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()));
+ },
+ 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].
- var loop = [];
+ 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]));
- // 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;
+ // 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(nt3d.closed_quadstrip(nt3d.zip(loop, prev_loop)));
+ result.points = result.points.concat(this.closed_quadstrip(this.zip(loop, prev_loop)));
}
prev_loop = loop;
}
a[1] - b[1],
a[2] - b[2]];
},
+ neg: function(a) {
+ return [-a[0], -a[1], -a[2]];
+ },
dot: function(a, b) {
return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
},
},
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(a, b) {
- return [a[0] + b[0], a[1] + b[1], a[2] + b[2]];
+ translate: function(points, offset) {
+ var translated = [];
+ for (var i = 0; i < points.length; i++) {
+ 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: function(point, axis, angle) { // axis must be a unit vector
+ rotate_about_origin: function(points, 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];
+ var rotated = [];
+ for (var i = 0; i < points.length; i++) {
+ var p = points[i];
+ var tmp = this.dot(p, axis) * (1 - cosangle);
+ rotated[i] = [
+ axis[0]*tmp + p[0]*cosangle + (-axis[2]*p[1] + axis[1]*p[2])*sinangle,
+ axis[1]*tmp + p[1]*cosangle + ( axis[2]*p[0] - axis[0]*p[2])*sinangle,
+ axis[2]*tmp + p[2]*cosangle + (-axis[1]*p[0] + axis[0]*p[1])*sinangle];
+ }
+ return rotated;
},
- go: function() {
- // Get params from form
- var params = [];
- for (var i = 0; i < this.user_params.length; i++) {
- params[i] = this.form.elements["param"+i].value;
+ 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));
+ 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;
}
-
- // Run user_function
- this.points = this.user_function.apply(null, params);
- if (this.points.length % 3 != 0) {
+ 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
+ return this.translate(
+ this.rotate_about_origin(
+ this.translate(points, this.neg(center)),
+ axis,
+ 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);
+ },
+ validate: function(points) {
+ // Do a little validation
+ if (points.length % 3 != 0) {
alert("Points list length not divisble by 3!");
}
- var n = this.points.length / 3;
-
- // Make STL
- this.stl = "solid " + this.user_function.name + "\n";
- for (var i = 0; i < n; i++) {
- var a = this.points[i*3+0];
- var b = this.points[i*3+1];
- var c = this.points[i*3+2];
+ var nan_count = 0;
+ var nan_point_count = 0;
+ var nan_face_count = 0;
+ for (var i = 0; i < 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(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 / (points.length/3)) + "% of faces).");
+ }
+ },
+ remove_degenerate_faces: function(points) {
+ // Note: This modifies points
+ var degenerate_face_count = 0;
+ for (var i = 0; i < points.length/3; i++) {
+ if (this.is_degenerate(points[i*3+0],
+ points[i*3+1],
+ points[i*3+2])) {
+ points.splice(i*3, 3);
+ i--;
+ degenerate_face_count ++;
+ }
+ }
+ if (degenerate_face_count != 0) {
+ console.log("Removed " + degenerate_face_count + " degenerate faces");
+ }
+ return points;
+ },
+ to_stl: function(points, name) {
+ var stl = "solid " + name + "\n";
+ for (var i = 0; i < points.length/3; i++) {
+ var a = points[i*3+0];
+ var b = points[i*3+1];
+ var c = points[i*3+2];
var normal = this.normal(a, b, c);
- this.stl += "facet normal " + normal[0] + " " + normal[1] + " " + normal[2] + "\n" +
+ stl += "facet normal " + normal[0] + " " + normal[1] + " " + normal[2] + "\n" +
"outer loop\n" +
"vertex " + a[0] + " " + a[1] + " " + a[2] + "\n"+
"vertex " + b[0] + " " + b[1] + " " + b[2] + "\n"+
"endloop\n" +
"endfacet\n";
}
- this.stl += "endsolid " + this.user_function.name + "\n";
-
+ stl += "endsolid " + name + "\n";
+ return stl;
+ },
+ go: function() {
// Remove any previous download links
var old_download_link = document.getElementById("nt3d_download");
if (old_download_link) {
old_download_link.parentNode.removeChild(old_download_link);
}
+ // Continue in a callback, so that there's not a stale download
+ // link hanging around while we process.
+ setTimeout(function() {
+
+ // Get params from form
+ var params = {};
+ for (var i = 0; i < this.user_params.length; i++) {
+ var as_string = this.form.elements["param"+i].value;
+ var as_num = +as_string;
+ params[this.user_params[i][0]] = isNaN(as_num) ? as_string : as_num;
+ }
+
+ this.points = this.user_function.call(null, params);
+
+ this.validate(this.points);
+
+ this.remove_degenerate_faces(this.points);
+
+ this.stl = this.to_stl(this.points, this.user_function.name);
+
// Offer result as download
var download_link = document.createElement("a");
download_link.appendChild(document.createTextNode("Download!"));
download_link.setAttribute("href", "data:application/sla," + encodeURIComponent(this.stl));
this.ui.appendChild(download_link);
setTimeout(function() { download_link.setAttribute("style", "-webkit-transition: background-color 0.4s; -moz-transition: background-color 0.4s; -o-transition: background-color 0.4s; -ms-transition: background-color 0.4s; transition: background-color 0.4s; background-color: inherit"); }, 0);
+
+ }.bind(this), 0); // (We were in a callback this whole time, remember?)
},
framework: function (f, params) {
this.user_function = f;
tr = document.createElement("tr");
table.appendChild(tr);
var td = document.createElement("td");
- td.appendChild(document.createTextNode(params[i][0]));
+ var description;
+ if (params[i].length > 2) {
+ description = params[i][2];
+ } else {
+ description = params[i][0];
+ description = description[0].toUpperCase() + description.substr(1);
+ description = description.replace(/_(.)/g, function(_, c) {
+ return " " + c.toUpperCase();
+ });
+ description = description.replace("Num ", "Number of ");
+ }
+ td.appendChild(document.createTextNode(description));
tr.appendChild(td);
td = document.createElement("td");
var input = document.createElement("input");
projects / nt3d / blobdiff