three.js/src/math/Triangle.js

import { Vector3 } from './Vector3';
import { Line3 } from './Line3';
import { Plane } from './Plane';

/**
 * @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();

}

Triangle.normal = function () {

	var v0 = new Vector3();

	return function normal( a, b, c, optionalTarget ) {

		var result = optionalTarget || new Vector3();

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

		var resultLengthSq = result.lengthSq();
		if ( resultLengthSq > 0 ) {

			return result.multiplyScalar( 1 / Math.sqrt( resultLengthSq ) );

		}

		return result.set( 0, 0, 0 );

	};

}();

// static/instance method to calculate barycentric coordinates
// based on: http://www.blackpawn.com/texts/pointinpoly/default.html
Triangle.barycoordFromPoint = function () {

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

	return function barycoordFromPoint( point, a, b, c, optionalTarget ) {

		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 );

		var result = optionalTarget || 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 result.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 result.set( 1 - u - v, v, u );

	};

}();

Triangle.containsPoint = function () {

	var v1 = new Vector3();

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

		var result = Triangle.barycoordFromPoint( point, a, b, c, v1 );

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

	};

}();

Triangle.prototype = {

	constructor: Triangle,

	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;

	},

	area: function () {

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

		return function area() {

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

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

		};

	}(),

	midpoint: function ( optionalTarget ) {

		var result = optionalTarget || new Vector3();
		return result.addVectors( this.a, this.b ).add( this.c ).multiplyScalar( 1 / 3 );

	},

	normal: function ( optionalTarget ) {

		return Triangle.normal( this.a, this.b, this.c, optionalTarget );

	},

	plane: function ( optionalTarget ) {

		var result = optionalTarget || new Plane();

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

	},

	barycoordFromPoint: function ( point, optionalTarget ) {

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

	},

	containsPoint: function ( point ) {

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

	},

	closestPointToPoint: function () {

		var plane, edgeList, projectedPoint, closestPoint;

		return function closestPointToPoint( point, optionalTarget ) {

			if ( plane === undefined ) {

				plane = new Plane();
				edgeList = [ new Line3(), new Line3(), new Line3() ];
				projectedPoint = new Vector3();
				closestPoint = new Vector3();

			}

			var result = optionalTarget || new Vector3();
			var minDistance = Infinity;

			// project the point onto the plane of the triangle

			plane.setFromCoplanarPoints( this.a, this.b, this.c );
			plane.projectPoint( point, projectedPoint );

			// check if the projection lies within the triangle

			if( this.containsPoint( projectedPoint ) === true ) {

				// if so, this is the closest point

				result.copy( projectedPoint );

			} else {

				// if not, the point falls outside the triangle. the result is the closest point to the triangle's edges or vertices

				edgeList[ 0 ].set( this.a, this.b );
				edgeList[ 1 ].set( this.b, this.c );
				edgeList[ 2 ].set( this.c, this.a );

				for( var i = 0; i < edgeList.length; i ++ ) {

					edgeList[ i ].closestPointToPoint( projectedPoint, true, closestPoint );

					var distance = projectedPoint.distanceToSquared( closestPoint );

					if( distance < minDistance ) {

						minDistance = distance;

						result.copy( closestPoint );

					}

				}

			}

			return result;

		};

	}(),

	equals: function ( triangle ) {

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

	}

};


export { Triangle };