0deg,
    stop: 90deg,
    stroke: (paint: green),
    name: "C-arc",
    anchor: "start",
  )
  content("C-arc.40%", $C$, fill: green, anchor: "north-east", padding: 2pt)

  arc(
    (0, 0),
    radius: 1,
    start: 90deg,
    stop: 180deg,
    stroke: (paint: green),
    name: "C-prime-arc",
    anchor: "end",
  )
  content("C-prime-arc.60%", $C'$, fill: green, anchor: "north-west", padding: 2pt)
})

[johannes-wolf]

Cetz has no path clipping at the moment. But that's def. on the to-do list! It is quite complex, though. The only option right now is to manually build those paths :(.