BezierInfo-2/lib/spline.js

// https://github.com/thibauts/b-spline
module.exports = function interpolate(t, degree, points, knots, weights, result, scaled) {
  
  var i,j,s,l;              // function-scoped iteration variables
  var n = points.length;    // points count
  var d = points[0].length; // point dimensionality

  if(degree < 1) throw new Error('degree must be at least 1 (linear)');
  if(degree > (n-1)) throw new Error('degree must be less than or equal to point count - 1');

  if(!weights) {
    // build weight vector of length [n]
    weights = [];
    for(i=0; i<n; i++) {
      weights[i] = 1;
    }
  }

  if(!knots) {
    // build knot vector of length [n + degree + 1]
    var knots = [];
    for(i=0; i<n+degree+1; i++) {
      knots[i] = i;
    }
  } else {
    if(knots.length !== n+degree+1) throw new Error('bad knot vector length');
  }

  var domain = [
    degree,
    knots.length-1 - degree
  ];

  var low  = knots[domain[0]];
  var high = knots[domain[1]];
  
  // remap t to the domain where the spline is defined
  if (!scaled) {
    t = t * (high - low) + low;
  }

  if(t < low || t > high) throw new Error('out of bounds');

  // find s (the spline segment) for the [t] value provided
  for(s=domain[0]; s<domain[1]; s++) {
    if(t >= knots[s] && t <= knots[s+1]) {
      break;
    }
  }

  // convert points to homogeneous coordinates
  var v = [];
  for(i=0; i<n; i++) {
    v[i] = [];
    for(j=0; j<d; j++) {
      v[i][j] = points[i][j] * weights[i];
    }
    v[i][d] = weights[i];
  }

  // l (level) goes from 1 to the curve degree + 1
  var alpha;
  for(l=1; l<=degree+1; l++) {
    // build level l of the pyramid
    for(i=s; i>s-degree-1+l; i--) {
      alpha = (t - knots[i]) / (knots[i+degree+1-l] - knots[i]);

      // interpolate each component
      for(j=0; j<d+1; j++) {
        v[i][j] = (1 - alpha) * v[i-1][j] + alpha * v[i][j];
      }
    }
  }

  // convert back to cartesian and return
  var result = result || [];
  for(i=0; i<d; i++) {
    result[i] = v[s][i] / v[s][d];
  }

  return result;
};