three.js/src/math/Ray.js

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

THREE.Ray = function ( origin, direction ) {

	this.origin = ( origin !== undefined ) ? origin : new THREE.Vector3();
	this.direction = ( direction !== undefined ) ? direction : new THREE.Vector3();

};

THREE.Ray.prototype = {

	constructor: THREE.Ray,

	set: function ( origin, direction ) {

		this.origin.copy( origin );
		this.direction.copy( direction );

		return this;

	},

	copy: function ( ray ) {

		this.origin.copy( ray.origin );
		this.direction.copy( ray.direction );

		return this;

	},

	at: function ( t, optionalTarget ) {

		var result = optionalTarget || new THREE.Vector3();

		return result.copy( this.direction ).multiplyScalar( t ).add( this.origin );

	},

	recast: function () {

		var v1 = new THREE.Vector3();

		return function ( t ) {

			this.origin.copy( this.at( t, v1 ) );

			return this;

		};

	}(),

	closestPointToPoint: function ( point, optionalTarget ) {

		var result = optionalTarget || new THREE.Vector3();
		result.subVectors( point, this.origin );
		var directionDistance = result.dot( this.direction );

		if ( directionDistance < 0 ) {

			return this.origin.clone();

		}

		return result.copy( this.direction ).multiplyScalar( directionDistance ).add( this.origin );

	},

	distanceToPoint: function () {

		var v1 = new THREE.Vector3();

		return function ( point ) {

			var directionDistance = v1.subVectors( point, this.origin ).dot( this.direction );

			// point behind the ray

			if ( directionDistance < 0 ) {

				return this.origin.distanceTo( point );

			}

			v1.copy( this.direction ).multiplyScalar( directionDistance ).add( this.origin );

			return v1.distanceTo( point );

		};

	}(),

	distanceToSegment: function( v0, v1, optionalPointOnRay, optionalPointOnSegment ) {

		// from http://www.geometrictools.com/LibMathematics/Distance/Wm5DistRay3Segment3.cpp
		// It returns the min distance between the ray and the segment
		// defined by v0 and v1
		// It can also set two optional targets :
		// - The closest point on the ray
		// - The closest point on the segment

		var segCenter = v0.clone().add( v1 ).multiplyScalar( 0.5 );
		var segDir = v1.clone().sub( v0 ).normalize();
		var segExtent = v0.distanceTo( v1 ) * 0.5;
		var diff = this.origin.clone().sub( segCenter );
		var a01 = - this.direction.dot( segDir );
		var b0 = diff.dot( this.direction );
		var b1 = - diff.dot( segDir );
		var c = diff.lengthSq();
		var det = Math.abs( 1 - a01 * a01 );
		var s0, s1, sqrDist, extDet;
		if (det >= 0) {

			// The ray and segment are not parallel.

			s0 = a01 * b1 - b0;
			s1 = a01 * b0 - b1;
			extDet = segExtent * det;

			if (s0 >= 0) {

				if (s1 >= -extDet) {

					if (s1 <= extDet) {

						// region 0
						// Minimum at interior points of ray and segment.

						var invDet = 1 / det;
						s0 *= invDet;
						s1 *= invDet;
						sqrDist = s0 * ( s0 + a01 * s1 + 2 * b0 ) + s1 * ( a01 * s0 + s1 + 2 * b1 ) + c;

					} else {

						// region 1

						s1 = segExtent;
						s0 = Math.max( 0, - ( a01 * s1 + b0) );
						sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c;

					}

				}

				else {

					// region 5

					s1 = - segExtent;
					s0 = Math.max( 0, - ( a01 * s1 + b0) );
					sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c;

				}

			} else {

				if ( s1 <= - extDet) {

					// region 4

					s0 = Math.max( 0, - ( - a01 * segExtent + b0 ) );
					s1 = ( s0 > 0 ) ? - segExtent : Math.min( Math.max( - segExtent, - b1 ), segExtent );
					sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c;

				} else if (s1 <= extDet) {

					// region 3

					s0 = 0;
					s1 = Math.min( Math.max( - segExtent, - b1 ), segExtent );
					sqrDist = s1 * ( s1 + 2 * b1 ) + c;

				}	else {

					// region 2

					s0 = Math.max( 0, - ( a01 * segExtent + b0 ) );
					s1 = ( s0 > 0 ) ? segExtent : Math.min( Math.max( - segExtent, - b1 ), segExtent );
					sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c;

				}

			}

		}	else {

			// Ray and segment are parallel.

			s1 = ( a01 > 0 ) ? - segExtent : segExtent;
			s0 = Math.max( 0, - ( a01 * s1 + b0 ) );
			sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c;

		}

		if ( optionalPointOnRay ) {

			optionalPointOnRay.copy( this.direction.clone().multiplyScalar( s0 ).add( this.origin ) );

		}

		if ( optionalPointOnSegment ) {

			optionalPointOnSegment.copy( segDir.clone().multiplyScalar( s1 ).add( segCenter ) );

		}

		return sqrDist;

	},

	isIntersectionSphere: function ( sphere ) {

		return this.distanceToPoint( sphere.center ) <= sphere.radius;

	},

	isIntersectionPlane: function ( plane ) {

		// check if the ray lies on the plane first

		var distToPoint = plane.distanceToPoint( this.origin );

		if ( distToPoint === 0 ) {

			return true;

		}

		var denominator = plane.normal.dot( this.direction );

		if ( denominator * distToPoint < 0 ) {

			return true

		}

		// ray origin is behind the plane (and is pointing behind it)

		return false;

	},

	distanceToPlane: function ( plane ) {

		var denominator = plane.normal.dot( this.direction );
		if ( denominator == 0 ) {

			// line is coplanar, return origin
			if( plane.distanceToPoint( this.origin ) == 0 ) {

				return 0;

			}

			// Null is preferable to undefined since undefined means.... it is undefined

			return null;

		}

		var t = - ( this.origin.dot( plane.normal ) + plane.constant ) / denominator;

		// Return if the ray never intersects the plane

		return t >= 0 ? t :  null;

	},

	intersectPlane: function ( plane, optionalTarget ) {

		var t = this.distanceToPlane( plane );

		if ( t === null ) {

			return null;
		}

		return this.at( t, optionalTarget );

	},

	applyMatrix4: function ( matrix4 ) {

		this.direction.add( this.origin ).applyMatrix4( matrix4 );
		this.origin.applyMatrix4( matrix4 );
		this.direction.sub( this.origin );

		return this;
	},

	equals: function ( ray ) {

		return ray.origin.equals( this.origin ) && ray.direction.equals( this.direction );

	},

	clone: function () {

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

	}

};