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);
+ 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()));
+ },
+ 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(
- nt3d.trianglefan(guts_result.first_loop.reverse()),
- nt3d.trianglefan(guts_result.last_loop));
+ this.trianglefan(guts_result.first_loop.reverse()),
+ this.trianglefan(guts_result.last_loop));
},
- closed_extrude: function(shape, path, shapenormals, pathnormals) {
- var guts_result = nt3d._extrude_guts(shape, path, shapenormals, pathnormals);
+ 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(
- 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;
+ this.closed_quadstrip(this.zip(guts_result.first_loop, guts_result.last_loop)));
},
- _extrude_guts: function(shape, path, shapenormals, pathnormals) {
- var fixedpathnormals = this._fix_pathnormals(shapenormals, pathnormals);
+ _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++) {
- // 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 = shape;
+ 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 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]));
- if (rot1angle > 1e-7) {
- loop = this.rotate_about_origin(loop, rot1axis, rot1angle);
- }
+ // 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 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]));
- if (rot2angle > 1e-7) {
- loop = this.rotate_about_origin(loop, rot2axis, rot2angle);
- }
- // This would probably be faster and more numerically stable
+ // 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.
+ // 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)));
+ result.points = result.points.concat(this.closed_quadstrip(this.zip(loop, prev_loop)));
}
prev_loop = loop;
}
},
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);
+ 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] = [points[i][0] + offset[0],
- points[i][1] + offset[1],
- points[i][2] + offset[2]];
+ 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
return Math.acos(this.dot(a, b));
},
}
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(
projects / nt3d / blobdiff