Explicitly bounds-check in angle_between()

[nt3d] / nt3d.js

/* nt3d - Javascript library for doing some 3D stuff.
 * Copyright (C) 2012  Scott Worley <ScottWorley@ScottWorley.com>
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU Affero General Public License as
 *  published by the Free Software Foundation, either version 3 of the
 *  License, or (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU Affero General Public License for more details.
 *
 *  You should have received a copy of the GNU Affero General Public License
 *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

nt3d = {
	triangle: function(a, b, c) {
		return [a, b, c];
	},
	quad: function(a, b, c, d) {
		return this.triangle(a, b, c).concat(
		       this.triangle(c, d, a));
	},
	trianglefan: function(fan) {
		var result = [];
		for (var i = 2; i < fan.length; i++) {
			result.push(fan[0], fan[i-1], fan[i]);
		}
		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(this.quad(strip[i-2], strip[i-1], strip[i+1], strip[i]));
		}
		return result;
	},
	closed_quadstrip: function(strip) {
		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.
			loop = this.rotate_onto(loop, shapex, pathnormali);

			// (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],
		        a[0]*b[1] - a[1]*b[0]];
	},
	normal: function(a, b, c) {
		return this.cross(this.sub(a, b), this.sub(b, c));
	},
	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);
		}
		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;
	},
	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
			// NaNs and numerical error
			return points;
		}
		var 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);
	},
	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(the_this) { (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[i] = isNaN(as_num) ? as_string : as_num;
		}

		// Run user_function
		this.points = this.user_function.apply(null, params);

		// Do a little validation
		if (this.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 < this.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(this.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 / (this.points.length/3)) + "% of faces).");
		}

		// Remove degenerate faces
		var degenerate_face_count = 0;
		for (var i = 0; i < this.points.length/3; i++) {
			if (this.is_degenerate(this.points[i*3+0], 
			                       this.points[i*3+1], 
			                       this.points[i*3+2])) {
				this.points.splice(i*3, 3);
				i--;
				degenerate_face_count ++;
			}
		}
		if (degenerate_face_count != 0) {
			console.log("Removed " + degenerate_face_count + " degenerate faces");
		}

		// Make STL
		this.stl = "solid " + this.user_function.name + "\n";
		for (var i = 0; i < this.points.length/3; 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";


		// Offer result as download
		var download_link = document.createElement("a");
		download_link.appendChild(document.createTextNode("Download!"));
		download_link.setAttribute("id", "nt3d_download");
		download_link.setAttribute("style", "background-color: blue");
		download_link.setAttribute("download", this.user_function.name + ".stl");
		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);

		}).call(the_this); }, 0, this); // (We were in a callback this whole time, remember?)
	},
	framework: function (f, params) {
		this.user_function = f;
		this.user_params = params;

		// Make the UI
		this.ui = document.getElementById("nt3dui");
		if (!this.ui) {
			this.ui = document.createElement("div");
			this.ui.setAttribute("id", "nt3dui");
			document.body.appendChild(this.ui);
		}
		this.form = document.createElement("form");
		this.form.setAttribute("onsubmit", "nt3d.go(); return false");
		this.ui.appendChild(this.form);
		var table = document.createElement("table");
		this.form.appendChild(table);
		var tr = document.createElement("tr");
		table.appendChild(tr);
		var th = document.createElement("th");
		th.appendChild(document.createTextNode("Variable"));
		tr.appendChild(th);
		th = document.createElement("th");
		th.appendChild(document.createTextNode("Value"));
		tr.appendChild(th);
		for (var i = 0; i < params.length; i++) {
			tr = document.createElement("tr");
			table.appendChild(tr);
			var td = document.createElement("td");
			td.appendChild(document.createTextNode(params[i][0]));
			tr.appendChild(td);
			td = document.createElement("td");
			var input = document.createElement("input");
			input.setAttribute("name", "param" + i);
			input.setAttribute("value", params[i][1]);
			td.appendChild(input);
			tr.appendChild(td);
		}
		var go = document.createElement("input");
		go.setAttribute("type", "button");
		go.setAttribute("value", "Go!");
		go.setAttribute("onclick", "nt3d.go()");
		this.form.appendChild(go);
	}
};