three.js/src/math/Triangle.js

import { Vector2 } from './Vector2.js';
import { Vector3 } from './Vector3.js';

/**
 * @author bhouston / http://clara.io
 * @author mrdoob / http://mrdoob.com/
 */

function Triangle( a, b, c ) {

	this.a = ( a !== undefined ) ? a : new Vector3();
	this.b = ( b !== undefined ) ? b : new Vector3();
	this.c = ( c !== undefined ) ? c : new Vector3();

}

Object.assign( Triangle, {

	getNormal: function () {

		var v0 = new Vector3();

		return function getNormal( a, b, c, target ) {

			if ( target === undefined ) {

				console.warn( 'THREE.Triangle: .getNormal() target is now required' );
				target = new Vector3();

			}

			target.subVectors( c, b );
			v0.subVectors( a, b );
			target.cross( v0 );

			var 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
	getBarycoord: function () {

		var v0 = new Vector3();
		var v1 = new Vector3();
		var v2 = new Vector3();

		return function getBarycoord( point, a, b, c, target ) {

			v0.subVectors( c, a );
			v1.subVectors( b, a );
			v2.subVectors( point, a );

			var dot00 = v0.dot( v0 );
			var dot01 = v0.dot( v1 );
			var dot02 = v0.dot( v2 );
			var dot11 = v1.dot( v1 );
			var dot12 = v1.dot( v2 );

			var denom = ( dot00 * dot11 - dot01 * dot01 );

			if ( target === undefined ) {

				console.warn( 'THREE.Triangle: .getBarycoord() target is now required' );
				target = new Vector3();

			}

			// 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 );

			}

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

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

		};

	}(),

	containsPoint: function () {

		var v1 = new Vector3();

		return function containsPoint( point, a, b, c ) {

			Triangle.getBarycoord( point, a, b, c, v1 );

			return ( v1.x >= 0 ) && ( v1.y >= 0 ) && ( ( v1.x + v1.y ) <= 1 );

		};

	}(),

	uvIntersection: function () {

		var barycoord = new Vector3();
		var v1 = new Vector2();
		var v2 = new Vector2();
		var v3 = new Vector2();

		return function uvIntersection( point, p1, p2, p3, uv1, uv2, uv3, result ) {

			this.getBarycoord( point, p1, p2, p3, barycoord );

			v1.copy( uv1 ).multiplyScalar( barycoord.x );
			v2.copy( uv2 ).multiplyScalar( barycoord.y );
			v3.copy( uv3 ).multiplyScalar( barycoord.z );

			v1.add( v2 ).add( v3 );

			return result.copy( v1 );

		};

	}()

} );

Object.assign( Triangle.prototype, {

	set: function ( a, b, c ) {

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

		return this;

	},

	setFromPointsAndIndices: function ( points, i0, i1, i2 ) {

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

		return this;

	},

	clone: function () {

		return new this.constructor().copy( this );

	},

	copy: function ( triangle ) {

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

		return this;

	},

	getArea: function () {

		var v0 = new Vector3();
		var v1 = new Vector3();

		return function getArea() {

			v0.subVectors( this.c, this.b );
			v1.subVectors( this.a, this.b );

			return v0.cross( v1 ).length() * 0.5;

		};

	}(),

	getMidpoint: function ( target ) {

		if ( target === undefined ) {

			console.warn( 'THREE.Triangle: .getMidpoint() target is now required' );
			target = new Vector3();

		}

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

	},

	getNormal: function ( target ) {

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

	},

	getPlane: function ( target ) {

		if ( target === undefined ) {

			console.warn( 'THREE.Triangle: .getPlane() target is now required' );
			target = new Vector3();

		}

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

	},

	getBarycoord: function ( point, target ) {

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

	},

	containsPoint: function ( point ) {

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

	},

	uvIntersection: function ( point, uv1, uv2, uv3, result ) {

		return Triangle.uvIntersection( point, this.a, this.b, this.c, uv1, uv2, uv3, result );

	},

	intersectsBox: function ( box ) {

		return box.intersectsTriangle( this );

	},

	closestPointToPoint: function () {

		var vab = new Vector3();
		var vac = new Vector3();
		var vbc = new Vector3();
		var vap = new Vector3();
		var vbp = new Vector3();
		var vcp = new Vector3();

		return function closestPointToPoint( p, target ) {

			if ( target === undefined ) {

				console.warn( 'THREE.Triangle: .closestPointToPoint() target is now required' );
				target = new Vector3();

			}

			var a = this.a, b = this.b, c = this.c;
			var 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 );
			var d1 = vab.dot( vap );
			var 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 );
			var d3 = vab.dot( vbp );
			var d4 = vac.dot( vbp );
			if ( d3 >= 0 && d4 <= d3 ) {

				// vertex region of B; barycentric coords (0, 1, 0)
				return target.copy( b );

			}

			var 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 );
			var d5 = vab.dot( vcp );
			var d6 = vac.dot( vcp );
			if ( d6 >= 0 && d5 <= d6 ) {

				// vertex region of C; barycentric coords (0, 0, 1)
				return target.copy( c );

			}

			var 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 );

			}

			var 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
			var 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: function ( triangle ) {

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

	}

} );


export { Triangle };