From 2f6b97f8bc892064a1ca781c11b08104182f862a Mon Sep 17 00:00:00 2001
From: Scott Worley <ScottWorley@ScottWorley.com>
Date: Wed, 19 Dec 2012 05:27:59 -0800
Subject: [PATCH] Rotate and translate operate on lists of points

Also, change extrude's interface to take 3d points, just with the z
values at zero.
---
 box_by_extrude.html |  8 +++----
 nt3d.js             | 52 ++++++++++++++++++++++++++++-----------------
 2 files changed, 36 insertions(+), 24 deletions(-)

diff --git a/box_by_extrude.html b/box_by_extrude.html
index e8183f2..6a883a6 100644
--- a/box_by_extrude.html
+++ b/box_by_extrude.html
@@ -5,10 +5,10 @@
     <script type="text/javascript">
       function box_by_extrude(size_as_string) {
         var size = parseFloat(size_as_string);
-        var origin = [0,    0   ];
-        var x      = [size, 0   ];
-        var y      = [0,    size];
-        var xy     = [size, size];
+        var origin = [0,    0,    0];
+        var x      = [size, 0,    0];
+        var y      = [0,    size, 0];
+        var xy     = [size, size, 0];
       	return nt3d.extrude([origin, x, xy, y],
       	                    [[0, 0, 0], [0, 0, 1]],
       	                    [[0, 0, 1], [0, 0, 1]],
diff --git a/nt3d.js b/nt3d.js
index d0d7161..3d87ffb 100644
--- a/nt3d.js
+++ b/nt3d.js
@@ -80,7 +80,8 @@ 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 = [];
+			var loop = shape;
+
 			// 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
@@ -90,25 +91,24 @@ nt3d = {
 			//    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]));
+			if (rot1angle > 1e-7) {
+				loop = this.rotate(loop, rot1axis, rot1angle);
+			}
+
 			// 2. Rotate around shapenormals[i] so that [1,0,0]
 			//    becomes fixedpathnormals[i].
 			var rot2axis = this.unit(shapenormals[i]);
 			var rot2angle = this.angle_between([1,0,0], this.unit(fixedpathnormals[i]));
-			// 3. Translate to path[i].
+			if (rot2angle > 1e-7) {
+				loop = this.rotate(loop, rot2axis, rot2angle);
+			}
 			// This would probably be faster and more numerically stable
 			// if the two rotations were applied as one combined operation
 			// rather than separate steps.
-			for (var j = 0; j < shape.length; j++) {
-				var p = [shape[j][0], shape[j][1], 0];
-				if (rot1angle > 1e-7) {
-					p = this.rotate(p, rot1axis, rot1angle);
-				}
-				if (rot2angle > 1e-7) {
-					p = this.rotate(p, rot2axis, rot2angle);
-				}
-				p = this.translate(p, path[i]);
-				loop[j] = p;
-			}
+
+			// 3. Translate to path[i].
+			loop = this.translate(loop, path[i]);
+
 			if (i == 0) {
 				result.first_loop = loop;
 			} else {
@@ -158,20 +158,32 @@ nt3d = {
 		var a_magnitude = this.magnitude(a);
 		return this.scale(a, this.dot(a, b) / a_magnitude * a_magnitude);
 	},
-	translate: function(a, b) {
-		return [a[0] + b[0], a[1] + b[1], a[2] + b[2]];
+	translate: function(points, offset) {
+		var translated = [];
+		for (var i = 0; i < points.length; i++) {
+			translated[i] = [points[i][0] + offset[0],
+			                 points[i][1] + offset[1],
+			                 points[i][2] + offset[2]];
+		}
+		return translated;
 	},
 	angle_between: function(a, b) { // a and b must be unit vectors
 		return Math.acos(this.dot(a, b));
 	},
-	rotate: function(point, axis, angle) { // axis must be a unit vector
+	rotate: function(points, axis, angle) { // axis must be a unit vector
 		// From http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/
 		var cosangle = Math.cos(angle);
 		var sinangle = Math.sin(angle);
-		var tmp = this.dot(point, axis) * (1 - cosangle);
-		return [axis[0]*tmp + point[0]*cosangle + (-axis[2]*point[1] + axis[1]*point[2])*sinangle,
-		        axis[1]*tmp + point[1]*cosangle + ( axis[2]*point[0] - axis[0]*point[2])*sinangle,
-		        axis[2]*tmp + point[2]*cosangle + (-axis[1]*point[0] + axis[0]*point[1])*sinangle];
+		var rotated = [];
+		for (var i = 0; i < points.length; i++) {
+			var p = points[i];
+			var tmp = this.dot(p, axis) * (1 - cosangle);
+			rotated[i] = [
+				axis[0]*tmp + p[0]*cosangle + (-axis[2]*p[1] + axis[1]*p[2])*sinangle,
+				axis[1]*tmp + p[1]*cosangle + ( axis[2]*p[0] - axis[0]*p[2])*sinangle,
+				axis[2]*tmp + p[2]*cosangle + (-axis[1]*p[0] + axis[0]*p[1])*sinangle];
+		}
+		return rotated;
 	},
 	go: function() {
 		// Get params from form
-- 
2.44.1