X-Git-Url: http://git.scottworley.com/nt3d/blobdiff_plain/4a6f6f14490c1c6f51843229d2d521368aa25c7f..8d119f4c44e035f04c11e5fee7f17d26ba57f44a:/nt3d.js diff --git a/nt3d.js b/nt3d.js index 239b03c..7e0fa25 100644 --- a/nt3d.js +++ b/nt3d.js @@ -62,6 +62,27 @@ nt3d = { 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; @@ -160,7 +181,16 @@ nt3d = { // 2. Rotate around shapenormali so that [1,0,0] // becomes pathnormali. - loop = this.rotate_onto(loop, shapex, 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 @@ -238,7 +268,14 @@ nt3d = { 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/ @@ -255,17 +292,40 @@ nt3d = { } 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 @@ -276,6 +336,17 @@ nt3d = { 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"); @@ -297,14 +368,51 @@ nt3d = { // 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];