X-Git-Url: http://git.scottworley.com/nt3d/blobdiff_plain/94faa4e58b86d3e6acdbe4f56d15d8fe21adf5c0..1e62819c99e2c97c4f11c9612012c83cf36dd4ff:/nt3d.js

diff --git a/nt3d.js b/nt3d.js
index d0d7161..1cabfb1 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_about_origin(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_about_origin(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 {
@@ -140,6 +140,9 @@ nt3d = {
 		        a[1] - b[1],
 		        a[2] - b[2]];
 	},
+	neg: function(a) {
+		return [-a[0], -a[1], -a[2]];
+	},
 	dot: function(a, b) {
 		return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
 	},
@@ -158,20 +161,40 @@ 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_about_origin: 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;
+	},
+	rotate: function(points, center, axis, angle) { // axis must be a unit vector
+		return this.translate(
+			this.rotate_about_origin(
+				this.translate(points, this.neg(center)),
+				axis,
+				angle),
+			center);
 	},
 	go: function() {
 		// Get params from form