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);
        }
};