+ 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()));
+ },
+ extrude: function(path, shape, shapenormals, pathnormals) {
+
+ var guts_result = nt3d._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(
+ nt3d.trianglefan(guts_result.first_loop.reverse()),
+ nt3d.trianglefan(guts_result.last_loop));
+
+ },
+ closed_extrude: function(path, shape, shapenormals, pathnormals) {
+ var guts_result = nt3d._extrude_guts(path, shape, shapenormals, pathnormals);
+ // Stitch the ends together
+ return guts_result.points.concat(
+ nt3d.closed_quadstrip(nt3d.zip(guts_result.first_loop, guts_result.last_loop)));
+ },
+ _fix_pathnormals: function(shapenormals, pathnormals) {
+ // Fix pathnormals[i] to be perfectly perpendicular to
+ // shapenormals[i]. This lets extrude callers be sloppy
+ // with pathnormals, which can greatly simplify things.
+ var fixedpathnormals = [];
+ for (var i = 0; i < pathnormals.length; i++) {
+ var proj = this.project(shapenormals[i], pathnormals[i]);
+ fixedpathnormals[i] = this.sub(pathnormals[i], proj);
+ }
+ return fixedpathnormals;
+ },
+ _extrude_guts: function(path, shape, shapenormals, pathnormals) {
+ var fixedpathnormals = this._fix_pathnormals(shapenormals, pathnormals);
+ var result = { points: [] };
+ var prev_loop;
+ for (var i = 0; i < path.length; i++) {
+ // loop is shape in 3d with (0,0) at path[i], shape's
+ // z axis in the direction of shapenormals[i], and
+ // shape's x axis in the direction of pathnormals[i].
+ // We tack [1,0,0] onto the end as a hack to see where
+ // it ends up after rotation. This is removed later.
+ var loop = shape.concat([[1,0,0]]);
+
+ // This is done in three steps:
+ // 1. Rotate shape out of the xy plane so that [0,0,1]
+ // becomes shapenormals[i]. This puts the shape in
+ // the correct plane, but does not constrain its
+ // rotation about shapenormals[i].
+ loop = this.rotate_onto(loop, [0,0,1], shapenormals[i]);
+ var shapex = loop.pop();
+
+ // 2. Rotate around shapenormals[i] so that [1,0,0]
+ // becomes fixedpathnormals[i].
+ loop = this.rotate_onto(loop, shapex, fixedpathnormals[i]);
+
+ // (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(nt3d.closed_quadstrip(nt3d.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