B-Spline

lib/spline.js

@@ -0,0 +1,82 @@
+// 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;
+};