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]]));
+ },
+ extrude: function(shape, path, shapenormals, pathnormals) {
+ var guts_result = nt3d._extrude_guts(shape, path, 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(shape, path, shapenormals, pathnormals) {
+ var guts_result = nt3d._extrude_guts(shape, path, 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(shape, path, 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].
+ var loop = [];
+ // This is done in three steps:
+ // 1. Rotate shape out of the xy plane so that [0,0,1]
+ // becomes shapenormals[i] by crossing [0,0,1] and
+ // shapenormals[i] to get a rotation axis and taking
+ // their dot product to get a rotation angle. This
+ // puts the shape in the correct plane, but does not
+ // constrain its rotation about shapenormals[i].
+ var rot1axis = this.unit(this.cross([0,0,1], shapenormals[i]));
+ var rot1angle = this.angle_between([0,0,1], this.unit(shapenormals[i]));
+ // 2. Rotate around shapenormals[i] so that [1,0,0]
+ // becomes fixedpathnormals[i].
+ var rot2axis = this.unit(shapenormals[i]);
+ var rot2angle = this.angle_between([1,0,0], this.unit(fixedpathnormals[i]));
+ // 3. Translate to path[i].
+ // This would probably be faster and more numerically stable
+ // if the two rotations were applied as one combined operation
+ // rather than separate steps.
+ for (var j = 0; j < shape.length; j++) {
+ var p = [shape[j][0], shape[j][1], 0];
+ if (rot1angle > 1e-7) {
+ p = this.rotate(p, rot1axis, rot1angle);
+ }
+ if (rot2angle > 1e-7) {
+ p = this.rotate(p, rot2axis, rot2angle);
+ }
+ p = this.translate(p, path[i]);
+ loop[j] = p;
+ }
+ 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));
+ },
sub: function(a, b) {
return [a[0] - b[0],
a[1] - b[1],
a[2] - b[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],
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);
+ },
+ translate: function(a, b) {
+ return [a[0] + b[0], a[1] + b[1], a[2] + b[2]];
+ },
+ angle_between: function(a, b) { // a and b must be unit vectors
+ return Math.acos(this.dot(a, b));
+ },
+ rotate: function(point, 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 tmp = this.dot(point, axis) * (1 - cosangle);
+ return [axis[0]*tmp + point[0]*cosangle + (-axis[2]*point[1] + axis[1]*point[2])*sinangle,
+ axis[1]*tmp + point[1]*cosangle + ( axis[2]*point[0] - axis[0]*point[2])*sinangle,
+ axis[2]*tmp + point[2]*cosangle + (-axis[1]*point[0] + axis[0]*point[1])*sinangle];
+ },
go: function() {
// Get params from form
var params = [];
projects / nt3d / blobdiff