X-Git-Url: http://git.scottworley.com/nt3d/blobdiff_plain/0ab5ca18fc7c4d26a3a7cf30cd902d2ebc190f4d..cf4bf59f0dce374bb78bbd2197c4ef9818f48362:/nt3d.js

diff --git a/nt3d.js b/nt3d.js
index 623c0f1..80390b9 100644
--- a/nt3d.js
+++ b/nt3d.js
@@ -30,24 +30,215 @@ nt3d = {
 		}
 		return result;
 	},
+	closed_trianglefan: function(fan) {
+		return this.trianglefan(fan.concat([fan[1]]));
+	},
 	quadstrip: function(strip) {
 		if (strip.length % 2 != 0) {
 			alert("quadstrip length not divisble by 2!");
 		}
 		var result = [];
 		for (var i = 2; i < strip.length; i += 2) {
-			result = result.concat(nt3d.quad(strip[i-2], strip[i-1], strip[i+1], strip[i]));
+			result = result.concat(this.quad(strip[i-2], strip[i-1], strip[i+1], strip[i]));
 		}
 		return result;
 	},
 	closed_quadstrip: function(strip) {
-		return nt3d.quadstrip(strip).concat(nt3d.quad(strip[strip.length-2], strip[strip.length-1], strip[1], strip[0]));
+		return this.quadstrip(strip.concat([strip[0], strip[1]]));
+	},
+	circle: function(r, n) {
+		var points = [];
+		for (var i = 0; i < n; i++) {
+			points.push([r*Math.cos(2*Math.PI*i/n),
+			             r*Math.sin(2*Math.PI*i/n),
+			             0]);
+		}
+		return points;
+	},
+	cone: function(base_center, apex, radius, steps) {
+		var base = this.circle(radius, steps);
+		base = this.rotate_onto(base, [0,0,1], this.sub(apex, base_center));
+		base = this.translate(base, base_center);
+		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;
+			var next = (i == path.length-1) ? 0 : i+1;
+			return nt3d.sub(path[next], path[prev]);
+		};
+	},
+	shapenormals_from_path_and_extra_points: function(path, first_point, last_point) {
+		return function(i) {
+			var prev = (i == 0) ? first_point : path[i-1];
+			var next = (i == path.length-1) ? last_point : path[i+1];
+			return nt3d.sub(next, prev);
+		};
+	},
+	shapenormals_from_path_and_first_and_last_normals: function(path, first_normal, last_normal) {
+		return function(i) {
+			if (i == 0) { return first_normal; }
+			if (i == path.length-1) { return last_normal; }
+			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.
+		// If thing is already a function, just return it.
+		if (({}).toString.call(thing) === "[object Function]") {
+			return thing;  // Already a function
+		}
+		if (make_indexer && Array.isArray(thing[0])) {
+			// Looks like a list of points.
+			return function(i) { return thing[i]; }
+		}
+		return function() { return thing; }
+	},
+	extrude: function(path, shape, shapenormals, pathnormals) {
+
+		var guts_result = this._extrude_guts(path, shape, shapenormals, pathnormals);
+		// Add the end-caps
+		// XXX: This doesn't work if shape is not convex
+		return guts_result.points.concat(
+			this.trianglefan(guts_result.first_loop.reverse()),
+			this.trianglefan(guts_result.last_loop));
+
+	},
+	closed_extrude: function(path, shape, shapenormals, pathnormals) {
+		var guts_result = this._extrude_guts(path, shape, shapenormals, pathnormals);
+		// Stitch the ends together
+		return guts_result.points.concat(
+			this.closed_quadstrip(this.zip(guts_result.first_loop, guts_result.last_loop)));
+	},
+	_extrude_guts: function(path, shape, shapenormals, pathnormals) {
+		var shape_fun = this.to_function(shape, false);
+		var shapenormal_fun = this.to_function(shapenormals, true);
+		var pathnormal_fun = this.to_function(pathnormals, true);
+		var result = { points: [] };
+		var prev_loop;
+		for (var i = 0; i < path.length; i++) {
+			var shapenormali = shapenormal_fun(i, path[i]);
+			var pathnormali = pathnormal_fun(i, path[i], shapenormali);
+
+			// Fix pathnormali to be perfectly perpendicular to
+			// shapenormali.  pathnormali must be perpendicular to
+			// shapenormali or the second rotation will take loop
+			// back out of the shapenormali plane that the first
+			// rotation so carefully placed it in.  But, letting
+			// callers be sloppy with the pathnormals can greatly
+			// simplify generating them -- so much so that you can
+			// often just pass a constant to use the same value
+			// along the whole path.
+			pathnormali = this.project_to_orthogonal(shapenormali, pathnormali);
+
+			var shapei = shape_fun(i, path[i], shapenormali, pathnormali);
+
+			// loop is shapei in 3d with (0,0) at path[i], shape's
+			// z axis in the direction of shapenormali, and shape's
+			// x axis in the direction of pathnormali.  We tack
+			// [1,0,0] onto the end as a hack to see where it ends
+			// up after the first rotation.  This is removed later.
+			var loop = shapei.concat([[1,0,0]]);
+
+			// This is done in three steps:
+			// 1. Rotate shape out of the xy plane so that [0,0,1]
+			//    becomes shapenormali.  This puts the shape in
+			//    the correct plane, but does not constrain its
+			//    rotation about shapenormali.
+			loop = this.rotate_onto(loop, [0,0,1], shapenormali);
+			var shapex = loop.pop();
+
+			// 2. Rotate around shapenormali so that [1,0,0]
+			//    becomes 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
+			// rather than separate steps.)
+
+			// 3. Translate to path[i].
+			loop = this.translate(loop, path[i]);
+
+			if (i == 0) {
+				result.first_loop = loop;
+			} else {
+				result.points = result.points.concat(this.closed_quadstrip(this.zip(loop, prev_loop)));
+			}
+			prev_loop = loop;
+		}
+		result.last_loop = prev_loop;
+		return result;
+	},
+	zip: function(a, b) {
+		var result = [];
+		if (a.length != b.length) {
+			alert("Zip over different-sized inputs");
+		}
+		for (var i = 0; i < a.length; i++) {
+			result.push(a[i], b[i]);
+		}
+		return result;
+	},
+	magnitude: function(a) {
+		return Math.sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
+	},
+	unit: function(a) {
+		return this.scale(a, 1 / this.magnitude(a));
 	},
 	sub: function(a, b) {
 		return [a[0] - b[0],
 		        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];
+	},
+	scale: function(v, s) { // Scale vector v by scalar s
+		return [s*v[0], s*v[1], s*v[2]];
+	},
 	cross: function(a, b) {
 		return [a[1]*b[2] - a[2]*b[1],
 		        a[2]*b[0] - a[0]*b[2],
@@ -56,28 +247,158 @@ nt3d = {
 	normal: function(a, b, c) {
 		return this.cross(this.sub(a, b), this.sub(b, c));
 	},
-	go: function() {
-		// Get params from form
-		var params = [];
-		for (var i = 0; i < this.user_params.length; i++) {
-			params[i] = this.form.elements["param"+i].value;
+	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));
+	},
+	project_to_orthogonal: function(a, b) {
+		// The nearest thing to b that is orthogonal to a
+		return this.sub(b, this.project(a, b));
+	},
+	translate: function(points, offset) {
+		var translated = [];
+		for (var i = 0; i < points.length; i++) {
+			translated[i] = this.translate_point(points[i], offset);
 		}
-
-		// Run user_function
-		this.points = this.user_function.apply(null, params);
-		if (this.points.length % 3 != 0) {
+		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
+		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/
+		var cosangle = Math.cos(angle);
+		var sinangle = Math.sin(angle);
+		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;
+	},
+	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));
+		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;
+		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
+		return this.translate(
+			this.rotate_about_origin(
+				this.translate(points, this.neg(center)),
+				axis,
+				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 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 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);
-			this.stl += "facet normal " + normal[0] + " " + normal[1] + " " + normal[2] + "\n" +
+			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"+
@@ -85,14 +406,36 @@ nt3d = {
 				"endloop\n" +
 				"endfacet\n";
 		}
-		this.stl += "endsolid " + this.user_function.name + "\n";
-
+		stl += "endsolid " + name + "\n";
+		return stl;
+	},
+	go: function() {
 		// Remove any previous download links
 		var old_download_link = document.getElementById("nt3d_download");
 		if (old_download_link) {
 			old_download_link.parentNode.removeChild(old_download_link);
 		}
 
+		// Continue in a callback, so that there's not a stale download
+		// link hanging around while we process.
+		setTimeout(function() {
+
+		// Get params from form
+		var params = {};
+		for (var i = 0; i < this.user_params.length; i++) {
+			var as_string = this.form.elements["param"+i].value;
+			var as_num = +as_string;
+			params[this.user_params[i][0]] = isNaN(as_num) ? as_string : as_num;
+		}
+
+		this.points = this.user_function.call(null, params);
+
+		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");
 		download_link.appendChild(document.createTextNode("Download!"));
@@ -102,6 +445,8 @@ nt3d = {
 		download_link.setAttribute("href", "data:application/sla," + encodeURIComponent(this.stl));
 		this.ui.appendChild(download_link);
 		setTimeout(function() { download_link.setAttribute("style", "-webkit-transition: background-color 0.4s; -moz-transition: background-color 0.4s; -o-transition: background-color 0.4s; -ms-transition: background-color 0.4s; transition: background-color 0.4s; background-color: inherit"); }, 0);
+
+		}.bind(this), 0); // (We were in a callback this whole time, remember?)
 	},
 	framework: function (f, params) {
 		this.user_function = f;
@@ -131,7 +476,18 @@ nt3d = {
 			tr = document.createElement("tr");
 			table.appendChild(tr);
 			var td = document.createElement("td");
-			td.appendChild(document.createTextNode(params[i][0]));
+			var description;
+			if (params[i].length > 2) {
+				description = params[i][2];
+			} else {
+				description = params[i][0];
+				description = description[0].toUpperCase() + description.substr(1);
+				description = description.replace(/_(.)/g, function(_, c) {
+					return " " + c.toUpperCase();
+				});
+				description = description.replace("Num ", "Number of ");
+			}
+			td.appendChild(document.createTextNode(description));
 			tr.appendChild(td);
 			td = document.createElement("td");
 			var input = document.createElement("input");