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https://github.com/Doodle3D/Doodle3D-Slicer.git
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596 lines
18 KiB
JavaScript
Executable File
596 lines
18 KiB
JavaScript
Executable File
// Constructive Solid Geometry (CSG) is a modeling technique that uses Boolean
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// operations like union and intersection to combine 3D solids. This library
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// implements CSG operations on meshes elegantly and concisely using BSP trees,
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// and is meant to serve as an easily understandable implementation of the
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// algorithm. All edge cases involving overlapping coplanar polygons in both
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// solids are correctly handled.
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//
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// Example usage:
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//
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// var cube = CSG.cube();
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// var sphere = CSG.sphere({ radius: 1.3 });
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// var polygons = cube.subtract(sphere).toPolygons();
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//
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// ## Implementation Details
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//
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// All CSG operations are implemented in terms of two functions, `clipTo()` and
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// `invert()`, which remove parts of a BSP tree inside another BSP tree and swap
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// solid and empty space, respectively. To find the union of `a` and `b`, we
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// want to remove everything in `a` inside `b` and everything in `b` inside `a`,
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// then combine polygons from `a` and `b` into one solid:
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//
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// a.clipTo(b);
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// b.clipTo(a);
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// a.build(b.allPolygons());
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//
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// The only tricky part is handling overlapping coplanar polygons in both trees.
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// The code above keeps both copies, but we need to keep them in one tree and
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// remove them in the other tree. To remove them from `b` we can clip the
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// inverse of `b` against `a`. The code for union now looks like this:
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//
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// a.clipTo(b);
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// b.clipTo(a);
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// b.invert();
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// b.clipTo(a);
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// b.invert();
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// a.build(b.allPolygons());
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//
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// Subtraction and intersection naturally follow from set operations. If
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// union is `A | B`, subtraction is `A - B = ~(~A | B)` and intersection is
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// `A & B = ~(~A | ~B)` where `~` is the complement operator.
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//
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// ## License
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//
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// Copyright (c) 2011 Evan Wallace (http://madebyevan.com/), under the MIT license.
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// # class CSG
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// Holds a binary space partition tree representing a 3D solid. Two solids can
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// be combined using the `union()`, `subtract()`, and `intersect()` methods.
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CSG = function() {
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this.polygons = [];
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};
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// Construct a CSG solid from a list of `CSG.Polygon` instances.
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CSG.fromPolygons = function(polygons) {
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var csg = new CSG();
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csg.polygons = polygons;
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return csg;
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};
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CSG.prototype = {
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clone: function() {
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var csg = new CSG();
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csg.polygons = this.polygons.map(function(p) { return p.clone(); });
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return csg;
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},
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toPolygons: function() {
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return this.polygons;
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},
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// Return a new CSG solid representing space in either this solid or in the
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// solid `csg`. Neither this solid nor the solid `csg` are modified.
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//
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// A.union(B)
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//
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// +-------+ +-------+
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// | | | |
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// | A | | |
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// | +--+----+ = | +----+
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// +----+--+ | +----+ |
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// | B | | |
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// | | | |
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// +-------+ +-------+
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//
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union: function(csg) {
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var a = new CSG.Node(this.clone().polygons);
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var b = new CSG.Node(csg.clone().polygons);
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a.clipTo(b);
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b.clipTo(a);
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b.invert();
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b.clipTo(a);
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b.invert();
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a.build(b.allPolygons());
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return CSG.fromPolygons(a.allPolygons());
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},
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// Return a new CSG solid representing space in this solid but not in the
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// solid `csg`. Neither this solid nor the solid `csg` are modified.
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//
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// A.subtract(B)
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//
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// +-------+ +-------+
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// | | | |
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// | A | | |
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// | +--+----+ = | +--+
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// +----+--+ | +----+
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// | B |
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// | |
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// +-------+
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//
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subtract: function(csg) {
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var a = new CSG.Node(this.clone().polygons);
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var b = new CSG.Node(csg.clone().polygons);
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a.invert();
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a.clipTo(b);
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b.clipTo(a);
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b.invert();
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b.clipTo(a);
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b.invert();
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a.build(b.allPolygons());
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a.invert();
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return CSG.fromPolygons(a.allPolygons());
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},
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// Return a new CSG solid representing space both this solid and in the
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// solid `csg`. Neither this solid nor the solid `csg` are modified.
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//
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// A.intersect(B)
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//
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// +-------+
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// | |
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// | A |
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// | +--+----+ = +--+
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// +----+--+ | +--+
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// | B |
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// | |
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// +-------+
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//
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intersect: function(csg) {
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var a = new CSG.Node(this.clone().polygons);
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var b = new CSG.Node(csg.clone().polygons);
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a.invert();
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b.clipTo(a);
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b.invert();
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a.clipTo(b);
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b.clipTo(a);
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a.build(b.allPolygons());
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a.invert();
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return CSG.fromPolygons(a.allPolygons());
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},
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// Return a new CSG solid with solid and empty space switched. This solid is
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// not modified.
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inverse: function() {
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var csg = this.clone();
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csg.polygons.map(function(p) { p.flip(); });
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return csg;
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}
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};
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// Construct an axis-aligned solid cuboid. Optional parameters are `center` and
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// `radius`, which default to `[0, 0, 0]` and `[1, 1, 1]`. The radius can be
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// specified using a single number or a list of three numbers, one for each axis.
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//
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// Example code:
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//
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// var cube = CSG.cube({
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// center: [0, 0, 0],
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// radius: 1
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// });
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CSG.cube = function(options) {
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options = options || {};
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var c = new CSG.Vector(options.center || [0, 0, 0]);
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var r = !options.radius ? [1, 1, 1] : options.radius.length ?
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options.radius : [options.radius, options.radius, options.radius];
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return CSG.fromPolygons([
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[[0, 4, 6, 2], [-1, 0, 0]],
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[[1, 3, 7, 5], [+1, 0, 0]],
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[[0, 1, 5, 4], [0, -1, 0]],
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[[2, 6, 7, 3], [0, +1, 0]],
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[[0, 2, 3, 1], [0, 0, -1]],
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[[4, 5, 7, 6], [0, 0, +1]]
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].map(function(info) {
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return new CSG.Polygon(info[0].map(function(i) {
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var pos = new CSG.Vector(
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c.x + r[0] * (2 * !!(i & 1) - 1),
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c.y + r[1] * (2 * !!(i & 2) - 1),
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c.z + r[2] * (2 * !!(i & 4) - 1)
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);
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return new CSG.Vertex(pos, new CSG.Vector(info[1]));
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}));
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}));
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};
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// Construct a solid sphere. Optional parameters are `center`, `radius`,
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// `slices`, and `stacks`, which default to `[0, 0, 0]`, `1`, `16`, and `8`.
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// The `slices` and `stacks` parameters control the tessellation along the
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// longitude and latitude directions.
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//
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// Example usage:
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//
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// var sphere = CSG.sphere({
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// center: [0, 0, 0],
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// radius: 1,
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// slices: 16,
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// stacks: 8
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// });
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CSG.sphere = function(options) {
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options = options || {};
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var c = new CSG.Vector(options.center || [0, 0, 0]);
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var r = options.radius || 1;
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var slices = options.slices || 16;
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var stacks = options.stacks || 8;
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var polygons = [], vertices;
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function vertex(theta, phi) {
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theta *= Math.PI * 2;
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phi *= Math.PI;
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var dir = new CSG.Vector(
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Math.cos(theta) * Math.sin(phi),
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Math.cos(phi),
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Math.sin(theta) * Math.sin(phi)
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);
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vertices.push(new CSG.Vertex(c.plus(dir.times(r)), dir));
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}
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for (var i = 0; i < slices; i++) {
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for (var j = 0; j < stacks; j++) {
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vertices = [];
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vertex(i / slices, j / stacks);
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if (j > 0) vertex((i + 1) / slices, j / stacks);
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if (j < stacks - 1) vertex((i + 1) / slices, (j + 1) / stacks);
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vertex(i / slices, (j + 1) / stacks);
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polygons.push(new CSG.Polygon(vertices));
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}
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}
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return CSG.fromPolygons(polygons);
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};
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// Construct a solid cylinder. Optional parameters are `start`, `end`,
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// `radius`, and `slices`, which default to `[0, -1, 0]`, `[0, 1, 0]`, `1`, and
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// `16`. The `slices` parameter controls the tessellation.
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//
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// Example usage:
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//
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// var cylinder = CSG.cylinder({
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// start: [0, -1, 0],
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// end: [0, 1, 0],
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// radius: 1,
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// slices: 16
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// });
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CSG.cylinder = function(options) {
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options = options || {};
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var s = new CSG.Vector(options.start || [0, -1, 0]);
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var e = new CSG.Vector(options.end || [0, 1, 0]);
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var ray = e.minus(s);
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var r = options.radius || 1;
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var slices = options.slices || 16;
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var axisZ = ray.unit(), isY = (Math.abs(axisZ.y) > 0.5);
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var axisX = new CSG.Vector(isY, !isY, 0).cross(axisZ).unit();
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var axisY = axisX.cross(axisZ).unit();
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var start = new CSG.Vertex(s, axisZ.negated());
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var end = new CSG.Vertex(e, axisZ.unit());
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var polygons = [];
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function point(stack, slice, normalBlend) {
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var angle = slice * Math.PI * 2;
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var out = axisX.times(Math.cos(angle)).plus(axisY.times(Math.sin(angle)));
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var pos = s.plus(ray.times(stack)).plus(out.times(r));
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var normal = out.times(1 - Math.abs(normalBlend)).plus(axisZ.times(normalBlend));
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return new CSG.Vertex(pos, normal);
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}
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for (var i = 0; i < slices; i++) {
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var t0 = i / slices, t1 = (i + 1) / slices;
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polygons.push(new CSG.Polygon([start, point(0, t0, -1), point(0, t1, -1)]));
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polygons.push(new CSG.Polygon([point(0, t1, 0), point(0, t0, 0), point(1, t0, 0), point(1, t1, 0)]));
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polygons.push(new CSG.Polygon([end, point(1, t1, 1), point(1, t0, 1)]));
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}
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return CSG.fromPolygons(polygons);
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};
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// # class Vector
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// Represents a 3D vector.
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//
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// Example usage:
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//
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// new CSG.Vector(1, 2, 3);
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// new CSG.Vector([1, 2, 3]);
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// new CSG.Vector({ x: 1, y: 2, z: 3 });
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CSG.Vector = function(x, y, z) {
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if (arguments.length == 3) {
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this.x = x;
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this.y = y;
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this.z = z;
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} else if ('x' in x) {
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this.x = x.x;
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this.y = x.y;
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this.z = x.z;
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} else {
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this.x = x[0];
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this.y = x[1];
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this.z = x[2];
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}
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};
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CSG.Vector.prototype = {
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clone: function() {
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return new CSG.Vector(this.x, this.y, this.z);
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},
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negated: function() {
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return new CSG.Vector(-this.x, -this.y, -this.z);
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},
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plus: function(a) {
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return new CSG.Vector(this.x + a.x, this.y + a.y, this.z + a.z);
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},
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minus: function(a) {
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return new CSG.Vector(this.x - a.x, this.y - a.y, this.z - a.z);
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},
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times: function(a) {
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return new CSG.Vector(this.x * a, this.y * a, this.z * a);
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},
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dividedBy: function(a) {
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return new CSG.Vector(this.x / a, this.y / a, this.z / a);
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},
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dot: function(a) {
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return this.x * a.x + this.y * a.y + this.z * a.z;
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},
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lerp: function(a, t) {
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return this.plus(a.minus(this).times(t));
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},
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length: function() {
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return Math.sqrt(this.dot(this));
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},
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unit: function() {
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return this.dividedBy(this.length());
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},
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cross: function(a) {
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return new CSG.Vector(
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this.y * a.z - this.z * a.y,
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this.z * a.x - this.x * a.z,
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this.x * a.y - this.y * a.x
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);
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}
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};
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// # class Vertex
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// Represents a vertex of a polygon. Use your own vertex class instead of this
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// one to provide additional features like texture coordinates and vertex
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// colors. Custom vertex classes need to provide a `pos` property and `clone()`,
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// `flip()`, and `interpolate()` methods that behave analogous to the ones
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// defined by `CSG.Vertex`. This class provides `normal` so convenience
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// functions like `CSG.sphere()` can return a smooth vertex normal, but `normal`
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// is not used anywhere else.
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CSG.Vertex = function(pos, normal) {
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this.pos = new CSG.Vector(pos);
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this.normal = new CSG.Vector(normal);
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};
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CSG.Vertex.prototype = {
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clone: function() {
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return new CSG.Vertex(this.pos.clone(), this.normal.clone());
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},
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// Invert all orientation-specific data (e.g. vertex normal). Called when the
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// orientation of a polygon is flipped.
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flip: function() {
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this.normal = this.normal.negated();
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},
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// Create a new vertex between this vertex and `other` by linearly
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// interpolating all properties using a parameter of `t`. Subclasses should
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// override this to interpolate additional properties.
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interpolate: function(other, t) {
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return new CSG.Vertex(
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this.pos.lerp(other.pos, t),
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this.normal.lerp(other.normal, t)
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);
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}
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};
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// # class Plane
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// Represents a plane in 3D space.
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CSG.Plane = function(normal, w) {
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this.normal = normal;
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this.w = w;
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};
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// `CSG.Plane.EPSILON` is the tolerance used by `splitPolygon()` to decide if a
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// point is on the plane.
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CSG.Plane.EPSILON = 1e-5;
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CSG.Plane.fromPoints = function(a, b, c) {
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var n = b.minus(a).cross(c.minus(a)).unit();
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return new CSG.Plane(n, n.dot(a));
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};
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CSG.Plane.prototype = {
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clone: function() {
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return new CSG.Plane(this.normal.clone(), this.w);
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},
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flip: function() {
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this.normal = this.normal.negated();
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this.w = -this.w;
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},
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// Split `polygon` by this plane if needed, then put the polygon or polygon
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// fragments in the appropriate lists. Coplanar polygons go into either
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// `coplanarFront` or `coplanarBack` depending on their orientation with
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// respect to this plane. Polygons in front or in back of this plane go into
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// either `front` or `back`.
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splitPolygon: function(polygon, coplanarFront, coplanarBack, front, back) {
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var COPLANAR = 0;
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var FRONT = 1;
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var BACK = 2;
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var SPANNING = 3;
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// Classify each point as well as the entire polygon into one of the above
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// four classes.
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var polygonType = 0;
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var types = [];
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for (var i = 0; i < polygon.vertices.length; i++) {
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var t = this.normal.dot(polygon.vertices[i].pos) - this.w;
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var type = (t < -CSG.Plane.EPSILON) ? BACK : (t > CSG.Plane.EPSILON) ? FRONT : COPLANAR;
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polygonType |= type;
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types.push(type);
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}
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// Put the polygon in the correct list, splitting it when necessary.
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switch (polygonType) {
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case COPLANAR:
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(this.normal.dot(polygon.plane.normal) > 0 ? coplanarFront : coplanarBack).push(polygon);
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break;
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case FRONT:
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front.push(polygon);
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break;
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case BACK:
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back.push(polygon);
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break;
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case SPANNING:
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var f = [], b = [];
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for (var i = 0; i < polygon.vertices.length; i++) {
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var j = (i + 1) % polygon.vertices.length;
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var ti = types[i], tj = types[j];
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var vi = polygon.vertices[i], vj = polygon.vertices[j];
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if (ti != BACK) f.push(vi);
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if (ti != FRONT) b.push(ti != BACK ? vi.clone() : vi);
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if ((ti | tj) == SPANNING) {
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var t = (this.w - this.normal.dot(vi.pos)) / this.normal.dot(vj.pos.minus(vi.pos));
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var v = vi.interpolate(vj, t);
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f.push(v);
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b.push(v.clone());
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}
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}
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if (f.length >= 3) front.push(new CSG.Polygon(f, polygon.shared));
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if (b.length >= 3) back.push(new CSG.Polygon(b, polygon.shared));
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break;
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}
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}
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};
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// # class Polygon
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// Represents a convex polygon. The vertices used to initialize a polygon must
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// be coplanar and form a convex loop. They do not have to be `CSG.Vertex`
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// instances but they must behave similarly (duck typing can be used for
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// customization).
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//
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// Each convex polygon has a `shared` property, which is shared between all
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// polygons that are clones of each other or were split from the same polygon.
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// This can be used to define per-polygon properties (such as surface color).
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CSG.Polygon = function(vertices, shared) {
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this.vertices = vertices;
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this.shared = shared;
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this.plane = CSG.Plane.fromPoints(vertices[0].pos, vertices[1].pos, vertices[2].pos);
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};
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CSG.Polygon.prototype = {
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clone: function() {
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var vertices = this.vertices.map(function(v) { return v.clone(); });
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return new CSG.Polygon(vertices, this.shared);
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},
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flip: function() {
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this.vertices.reverse().map(function(v) { v.flip(); });
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this.plane.flip();
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}
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};
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// # class Node
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// Holds a node in a BSP tree. A BSP tree is built from a collection of polygons
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// by picking a polygon to split along. That polygon (and all other coplanar
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// polygons) are added directly to that node and the other polygons are added to
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// the front and/or back subtrees. This is not a leafy BSP tree since there is
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// no distinction between internal and leaf nodes.
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CSG.Node = function(polygons) {
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this.plane = null;
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this.front = null;
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this.back = null;
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this.polygons = [];
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if (polygons) this.build(polygons);
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};
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CSG.Node.prototype = {
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clone: function() {
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var node = new CSG.Node();
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node.plane = this.plane && this.plane.clone();
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node.front = this.front && this.front.clone();
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node.back = this.back && this.back.clone();
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node.polygons = this.polygons.map(function(p) { return p.clone(); });
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return node;
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},
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// Convert solid space to empty space and empty space to solid space.
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invert: function() {
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for (var i = 0; i < this.polygons.length; i++) {
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this.polygons[i].flip();
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}
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this.plane.flip();
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if (this.front) this.front.invert();
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if (this.back) this.back.invert();
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var temp = this.front;
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this.front = this.back;
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this.back = temp;
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},
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// Recursively remove all polygons in `polygons` that are inside this BSP
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// tree.
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clipPolygons: function(polygons) {
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if (!this.plane) return polygons.slice();
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var front = [], back = [];
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for (var i = 0; i < polygons.length; i++) {
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this.plane.splitPolygon(polygons[i], front, back, front, back);
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}
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if (this.front) front = this.front.clipPolygons(front);
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if (this.back) back = this.back.clipPolygons(back);
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else back = [];
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return front.concat(back);
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},
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// Remove all polygons in this BSP tree that are inside the other BSP tree
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// `bsp`.
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clipTo: function(bsp) {
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this.polygons = bsp.clipPolygons(this.polygons);
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if (this.front) this.front.clipTo(bsp);
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if (this.back) this.back.clipTo(bsp);
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},
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// Return a list of all polygons in this BSP tree.
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allPolygons: function() {
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var polygons = this.polygons.slice();
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if (this.front) polygons = polygons.concat(this.front.allPolygons());
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if (this.back) polygons = polygons.concat(this.back.allPolygons());
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return polygons;
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},
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// Build a BSP tree out of `polygons`. When called on an existing tree, the
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// new polygons are filtered down to the bottom of the tree and become new
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// nodes there. Each set of polygons is partitioned using the first polygon
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// (no heuristic is used to pick a good split).
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build: function(polygons) {
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if (!polygons.length) return;
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if (!this.plane) this.plane = polygons[0].plane.clone();
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var front = [], back = [];
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for (var i = 0; i < polygons.length; i++) {
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this.plane.splitPolygon(polygons[i], this.polygons, this.polygons, front, back);
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}
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if (front.length) {
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if (!this.front) this.front = new CSG.Node();
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this.front.build(front);
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}
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if (back.length) {
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if (!this.back) this.back = new CSG.Node();
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this.back.build(back);
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}
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}
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};
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