}
return points;
},
- extrude: function(shape, path, shapenormals, pathnormals) {
- var guts_result = nt3d._extrude_guts(shape, path, shapenormals, pathnormals);
+ 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(
- 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].
- // 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]]);
+ 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]. This puts the shape in
+ // becomes shapenormali. 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]);
+ // 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].
- loop = this.rotate_onto(loop, shapex, fixedpathnormals[i]);
+ // 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
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));
+ 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/
}
return rotated;
},
+ angle_epsilon: 1e-7,
+ opposite: function(a, b) {
+ // Do a and b point in exactly opposite directions?
+ return Math.abs(this.angle_between(this.unit(a), this.unit(b)) - Math.PI) < this.angle_epsilon;
+ },
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
+ var abs_angle = Math.abs(angle);
+ if (Math.abs(angle) < this.angle_epsilon) {
+ // No significant rotation to perform. Bail to avoid
// NaNs and numerical error
return points;
}
- var axis = this.unit(this.cross(a, b));
+ var axis;
+ if (Math.abs(abs_angle - Math.PI) < this.angle_epsilon) {
+ // a and b point in opposite directions, so
+ // we cannot cross them. So just pick something.
+ // If the caller wishes to avoid this behaviour,
+ // they should check with this.opposite() first.
+ axis = this.project_to_orthogonal(a, [1,0,0]);
+ console.log("rotate_onto: a and b are opposite! If you carefully chose them to meet some other constraint, you will be sad! Arbitrarily using axis [1,0,0] ->", axis);
+ if (this.magnitude(axis) < this.angle_epsilon) {
+ // Oh, double bad luck! Our arbitrary choice
+ // lines up too! A second, orthogonal arbitrary
+ // choice is now guaranteed to succeed.
+ axis = this.project_to_orthogonal(a, [0,1,0]);
+ console.log("rotate_onto: Double bad luck! Arbitrarily using axis [0,1,0] ->", axis);
+ }
+ } else {
+ 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
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");
// 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 n = this.points.length / 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 < n; i++) {
+ 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];
projects / nt3d / blobdiff