Bezier curve function for OpenSCAD (any order curve, any dimension points)

BezierHans.scad

BezierExample();

//BezierCircleApprox(10);

// cubic bezier circle approximation example
module BezierCircleApprox(r) {
  $fn=1000;
  c = 0.551915024494;
  points = BezierPath([
    [ 0, 1], [ c, 1], [ 1, c], [ 1, 0], 
             [ 1,-c], [ c,-1], [ 0,-1], 
             [-c,-1], [-1,-c], [-1, 0], 
             [-1, c], [-c, 1], [ 0, 1]
    ], index=0, n=3);
  echo(len(points));
  polygon(r*points);
}

module BezierExample() {

  points = [
    [0,0, 1],
    [1,1, -1],
    [3,-1, 1],
    [4,0, -1],
    [5,4, 1],
    [5,5, -1],
    [0,6, 1],
    [10,6, -1],
    [0,0,10],
    [0,0,5]
  ];
  
  $fn=1000;
  size = 0.02;
  
  //echo(len(BezierPath(points,n=7)));

  %showPoints(points, size*3);
  //*
  color("red") showPoints(BezierPath(points,n=1), size);
  color("green") showPoints(BezierPath(points,n=2), size);
  color("blue") showPoints(BezierPath(points,n=3), size);
  color("yellow") showPoints(BezierPath(points,n=4), size);
  color("magenta") showPoints(BezierPath(points,n=5), size);
  color("cyan") showPoints(BezierPath(points,n=6), size);
  color("white") showPoints(BezierPath(points,n=7), size);
  //*/
  
}

module showPoints(points, size=0.02) {
  for (c = points) translate(c) cube(size, center=true);
}

// return point along curve at position "t" in range [0,1]
// use ctlPts[index] as the first control point
// Bezier curve has order == n
function BezierPoint(ctlPts, t, n, index=0) = (n > 1) ? 
  _BezierPoint([for (i = [index:index+n-1]) ctlPts[i] + t * (ctlPts[i+1] - ctlPts[i])], t, n-1) :
  ctlPts[index] + t * (ctlPts[index+1] - ctlPts[index]);

// slightly optimized version takes less parameters
function _BezierPoint(ctlPts, t, n) = (n > 1) ? 
  _BezierPoint([for (i = [0:n-1]) ctlPts[i] + t * (ctlPts[i+1] - ctlPts[i])], t, n-1) :
  ctlPts[0] + t * (ctlPts[1] - ctlPts[0]);

// n sets the order of the Bezier curves that will be stitched together
// if no parameter n is given, points will be generated for a single curve of order == len(ctlPts) - 1
// Note: $fn is number of points *per segment*, not over the entire path.
function BezierPath(ctlPts, n, index=0) = 
  let (
    l1 = $fn > 3 ? $fn : 200,
    l2 = len(ctlPts),
    n = (n == undef || n > l2-1) ? l2 - 1 : n
  )
  //assert(n > 0)
  [for (segment = [index:n:l2-1-n], i = [0:l1-1])
    BezierPoint(ctlPts, i / l1, n, segment), ctlPts[l2-1]];