From: Scott Worley <ScottWorley@ScottWorley.com>
Date: Mon, 31 Dec 2012 08:54:08 +0000 (-0800)
Subject: Handle opposite vectors in rotate_onto
X-Git-Url: http://git.scottworley.com/nt3d/commitdiff_plain/df8f7c913f82a09f187927f8f201844a4e738060?ds=sidebyside

Handle opposite vectors in rotate_onto

And detect them in extrude() and avoid calling rotate_onto for the
second rotation in that case.
---

diff --git a/nt3d.js b/nt3d.js
index 7198e22..7e0fa25 100644
--- a/nt3d.js
+++ b/nt3d.js
@@ -181,7 +181,16 @@ nt3d = {
 
 			// 2. Rotate around shapenormali so that [1,0,0]
 			//    becomes pathnormali.
-			loop = this.rotate_onto(loop, shapex, pathnormali);
+			if (!this.opposite(shapex, pathnormali)) {
+				loop = this.rotate_onto(loop, shapex, pathnormali);
+			} else {
+				// Rare edge case: When shapex and pathnormali are
+				// opposite, rotate_onto cannot cross them to get
+				// an axis of rotation.  In this case, we (extrude)
+				// already know what to do -- just rotate PI around
+				// shapenormali!
+				loop = this.rotate_about_origin(loop, shapenormali, Math.PI);
+			}
 
 			// (This would probably be faster and more numerically stable
 			// if the two rotations were applied as one combined operation
@@ -283,17 +292,40 @@ nt3d = {
 		}
 		return rotated;
 	},
+	angle_epsilon: 1e-7,
+	opposite: function(a, b) {
+		// Do a and b point in exactly opposite directions?
+		return Math.abs(this.angle_between(this.unit(a), this.unit(b)) - Math.PI) < this.angle_epsilon;
+	},
 	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-7) {
+		var abs_angle = Math.abs(angle);
+		if (Math.abs(angle) < this.angle_epsilon) {
 			// No significant rotation to perform.  Bail to avoid
 			// NaNs and numerical error
 			return points;
 		}
-		var axis = this.unit(this.cross(a, b));
+		var axis;
+		if (Math.abs(abs_angle - Math.PI) < this.angle_epsilon) {
+			// a and b point in opposite directions, so
+			// we cannot cross them.  So just pick something.
+			// If the caller wishes to avoid this behaviour,
+			// they should check with this.opposite() first.
+			axis = this.project_to_orthogonal(a, [1,0,0]);
+			console.log("rotate_onto: a and b are opposite!  If you carefully chose them to meet some other constraint, you will be sad!  Arbitrarily using axis [1,0,0] ->", axis);
+			if (this.magnitude(axis) < this.angle_epsilon) {
+				// Oh, double bad luck!  Our arbitrary choice
+				// lines up too!  A second, orthogonal arbitrary
+				// choice is now guaranteed to succeed.
+				axis = this.project_to_orthogonal(a, [0,1,0]);
+				console.log("rotate_onto: Double bad luck!  Arbitrarily using axis [0,1,0] ->", axis);
+			}
+		} else {
+			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