// Hidden-triangle spiral art:
// One continuous spiral fills a disc; the line fattens (wider satin)
// wherever it passes through an invisible triangle in the centre.

seed 1
density 0.4

// --- spiral ---
let rmax  = 38         // [20:1:46] outer radius, mm
let r0    = 0.4        // [0.2:0.1:2] starting radius, mm
let turns = 24         // [6:1:40] revolutions
let pace  = 0.8        // [0.4:0.1:2] target segment length, mm
let thin  = 0.2        // [0.2:0.1:0.6] satin width outside
let thick = 0.8        // [0.4:0.1:1.5] satin width inside

// hidden equilateral triangle (point up), circumradius 22 mm
// heading convention: 0 deg = north, so x = r*sin(a), y = r*cos(a)
let tri_r = 30         // [8:1:38] hidden triangle radius, mm
let tri = [
  [tri_r * sin(0),   tri_r * cos(0)],
  [tri_r * sin(120), tri_r * cos(120)],
  [tri_r * sin(240), tri_r * cos(240)]
]

// Archimedean spiral: r = r0 + b * theta   (theta in degrees)
let theta_max = turns * 360
let b = (rmax - r0) / theta_max

// declare loop state ONCE, before the loop
let theta  = 0
let r      = r0
let dtheta = 0

moveto(0, r0)                  // spiral start: theta = 0 -> (0, r0)
down

while theta < theta_max [
  // pick the line weight from where the needle is right now
  if inpath(pos(), tri) [
    satin thick
  ] else [
    satin thin
  ]

  // advance ~pace mm along the arc; cap the turn near the centre
  dtheta = pace / r * 57.2958
  if dtheta > 15 [ dtheta = 15 ]
  theta += dtheta
  r = r0 + b * theta

  setxy(r * sin(theta), r * cos(theta))
]

satin 0                        // flush the last satin column
trim