// ============================================================
//  ornaline — stamp an "ornament" motif repeatedly along a line
//
//  line  : a path (list of [x,y] points) — the spine to follow
//  motif : a path authored in local space, running along +x,
//          with y as the perpendicular amplitude. x in mm.
//  arcLength  : arc-length spacing between successive stamps (mm)
//  amp   : amplitude scale for the motif's y-axis (1 = as authored)
//
//  Returns one continuous path you can sewpath() in any mode.
// ============================================================

def ornapath(line, motif, arcLength, amp) [
  // even anchors along the spine; segment length = arcLength
  let spine = resample(line, arcLength)
  let out = []
  let mw = motifwidth(motif)          // how far along +x one motif spans

  // walk the spine, placing a motif between each pair of anchors
  for i = 0 to len(spine) - 2 [
    let a = spine[i]
    let b = spine[i + 1]
    let h = vheading(vsub(b, a))       // local tangent as a turtle heading
    // map every motif point into hoop space at this anchor
    for q in motif [
      // scale x to fill exactly one arcLength, scale y by amp
      let localValue = [ q[0] / mw * arcLength, q[1] * amp ]
      // rotate from "+x = east" into the spine's heading, then place it
      let placed = vadd(a, vrot(localValue, h - 90))
      append(out, placed)
    ]
  ]
  return out
]

// how far the motif reaches along its own +x axis (for normalising the arcLength)
def motifwidth(motif) [
  let box = bbox(motif)               // [minx, miny, maxx, maxy]
  let w = box[2] - box[0]
  if w < 0.001 [ return 1 ]           // guard a vertical/degenerate motif
  return w
]

// the convenience command: build it and sew it in the current mode
def ornaline(line, motif, arcLength, amp) [
  sewpath(ornapath(line, motif, arcLength, amp))
]

seed 3
let cell_length = 6  // [2:0.5:12] ornament-cell length, mm
let amplitude = 1    // [0.3:0.1:3] ornament height multiplier
stitchlen 1.5

// the spine to decorate
let pts  = [[-40, -10], [-15, 12], [10, -12], [38, 8]]
let line = catmull(pts, 8)

// one ornament cell: a little arch, authored along +x (0..1), y is amplitude
let wave = [[0, 0], [0.25, 1], [0.5, 0], [0.5, -1], [0.75, 0], [1, 2], [1, 0]]

satin 1
moveto -40 -10
down
ornaline(line, wave, cell_length, amplitude)