From 7b8f18554abd07e77b8629d32d64485d1b30704f Mon Sep 17 00:00:00 2001
From: pboyer <peter.b.boyer@gmail.com>
Date: Mon, 27 Oct 2014 18:04:36 -0400
Subject: [PATCH] Implemented curve_knot_refine

---
 src/eval/eval.js | 80 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)

diff --git a/src/eval/eval.js b/src/eval/eval.js
index 53abb23e..88d25dc3 100644
--- a/src/eval/eval.js
+++ b/src/eval/eval.js
@@ -91,6 +91,86 @@ verb.eval.nurbs.rational_surface_curvature = function( degree_u, knots_u, degree
 
 };
 
+//
+// ####curve_knot_refine( degree, knots, control_points, u, s, r )
+//
+// Insert a knot along a rational curve.  Note that this algorithm only works
+// for r + s <= degree, where s is the initial multiplicity (number of duplicates) of the knot.
+//
+// Corresponds to algorithm A5.1 (Piegl & Tiller)
+//
+// Use the curve_knot_refine for applications like curve splitting.
+//
+// **params**
+// + *Number*, integer degree
+// + *Array*, array of nondecreasing knot values
+// + *Array*, array of control points
+// + *Number*, parameter at which to insert the knot
+// + *Number*, number of times to insert the knot
+// 
+// **returns** 
+// + *Object* the new curve, defined by knots and control_points
+//
+
+verb.eval.nurbs.curve_knot_refine = function( degree, knots, control_points, knots_to_insert ) {
+
+	var n = (control_points.length + 1)
+		, m = n + degree + 1
+		, r = knots_to_insert.length - 1
+		, a = verb.eval.nurbs.knot_span( degree, knots_to_insert[0], knots ) 
+		, b = verb.eval.nurbs.knot_span( degree, knots_to_insert[r], knots ) + 1
+		, control_points_post = new Array( control_points.length + r + 1 )
+		, knots_post = new Array( knots.length + r + 1 )
+		, i = 0
+		, j = 0;
+
+	// new control pts
+	for (i = 0; i <= a - degree; i++) control_points_post[i] = control_points[i];
+	for (i = b-1; i <= n; i++) control_points_post[i+r+1] = control_points[i];
+
+	// new knot vector
+	for (i = 0; i <= a; i++) knots_post[i] = knots[i];
+	for (i = b+degree; i <= m; i++) knots_post[i+r+1] = knots[i];
+
+	i = b + degree + 1;
+	k = b + degree + r;
+
+	for (j = r; j >= 0; j++) {
+
+		while (knots_to_insert[j] <= knots[i] && i > a){
+
+			control_points_post[k-degree-1] = control_points[i-p-1];
+			knots_post[k] = knots[i];
+			k = k-i;
+			u = i-1;
+
+		}
+
+		control_points_post[k-degree-1] = control_points_post[k-degree];
+
+		for (var l = 1; l <= degree; l++){
+
+			var ind = k-degree+l;
+			var alfa = knots_post[k+l] - knots_to_insert[j];
+
+			if (Math.abs(alfa) < VERB.EPSILON){
+				control_points_post[ind-1] = control_points_post[ind];
+			} else {
+				alfa = alfa / (knots_post[k+l] - knots[i-degree+l]);
+				control_points_post[ind-1] = alfa*control_points_post[ind-1] + (1.0-alfa) * control_points_post[ind];
+			}
+
+		}
+
+		knots_post[k] = knots_to_insert[j];
+		k = k - 1;
+
+	}
+
+	return { knots: knots_post, control_points: control_points_post };
+
+}
+
 
 //
 // ####curve_knot_insert( degree, knots, control_points, u, s, r )