X-Git-Url: http://git.scottworley.com/nt3d/blobdiff_plain/2f26ede4efa95cc756a2b3240c2a9e29f0f48486..911d073bae58f93ab72a7afa242a0a478299b8e9:/nt3d.js?ds=inline

diff --git a/nt3d.js b/nt3d.js
index c69c185..bc11c71 100644
--- a/nt3d.js
+++ b/nt3d.js
@@ -62,6 +62,27 @@ nt3d = {
 		return this.closed_trianglefan([apex].concat(base)).concat(
 		       this.trianglefan(base.reverse()));
 	},
+	sphere: function(center, radius, latitude_steps, longitude_steps) {
+		return this.oriented_sphere(center, radius, [0,0,1], [1,0,0], latitude_steps, longitude_steps);
+	},
+	oriented_sphere: function(center, radius, north, greenwich, latitude_steps, longitude_steps) {
+		var unit_north = this.unit(north);
+		var north_pole = this.translate_point(this.scale(unit_north,  radius), center);
+		var south_pole = this.translate_point(this.scale(unit_north, -radius), center);
+		return this.spheroid(north_pole, south_pole, radius, greenwich, latitude_steps, longitude_steps);
+	},
+	spheroid: function(north_pole, south_pole, radius, greenwich, latitude_steps, longitude_steps) {
+		var delta = this.sub(north_pole, south_pole);
+		var path = [];
+		for (var i = 0; i < latitude_steps-1; i++) {
+			path.push(this.translate_point(south_pole, this.scale(delta, (1-Math.cos(Math.PI*i/(latitude_steps-1)))/2)));
+		}
+		path.push(north_pole);
+		function shape(i) {
+			return nt3d.circle(radius*Math.sin(Math.PI*i/(latitude_steps-1)), longitude_steps);
+		}
+		return this.extrude(path, shape, delta, greenwich);
+	},
 	shapenormals_from_closed_path: function(path) {
 		return function(i) {
 			var prev = (i == 0) ? path.length-1 : i-1;
@@ -83,6 +104,14 @@ nt3d = {
 			return nt3d.sub(path[i+1], path[i-1]);
 		};
 	},
+	pathnormals_from_point: function(path, p) {
+		// Use this with any point that is not on any path tangent line
+		var pathnormals = [];
+		for (var i = 0; i < path.length; i++) {
+			pathnormals.push(this.sub(path[i], p));
+		}
+		return pathnormals;
+	},
 	to_function: function(thing, make_indexer) {
 		// If thing is a point, just yield thing every time.
 		// If thing is a list of points && make_indexer, index into thing.
@@ -152,7 +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
@@ -211,7 +249,7 @@ 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
@@ -220,14 +258,24 @@ nt3d = {
 	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]];
+			translated[i] = this.translate_point(points[i], offset);
 		}
 		return translated;
 	},
+	translate_point: function(point, offset) {
+		return [point[0] + offset[0],
+		        point[1] + offset[1],
+		        point[2] + offset[2]];
+	},
 	angle_between: function(a, b) { // a and b must be unit vectors
-		return Math.acos(this.dot(a, b));
+		var the_dot = this.dot(a, b);
+		if (the_dot <= -1) {
+			return Math.PI;
+		}
+		if (the_dot >= 1) {
+			return 0;
+		}
+		return Math.acos(the_dot);
 	},
 	rotate_about_origin: function(points, axis, angle) { // axis must be a unit vector
 		// From http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/
@@ -244,17 +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-15) {
-			// No siginificant rotation to perform.  Bail to avoid
+		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
@@ -265,6 +336,79 @@ nt3d = {
 				angle),
 			center);
 	},
+	point_equal: function(a, b, epsilon) {
+		return Math.abs(a[0] - b[0]) < epsilon &&
+		       Math.abs(a[1] - b[1]) < epsilon &&
+		       Math.abs(a[2] - b[2]) < epsilon;
+	},
+	degenerate_face_epsilon: 1e-10,
+	is_degenerate: function(a, b, c) {
+		return this.point_equal(a, b, this.degenerate_face_epsilon) ||
+		       this.point_equal(b, c, this.degenerate_face_epsilon) ||
+		       this.point_equal(c, a, this.degenerate_face_epsilon);
+	},
+	validate: function(points) {
+		// Do a little validation
+		if (points.length % 3 != 0) {
+			alert("Points list length not divisble by 3!");
+		}
+		var nan_count = 0;
+		var nan_point_count = 0;
+		var nan_face_count = 0;
+		for (var i = 0; i < points.length/3; i++) {
+			var nan_in_face = false;
+			for (var j = 0; j < 3; j++) {
+				var nan_in_point = false;
+				for (var k = 0; k < 3; k++) {
+					if (isNaN(points[i*3+j][k])) {
+						nan_count++;
+						nan_in_point = true;
+						nan_in_face = true;
+					}
+				}
+				if (nan_in_point) nan_point_count ++;
+			}
+			if (nan_in_face) nan_face_count ++;
+		}
+		if (nan_count != 0) {
+			alert(nan_count + " NaNs in " + nan_point_count + " points in " + nan_face_count + " faces (" + (100 * nan_face_count / (points.length/3)) + "% of faces).");
+		}
+	},
+	remove_degenerate_faces: function(points) {
+		// Note: This modifies points
+		var degenerate_face_count = 0;
+		for (var i = 0; i < points.length/3; i++) {
+			if (this.is_degenerate(points[i*3+0], 
+			                       points[i*3+1], 
+			                       points[i*3+2])) {
+				points.splice(i*3, 3);
+				i--;
+				degenerate_face_count ++;
+			}
+		}
+		if (degenerate_face_count != 0) {
+			console.log("Removed " + degenerate_face_count + " degenerate faces");
+		}
+		return points;
+	},
+	to_stl: function(points, name) {
+		var stl = "solid " + name + "\n";
+		for (var i = 0; i < points.length/3; i++) {
+			var a = points[i*3+0];
+			var b = points[i*3+1];
+			var c = points[i*3+2];
+			var normal = this.normal(a, b, c);
+			stl += "facet normal " + normal[0] + " " + normal[1] + " " + normal[2] + "\n" +
+				"outer loop\n" +
+				"vertex " + a[0] + " " + a[1] + " " + a[2] + "\n"+
+				"vertex " + b[0] + " " + b[1] + " " + b[2] + "\n"+
+				"vertex " + c[0] + " " + c[1] + " " + c[2] + "\n"+
+				"endloop\n" +
+				"endfacet\n";
+		}
+		stl += "endsolid " + name + "\n";
+		return stl;
+	},
 	go: function() {
 		// Remove any previous download links
 		var old_download_link = document.getElementById("nt3d_download");
@@ -284,30 +428,13 @@ nt3d = {
 			params[i] = isNaN(as_num) ? as_string : as_num;
 		}
 
-		// Run user_function
 		this.points = this.user_function.apply(null, params);
-		if (this.points.length % 3 != 0) {
-			alert("Points list length not divisble by 3!");
-		}
-		var n = this.points.length / 3;
 
-		// Make STL
-		this.stl = "solid " + this.user_function.name + "\n";
-		for (var i = 0; i < n; i++) {
-			var a = this.points[i*3+0];
-			var b = this.points[i*3+1];
-			var c = this.points[i*3+2];
-			var normal = this.normal(a, b, c);
-			this.stl += "facet normal " + normal[0] + " " + normal[1] + " " + normal[2] + "\n" +
-				"outer loop\n" +
-				"vertex " + a[0] + " " + a[1] + " " + a[2] + "\n"+
-				"vertex " + b[0] + " " + b[1] + " " + b[2] + "\n"+
-				"vertex " + c[0] + " " + c[1] + " " + c[2] + "\n"+
-				"endloop\n" +
-				"endfacet\n";
-		}
-		this.stl += "endsolid " + this.user_function.name + "\n";
+		this.validate(this.points);
+
+		this.remove_degenerate_faces(this.points);
 
+		this.stl = this.to_stl(this.points, this.user_function.name);
 
 		// Offer result as download
 		var download_link = document.createElement("a");