backend/libs/three/math/Triangle.js

import { Vector3 } from './Vector3.js';

const _v0 = /*@__PURE__*/ new Vector3();
const _v1 = /*@__PURE__*/ new Vector3();
const _v2 = /*@__PURE__*/ new Vector3();
const _v3 = /*@__PURE__*/ new Vector3();

const _vab = /*@__PURE__*/ new Vector3();
const _vac = /*@__PURE__*/ new Vector3();
const _vbc = /*@__PURE__*/ new Vector3();
const _vap = /*@__PURE__*/ new Vector3();
const _vbp = /*@__PURE__*/ new Vector3();
const _vcp = /*@__PURE__*/ new Vector3();

class Triangle {
	constructor(a = new Vector3(), b = new Vector3(), c = new Vector3()) {
		this.a = a;
		this.b = b;
		this.c = c;
	}

	static getNormal(a, b, c, target) {
		target.subVectors(c, b);
		_v0.subVectors(a, b);
		target.cross(_v0);

		const targetLengthSq = target.lengthSq();
		if (targetLengthSq > 0) {
			return target.multiplyScalar(1 / Math.sqrt(targetLengthSq));
		}

		return target.set(0, 0, 0);
	}

	// static/instance method to calculate barycentric coordinates
	// based on: http://www.blackpawn.com/texts/pointinpoly/default.html
	static getBarycoord(point, a, b, c, target) {
		_v0.subVectors(c, a);
		_v1.subVectors(b, a);
		_v2.subVectors(point, a);

		const dot00 = _v0.dot(_v0);
		const dot01 = _v0.dot(_v1);
		const dot02 = _v0.dot(_v2);
		const dot11 = _v1.dot(_v1);
		const dot12 = _v1.dot(_v2);

		const denom = dot00 * dot11 - dot01 * dot01;

		// collinear or singular triangle
		if (denom === 0) {
			// arbitrary location outside of triangle?
			// not sure if this is the best idea, maybe should be returning undefined
			return target.set(-2, -1, -1);
		}

		const invDenom = 1 / denom;
		const u = (dot11 * dot02 - dot01 * dot12) * invDenom;
		const v = (dot00 * dot12 - dot01 * dot02) * invDenom;

		// barycentric coordinates must always sum to 1
		return target.set(1 - u - v, v, u);
	}

	static containsPoint(point, a, b, c) {
		this.getBarycoord(point, a, b, c, _v3);

		return _v3.x >= 0 && _v3.y >= 0 && _v3.x + _v3.y <= 1;
	}

	static getUV(point, p1, p2, p3, uv1, uv2, uv3, target) {
		this.getBarycoord(point, p1, p2, p3, _v3);

		target.set(0, 0);
		target.addScaledVector(uv1, _v3.x);
		target.addScaledVector(uv2, _v3.y);
		target.addScaledVector(uv3, _v3.z);

		return target;
	}

	static isFrontFacing(a, b, c, direction) {
		_v0.subVectors(c, b);
		_v1.subVectors(a, b);

		// strictly front facing
		return _v0.cross(_v1).dot(direction) < 0 ? true : false;
	}

	set(a, b, c) {
		this.a.copy(a);
		this.b.copy(b);
		this.c.copy(c);

		return this;
	}

	setFromPointsAndIndices(points, i0, i1, i2) {
		this.a.copy(points[i0]);
		this.b.copy(points[i1]);
		this.c.copy(points[i2]);

		return this;
	}

	setFromAttributeAndIndices(attribute, i0, i1, i2) {
		this.a.fromBufferAttribute(attribute, i0);
		this.b.fromBufferAttribute(attribute, i1);
		this.c.fromBufferAttribute(attribute, i2);

		return this;
	}

	clone() {
		return new this.constructor().copy(this);
	}

	copy(triangle) {
		this.a.copy(triangle.a);
		this.b.copy(triangle.b);
		this.c.copy(triangle.c);

		return this;
	}

	getArea() {
		_v0.subVectors(this.c, this.b);
		_v1.subVectors(this.a, this.b);

		return _v0.cross(_v1).length() * 0.5;
	}

	getMidpoint(target) {
		return target
			.addVectors(this.a, this.b)
			.add(this.c)
			.multiplyScalar(1 / 3);
	}

	getNormal(target) {
		return Triangle.getNormal(this.a, this.b, this.c, target);
	}

	getPlane(target) {
		return target.setFromCoplanarPoints(this.a, this.b, this.c);
	}

	getBarycoord(point, target) {
		return Triangle.getBarycoord(point, this.a, this.b, this.c, target);
	}

	getUV(point, uv1, uv2, uv3, target) {
		return Triangle.getUV(point, this.a, this.b, this.c, uv1, uv2, uv3, target);
	}

	containsPoint(point) {
		return Triangle.containsPoint(point, this.a, this.b, this.c);
	}

	isFrontFacing(direction) {
		return Triangle.isFrontFacing(this.a, this.b, this.c, direction);
	}

	intersectsBox(box) {
		return box.intersectsTriangle(this);
	}

	closestPointToPoint(p, target) {
		const a = this.a,
			b = this.b,
			c = this.c;
		let v, w;

		// algorithm thanks to Real-Time Collision Detection by Christer Ericson,
		// published by Morgan Kaufmann Publishers, (c) 2005 Elsevier Inc.,
		// under the accompanying license; see chapter 5.1.5 for detailed explanation.
		// basically, we're distinguishing which of the voronoi regions of the triangle
		// the point lies in with the minimum amount of redundant computation.

		_vab.subVectors(b, a);
		_vac.subVectors(c, a);
		_vap.subVectors(p, a);
		const d1 = _vab.dot(_vap);
		const d2 = _vac.dot(_vap);
		if (d1 <= 0 && d2 <= 0) {
			// vertex region of A; barycentric coords (1, 0, 0)
			return target.copy(a);
		}

		_vbp.subVectors(p, b);
		const d3 = _vab.dot(_vbp);
		const d4 = _vac.dot(_vbp);
		if (d3 >= 0 && d4 <= d3) {
			// vertex region of B; barycentric coords (0, 1, 0)
			return target.copy(b);
		}

		const vc = d1 * d4 - d3 * d2;
		if (vc <= 0 && d1 >= 0 && d3 <= 0) {
			v = d1 / (d1 - d3);
			// edge region of AB; barycentric coords (1-v, v, 0)
			return target.copy(a).addScaledVector(_vab, v);
		}

		_vcp.subVectors(p, c);
		const d5 = _vab.dot(_vcp);
		const d6 = _vac.dot(_vcp);
		if (d6 >= 0 && d5 <= d6) {
			// vertex region of C; barycentric coords (0, 0, 1)
			return target.copy(c);
		}

		const vb = d5 * d2 - d1 * d6;
		if (vb <= 0 && d2 >= 0 && d6 <= 0) {
			w = d2 / (d2 - d6);
			// edge region of AC; barycentric coords (1-w, 0, w)
			return target.copy(a).addScaledVector(_vac, w);
		}

		const va = d3 * d6 - d5 * d4;
		if (va <= 0 && d4 - d3 >= 0 && d5 - d6 >= 0) {
			_vbc.subVectors(c, b);
			w = (d4 - d3) / (d4 - d3 + (d5 - d6));
			// edge region of BC; barycentric coords (0, 1-w, w)
			return target.copy(b).addScaledVector(_vbc, w); // edge region of BC
		}

		// face region
		const denom = 1 / (va + vb + vc);
		// u = va * denom
		v = vb * denom;
		w = vc * denom;

		return target.copy(a).addScaledVector(_vab, v).addScaledVector(_vac, w);
	}

	equals(triangle) {
		return triangle.a.equals(this.a) && triangle.b.equals(this.b) && triangle.c.equals(this.c);
	}
}

export { Triangle };