From: Scott Worley <ScottWorley@ScottWorley.com>
Date: Thu, 20 Dec 2012 09:09:02 +0000 (-0800)
Subject: Factor out rotate_onto()
X-Git-Url: http://git.scottworley.com/nt3d/commitdiff_plain/aceb2da8b7e5ac5a9e5e1a994680bfff8f726209?hp=1b9ec3f33236204d027507b7dec5215677b51707

Factor out rotate_onto()
---

diff --git a/nt3d.js b/nt3d.js
index 59b11b2..bae29f2 100644
--- a/nt3d.js
+++ b/nt3d.js
@@ -80,35 +80,25 @@ nt3d = {
 			// loop is shape in 3d with (0,0) at path[i], shape's
 			// z axis in the direction of shapenormals[i], and
 			// shape's x axis in the direction of pathnormals[i].
-			var loop = shape;
+			// We tack [1,0,0] onto the end as a hack to see where
+			// it ends up after rotation.  This is removed later.
+			var loop = shape.concat([[1,0,0]]);
 
 			// This is done in three steps:
 			// 1. Rotate shape out of the xy plane so that [0,0,1]
-			//    becomes shapenormals[i] by crossing [0,0,1] and
-			//    shapenormals[i] to get a rotation axis and taking
-			//    their dot product to get a rotation angle.  This
-			//    puts the shape in the correct plane, but does not
-			//    constrain its rotation about shapenormals[i].
-			var rot1axis = this.unit(this.cross([0,0,1], shapenormals[i]));
-			var rot1angle = this.angle_between([0,0,1], this.unit(shapenormals[i]));
-			var shapex = [[1,0,0]];
-			if (rot1angle > 1e-7) {
-				loop = this.rotate_about_origin(loop, rot1axis, rot1angle);
-				shapex = this.rotate_about_origin(shapex, rot1axis, rot1angle);
-
-			}
+			//    becomes shapenormals[i].  This puts the shape in
+			//    the correct plane, but does not constrain its
+			//    rotation about shapenormals[i].
+			loop = this.rotate_onto(loop, [0,0,1], shapenormals[i]);
+			var shapex = loop.pop();
 
 			// 2. Rotate around shapenormals[i] so that [1,0,0]
 			//    becomes fixedpathnormals[i].
-			var rot2axis = this.unit(shapenormals[i]);
-			var rot2angle = this.angle_between(shapex[0], this.unit(fixedpathnormals[i]));
-			console.log(rot2angle);
-			if (rot2angle > 1e-7) {
-				loop = this.rotate_about_origin(loop, rot2axis, rot2angle);
-			}
-			// This would probably be faster and more numerically stable
+			loop = this.rotate_onto(loop, shapex, fixedpathnormals[i]);
+
+			// (This would probably be faster and more numerically stable
 			// if the two rotations were applied as one combined operation
-			// rather than separate steps.
+			// rather than separate steps.)
 
 			// 3. Translate to path[i].
 			loop = this.translate(loop, path[i]);
@@ -192,6 +182,19 @@ nt3d = {
 		}
 		return rotated;
 	},
+	rotate_onto: function(points, a, b) {
+		// Rotate points such that a (in points-space) maps onto b
+		// by crossing a and b to get a rotation axis and using
+		// angle_between to get a rotation angle.
+		var angle = this.angle_between(this.unit(a), this.unit(b));
+		if (Math.abs(angle) < 1e-15) {
+			// No siginificant rotation to perform.  Bail to avoid
+			// NaNs and numerical error
+			return points;
+		}
+		var axis = this.unit(this.cross(a, b));
+		return this.rotate_about_origin(points, axis, angle);
+	},
 	rotate: function(points, center, axis, angle) { // axis must be a unit vector
 		return this.translate(
 			this.rotate_about_origin(