389 lines
14 KiB
JavaScript
389 lines
14 KiB
JavaScript
'use strict';
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Object.defineProperty(exports, "__esModule", {
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value: true
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});
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exports.Plane = undefined;
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var _createClass = function () { function defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } } return function (Constructor, protoProps, staticProps) { if (protoProps) defineProperties(Constructor.prototype, protoProps); if (staticProps) defineProperties(Constructor, staticProps); return Constructor; }; }();
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var _line = require('./line');
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var _matrix = require('./matrix');
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var _sylvester = require('./sylvester');
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var _vector = require('./vector');
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function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
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var Plane = exports.Plane = function () {
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function Plane() {
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_classCallCheck(this, Plane);
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}
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_createClass(Plane, [{
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key: 'eql',
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// Returns true iff the plane occupies the same space as the argument
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value: function eql(plane) {
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return this.contains(plane.anchor) && this.isParallelTo(plane);
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}
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// Returns a copy of the plane
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}, {
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key: 'dup',
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value: function dup() {
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return Plane.create(this.anchor, this.normal);
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}
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// Returns the result of translating the plane by the given vector
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}, {
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key: 'translate',
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value: function translate(vector) {
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var V = vector.elements || vector;
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return Plane.create([this.anchor.elements[0] + V[0], this.anchor.elements[1] + V[1], this.anchor.elements[2] + (V[2] || 0)], this.normal);
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}
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// Returns true iff the plane is parallel to the argument. Will return true
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// if the planes are equal, or if you give a line and it lies in the plane.
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}, {
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key: 'isParallelTo',
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value: function isParallelTo(obj) {
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var theta = void 0;
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if (obj.normal) {
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// obj is a plane
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theta = this.normal.angleFrom(obj.normal);
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return Math.abs(theta) <= _sylvester.Sylvester.precision || Math.abs(Math.PI - theta) <= _sylvester.Sylvester.precision;
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} else if (obj.direction) {
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// obj is a line
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return this.normal.isPerpendicularTo(obj.direction);
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}
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return null;
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}
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// Returns true iff the receiver is perpendicular to the argument
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}, {
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key: 'isPerpendicularTo',
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value: function isPerpendicularTo(plane) {
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var theta = this.normal.angleFrom(plane.normal);
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return Math.abs(Math.PI / 2 - theta) <= _sylvester.Sylvester.precision;
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}
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// Returns the plane's distance from the given object (point, line or plane)
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}, {
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key: 'distanceFrom',
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value: function distanceFrom(obj) {
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if (this.intersects(obj) || this.contains(obj)) {
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return 0;
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}
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if (obj.anchor) {
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// obj is a plane or line
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var _A = this.anchor.elements;
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var B = obj.anchor.elements;
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var _N = this.normal.elements;
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return Math.abs((_A[0] - B[0]) * _N[0] + (_A[1] - B[1]) * _N[1] + (_A[2] - B[2]) * _N[2]);
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}
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// obj is a point
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var P = obj.elements || obj;
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var A = this.anchor.elements;
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var N = this.normal.elements;
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return Math.abs((A[0] - P[0]) * N[0] + (A[1] - P[1]) * N[1] + (A[2] - (P[2] || 0)) * N[2]);
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}
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// Returns true iff the plane contains the given point or line
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}, {
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key: 'contains',
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value: function contains(obj) {
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if (obj.normal) {
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return null;
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}
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if (obj.direction) {
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return this.contains(obj.anchor) && this.contains(obj.anchor.add(obj.direction));
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}
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var P = obj.elements || obj;
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var A = this.anchor.elements;
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var N = this.normal.elements;
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var diff = Math.abs(N[0] * (A[0] - P[0]) + N[1] * (A[1] - P[1]) + N[2] * (A[2] - (P[2] || 0)));
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return diff <= _sylvester.Sylvester.precision;
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}
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// Returns true iff the plane has a unique point/line of intersection with the argument
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}, {
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key: 'intersects',
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value: function intersects(obj) {
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if (typeof obj.direction === 'undefined' && typeof obj.normal === 'undefined') {
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return null;
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}
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return !this.isParallelTo(obj);
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}
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// Returns the unique intersection with the argument, if one exists. The result
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// will be a vector if a line is supplied, and a line if a plane is supplied.
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}, {
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key: 'intersectionWith',
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value: function intersectionWith(obj) {
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if (!this.intersects(obj)) {
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return null;
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}
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if (obj.direction) {
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// obj is a line
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var A = obj.anchor.elements;
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var D = obj.direction.elements;
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var P = this.anchor.elements;
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var N = this.normal.elements;
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var multiplier = (N[0] * (P[0] - A[0]) + N[1] * (P[1] - A[1]) + N[2] * (P[2] - A[2])) / (N[0] * D[0] + N[1] * D[1] + N[2] * D[2]);
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return _vector.Vector.create([A[0] + D[0] * multiplier, A[1] + D[1] * multiplier, A[2] + D[2] * multiplier]);
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}
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if (obj.normal) {
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// obj is a plane
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var direction = this.normal.cross(obj.normal).toUnitVector();
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// To find an anchor point, we find one co-ordinate that has a value
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// of zero somewhere on the intersection, and remember which one we picked
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var _N2 = this.normal.elements;
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var _A2 = this.anchor.elements;
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var O = obj.normal.elements;
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var B = obj.anchor.elements;
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var solver = _matrix.Matrix.Zero(2, 2);
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var i = 0;
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while (solver.isSingular()) {
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i++;
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solver = _matrix.Matrix.create([[_N2[i % 3], _N2[(i + 1) % 3]], [O[i % 3], O[(i + 1) % 3]]]);
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}
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// Then we solve the simultaneous equations in the remaining dimensions
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var inverse = solver.inverse().elements;
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var x = _N2[0] * _A2[0] + _N2[1] * _A2[1] + _N2[2] * _A2[2];
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var y = O[0] * B[0] + O[1] * B[1] + O[2] * B[2];
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var intersection = [inverse[0][0] * x + inverse[0][1] * y, inverse[1][0] * x + inverse[1][1] * y];
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var anchor = [];
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for (var j = 1; j <= 3; j++) {
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// This formula picks the right element from intersection by
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// cycling depending on which element we set to zero above
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anchor.push(i === j ? 0 : intersection[(j + (5 - i) % 3) % 3]);
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}
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return _line.Line.create(anchor, direction);
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}
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return null; // todo(connor4312): is this a case that needs to be handled?
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}
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// Returns the point in the plane closest to the given point
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}, {
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key: 'pointClosestTo',
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value: function pointClosestTo(point) {
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var P = point.elements || point;
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var A = this.anchor.elements;
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var N = this.normal.elements;
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var dot = (A[0] - P[0]) * N[0] + (A[1] - P[1]) * N[1] + (A[2] - (P[2] || 0)) * N[2];
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return _vector.Vector.create([P[0] + N[0] * dot, P[1] + N[1] * dot, (P[2] || 0) + N[2] * dot]);
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}
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// Returns a copy of the plane, rotated by t radians about the given line
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// See notes on Line#rotate.
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}, {
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key: 'rotate',
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value: function rotate(t, line) {
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var R = t.determinant ? t.elements : _matrix.Matrix.Rotation(t, line.direction).elements;
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var C = line.pointClosestTo(this.anchor).elements;
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var A = this.anchor.elements;
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var N = this.normal.elements;
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var C1 = C[0];
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var C2 = C[1];
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var C3 = C[2];
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var A1 = A[0];
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var A2 = A[1];
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var A3 = A[2];
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var x = A1 - C1;
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var y = A2 - C2;
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var z = A3 - C3;
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return Plane.create([C1 + R[0][0] * x + R[0][1] * y + R[0][2] * z, C2 + R[1][0] * x + R[1][1] * y + R[1][2] * z, C3 + R[2][0] * x + R[2][1] * y + R[2][2] * z], [R[0][0] * N[0] + R[0][1] * N[1] + R[0][2] * N[2], R[1][0] * N[0] + R[1][1] * N[1] + R[1][2] * N[2], R[2][0] * N[0] + R[2][1] * N[1] + R[2][2] * N[2]]);
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}
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// Returns the reflection of the plane in the given point, line or plane.
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}, {
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key: 'reflectionIn',
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value: function reflectionIn(obj) {
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if (obj.normal) {
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// obj is a plane
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var A = this.anchor.elements;
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var N = this.normal.elements;
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var A1 = A[0];
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var A2 = A[1];
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var A3 = A[2];
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var N1 = N[0];
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var N2 = N[1];
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var N3 = N[2];
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var newA = this.anchor.reflectionIn(obj).elements;
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// Add the plane's normal to its anchor, then mirror that in the other plane
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var AN1 = A1 + N1;
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var AN2 = A2 + N2;
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var AN3 = A3 + N3;
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var Q = obj.pointClosestTo([AN1, AN2, AN3]).elements;
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var newN = [Q[0] + (Q[0] - AN1) - newA[0], Q[1] + (Q[1] - AN2) - newA[1], Q[2] + (Q[2] - AN3) - newA[2]];
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return Plane.create(newA, newN);
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}
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if (obj.direction) {
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// obj is a line
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return this.rotate(Math.PI, obj);
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}
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// obj is a point
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var P = obj.elements || obj;
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return Plane.create(this.anchor.reflectionIn([P[0], P[1], P[2] || 0]), this.normal);
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}
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// Sets the anchor point and normal to the plane. If three arguments are specified,
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// the normal is calculated by assuming the three points should lie in the same plane.
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// If only two are sepcified, the second is taken to be the normal. Normal vector is
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// normalised before storage.
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}, {
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key: 'setVectors',
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value: function setVectors(anchor, v1, v2) {
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anchor = _vector.Vector.create(anchor);
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anchor = anchor.to3D();
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if (anchor === null) {
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return null;
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}
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v1 = _vector.Vector.create(v1);
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v1 = v1.to3D();
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if (v1 === null) {
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return null;
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}
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if (typeof v2 === 'undefined') {
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v2 = null;
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} else {
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v2 = _vector.Vector.create(v2);
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v2 = v2.to3D();
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if (v2 === null) {
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return null;
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}
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}
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var A1 = anchor.elements[0];
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var A2 = anchor.elements[1];
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var A3 = anchor.elements[2];
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var v11 = v1.elements[0];
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var v12 = v1.elements[1];
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var v13 = v1.elements[2];
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var normal = void 0;
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var mod = void 0;
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if (v2 === null) {
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mod = Math.sqrt(v11 * v11 + v12 * v12 + v13 * v13);
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if (mod === 0) {
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return null;
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}
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normal = _vector.Vector.create([v1.elements[0] / mod, v1.elements[1] / mod, v1.elements[2] / mod]);
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} else {
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var v21 = v2.elements[0];
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var v22 = v2.elements[1];
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var v23 = v2.elements[2];
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normal = _vector.Vector.create([(v12 - A2) * (v23 - A3) - (v13 - A3) * (v22 - A2), (v13 - A3) * (v21 - A1) - (v11 - A1) * (v23 - A3), (v11 - A1) * (v22 - A2) - (v12 - A2) * (v21 - A1)]);
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mod = normal.modulus();
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if (mod === 0) {
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return null;
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}
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normal = _vector.Vector.create([normal.elements[0] / mod, normal.elements[1] / mod, normal.elements[2] / mod]);
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}
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this.anchor = anchor;
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this.normal = normal;
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return this;
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}
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// Constructor function
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}], [{
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key: 'create',
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value: function create(anchor, v1, v2) {
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var P = new Plane();
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return P.setVectors(anchor, v1, v2);
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}
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// Returns the plane containing the given points (can be arrays as
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// well as vectors). If the points are not coplanar, returns null.
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}, {
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key: 'fromPoints',
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value: function fromPoints(points) {
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var np = points.length;
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var list = [];
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var i = void 0;
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var P = void 0;
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var n = void 0;
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var N = void 0;
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var A = void 0;
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var B = void 0;
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var C = void 0;
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var theta = void 0;
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var prevN = void 0;
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var totalN = _vector.Vector.Zero(3);
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for (i = 0; i < np; i++) {
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P = _vector.Vector.create(points[i]).to3D();
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if (P === null) {
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return null;
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}
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list.push(P);
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n = list.length;
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if (n > 2) {
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// Compute plane normal for the latest three points
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A = list[n - 1].elements;
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B = list[n - 2].elements;
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C = list[n - 3].elements;
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N = _vector.Vector.create([(A[1] - B[1]) * (C[2] - B[2]) - (A[2] - B[2]) * (C[1] - B[1]), (A[2] - B[2]) * (C[0] - B[0]) - (A[0] - B[0]) * (C[2] - B[2]), (A[0] - B[0]) * (C[1] - B[1]) - (A[1] - B[1]) * (C[0] - B[0])]).toUnitVector();
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if (n > 3) {
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// If the latest normal is not (anti)parallel to the previous one, we've strayed off the plane.
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// This might be a slightly long-winded way of doing things, but we need the sum of all the normals
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// to find which way the plane normal should point so that the points form an anticlockwise list.
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theta = N.angleFrom(prevN);
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if (theta !== null) {
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if (!(Math.abs(theta) <= _sylvester.Sylvester.precision || Math.abs(theta - Math.PI) <= _sylvester.Sylvester.precision)) {
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return null;
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}
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}
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}
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totalN = totalN.add(N);
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prevN = N;
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}
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}
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// We need to add in the normals at the start and end points, which the above misses out
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A = list[1].elements;
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B = list[0].elements;
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C = list[n - 1].elements;
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var D = list[n - 2].elements;
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totalN = totalN.add(_vector.Vector.create([(A[1] - B[1]) * (C[2] - B[2]) - (A[2] - B[2]) * (C[1] - B[1]), (A[2] - B[2]) * (C[0] - B[0]) - (A[0] - B[0]) * (C[2] - B[2]), (A[0] - B[0]) * (C[1] - B[1]) - (A[1] - B[1]) * (C[0] - B[0])]).toUnitVector()).add(_vector.Vector.create([(B[1] - C[1]) * (D[2] - C[2]) - (B[2] - C[2]) * (D[1] - C[1]), (B[2] - C[2]) * (D[0] - C[0]) - (B[0] - C[0]) * (D[2] - C[2]), (B[0] - C[0]) * (D[1] - C[1]) - (B[1] - C[1]) * (D[0] - C[0])]).toUnitVector());
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return Plane.create(list[0], totalN);
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}
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}]);
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return Plane;
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}();
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// X-Y-Z planes
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Plane.XY = Plane.YX = Plane.create(_vector.Vector.Zero(3), _vector.Vector.k);
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Plane.YZ = Plane.ZY = Plane.create(_vector.Vector.Zero(3), _vector.Vector.i);
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Plane.ZX = Plane.XZ = Plane.create(_vector.Vector.Zero(3), _vector.Vector.j); |