X-Git-Url: http://git.scottworley.com/nt3d/blobdiff_plain/f72a4188261299dcb24dd9a0d4ebb91fa0479227..efae2dc27628eb1c0d116b24418fc48cf48c14a3:/nt3d.js diff --git a/nt3d.js b/nt3d.js index 5f7fad7..2876698 100644 --- a/nt3d.js +++ b/nt3d.js @@ -46,65 +46,146 @@ nt3d = { 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 = 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]); @@ -112,7 +193,7 @@ nt3d = { 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; } @@ -159,17 +240,24 @@ nt3d = { }, 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)); }, @@ -188,6 +276,19 @@ nt3d = { } 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(