From c92a9d3f963401b999f661dde190a739ebbeafde Mon Sep 17 00:00:00 2001
From: Scott Worley <ScottWorley@ScottWorley.com>
Date: Mon, 24 Dec 2012 20:53:07 -0800
Subject: [PATCH] Fix a bug in project()

It was kind of sheer luck that any extrudes worked before this fix.

Also, add rotation to torus_by_extrude, which was an easy way to
reproduce this.
---
 nt3d.js               | 2 +-
 torus_by_extrude.html | 4 +++-
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/nt3d.js b/nt3d.js
index c69c185..fd57824 100644
--- a/nt3d.js
+++ b/nt3d.js
@@ -211,7 +211,7 @@ nt3d = {
 	},
 	project: function(a, b) { // Project b onto a
 		var a_magnitude = this.magnitude(a);
-		return this.scale(a, this.dot(a, b) / a_magnitude * a_magnitude);
+		return this.scale(a, this.dot(a, b) / (a_magnitude * a_magnitude));
 	},
 	project_to_orthogonal: function(a, b) {
 		// The nearest thing to b that is orthogonal to a
diff --git a/torus_by_extrude.html b/torus_by_extrude.html
index 4655519..10ae92e 100644
--- a/torus_by_extrude.html
+++ b/torus_by_extrude.html
@@ -3,8 +3,9 @@
     <title>Torus by extrude</title>
     <script type="text/javascript" src="nt3d.js"></script>
     <script type="text/javascript">
-      function torus_by_extrude(torus_radius, cross_section_radius, long_steps, short_steps) {
+      function torus_by_extrude(torus_radius, cross_section_radius, rotation, long_steps, short_steps) {
       	var path = nt3d.circle(torus_radius, long_steps);
+      	path = nt3d.rotate_about_origin(path, [0,1,0], rotation * 2*Math.PI);
       	return nt3d.closed_extrude(
       	  path,
 	  nt3d.circle(cross_section_radius, short_steps),
@@ -13,6 +14,7 @@
       }
       var params = [["Torus radus", 100],
                     ["Cross section radius", 40],
+                    ["Rotation (turns)", 0.001],
                     ["Steps around the long way", 50],
                     ["Steps around the short way", 16]];
     </script>
-- 
2.44.1