three.js/src/math/Triangle.js

/**
 * @author bhouston / http://exocortex.com
 * @author mrdoob / http://mrdoob.com/
 */

THREE.Triangle = function ( a, b, c ) {

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

};

THREE.Triangle.normal = function() {

	var v0 = new THREE.Vector3();

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

		var result = optionalTarget || new THREE.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 barycoordinates
// based on: http://www.blackpawn.com/texts/pointinpoly/default.html
THREE.Triangle.barycoordFromPoint = function() {

	var v0 = new THREE.Vector3(),
		v1 = new THREE.Vector3(),
		v2 = new THREE.Vector3();

	return function ( 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 THREE.Vector3();

		// colinear 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;

		// barycoordinates must always sum to 1
		return result.set( 1 - u - v, v, u );

	};

}();

THREE.Triangle.containsPoint = function() {

	var v1 = new THREE.Vector3();

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

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

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

	};

}();

THREE.extend( THREE.Triangle.prototype, {

	constructor: THREE.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;

	},

	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 THREE.Vector3(),
			v1 = new THREE.Vector3();
		
		return function () {

			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 THREE.Vector3();
		return result.addVectors( this.a, this.b ).add( this.c ).multiplyScalar( 1 / 3 );

	},

	normal: function ( optionalTarget ) {

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

	},

	plane: function ( optionalTarget ) {

		var result = optionalTarget || new THREE.Plane();

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

	},

	barycoordFromPoint: function ( point, optionalTarget ) {

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

	},

	containsPoint: function ( point ) {

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

	},

	equals: function ( triangle ) {

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

	},

	clone: function () {

		return new THREE.Triangle().copy( this );

	}

} );