+ 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.
+ 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));
+ },
projects / nt3d / blobdiff