parameterization.js

var order, pathPoints, knots; // the regular stuff goes in these

var nSegments = 500;

var segments = [0], p0;
for (var i = 0; i <= nSegments; i++) {
	var t = i / nSegments;
	var p1 = bSpline(t, order, pathPoints, knots);
	if (p0) {
		var dx = p0[0] - p1[0];
		var dy = p0[1] - p1[1];
		var d = Math.sqrt(dx * dx + dy * dy);
		segments.push(segments[segments.length - 1] + d);
	} else {
		p0 = [0, 0];
	}
	p0[0] = p1[0];
	p0[1] = p1[1];
}

var bSplinePoints = [];

for (var i = 0; i < nSegments; i++) {
	var u = i / a.length;
	var t = 0;
  
  	// From https://gist.github.com/DUznanski/ebdca354df614e78b4cd69fb13e138c3
  	// Also see: http://davis.wpi.edu/~matt/courses/biomed/reparam.htm
	  if (u == 1) {
	  	t = 1;
	  } else {
	  	// Convert u from 0..1 to the space given by the curve. The last index of the array 
	  	// corresponds to the arc length of the curve
	  	var segmentCount = segments.length - 1;
	  	var d = u * segments[segmentCount];
	  	var k = 0;
	  
	  	// Find the place in the segment distance list where d is
	  	while (segments[k] < d) {
	  		k++;
	  	}
	  
	  	// We overshoot, so go back one
	  	k = Math.max(0, --k);
	  	var lo = segments[k];
	  	var hi = segments[k + 1];
	  
	  	// Find out how far we've gone along the segment defined by the current and previous points
	  	var segmentIndex = (d - lo) / (hi - lo);
	  	var totalSegmentsPassed = k + segmentIndex;
	  	t = totalSegmentsPassed / segmentCount;
	  }
	  
	  bSplinePoints.push(t, order, pathPoints, knots);
}