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;

	},

	clone: function () {

		var ray = new this.constructor();
		return ray.copy( 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 result.copy( this.origin );

		}

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

	},

	distanceToPoint: function ( point ) {

		return Math.sqrt( this.distanceSqToPoint( point ) );

	},

	distanceSqToPoint: 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.distanceToSquared( point );

			}

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

			return v1.distanceToSquared( point );

		};

	}(),

	distanceSqToSegment: function () {

		var segCenter = new THREE.Vector3();
		var segDir = new THREE.Vector3();
		var diff = new THREE.Vector3();

		return 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

			segCenter.copy( v0 ).add( v1 ).multiplyScalar( 0.5 );
			segDir.copy( v1 ).sub( v0 ).normalize();
			diff.copy( this.origin ).sub( segCenter );

			var segExtent = v0.distanceTo( v1 ) * 0.5;
			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 ).multiplyScalar( s0 ).add( this.origin );

			}

			if ( optionalPointOnSegment ) {

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

			}

			return sqrDist;

		};

	}(),


	isIntersectionSphere: function ( sphere ) {

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

	},

	intersectSphere: function () {

		// from http://www.scratchapixel.com/lessons/3d-basic-lessons/lesson-7-intersecting-simple-shapes/ray-sphere-intersection/

		var v1 = new THREE.Vector3();

		return function ( sphere, optionalTarget ) {

			v1.subVectors( sphere.center, this.origin );

			var tca = v1.dot( this.direction );

			var d2 = v1.dot( v1 ) - tca * tca;

			var radius2 = sphere.radius * sphere.radius;

			if ( d2 > radius2 ) return null;

			var thc = Math.sqrt( radius2 - d2 );

			// t0 = first intersect point - entrance on front of sphere
			var t0 = tca - thc;

			// t1 = second intersect point - exit point on back of sphere
			var t1 = tca + thc;

			// test to see if both t0 and t1 are behind the ray - if so, return null
			if ( t0 < 0 && t1 < 0 ) return null;

			// test to see if t0 is behind the ray:
			// if it is, the ray is inside the sphere, so return the second exit point scaled by t1,
			// in order to always return an intersect point that is in front of the ray.
			if ( t0 < 0 ) return this.at( t1, optionalTarget );

			// else t0 is in front of the ray, so return the first collision point scaled by t0
			return this.at( t0, optionalTarget );

		}

	}(),

	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 );

	},

	isIntersectionBox: function () {

		var v = new THREE.Vector3();

		return function ( box ) {

			return this.intersectBox( box, v ) !== null;

		};

	}(),

	intersectBox: function ( box, optionalTarget ) {

		// http://www.scratchapixel.com/lessons/3d-basic-lessons/lesson-7-intersecting-simple-shapes/ray-box-intersection/

		var tmin, tmax, tymin, tymax, tzmin, tzmax;

		var invdirx = 1 / this.direction.x,
			invdiry = 1 / this.direction.y,
			invdirz = 1 / this.direction.z;

		var origin = this.origin;

		if ( invdirx >= 0 ) {

			tmin = ( box.min.x - origin.x ) * invdirx;
			tmax = ( box.max.x - origin.x ) * invdirx;

		} else {

			tmin = ( box.max.x - origin.x ) * invdirx;
			tmax = ( box.min.x - origin.x ) * invdirx;

		}

		if ( invdiry >= 0 ) {

			tymin = ( box.min.y - origin.y ) * invdiry;
			tymax = ( box.max.y - origin.y ) * invdiry;

		} else {

			tymin = ( box.max.y - origin.y ) * invdiry;
			tymax = ( box.min.y - origin.y ) * invdiry;

		}

		if ( ( tmin > tymax ) || ( tymin > tmax ) ) return null;

		// These lines also handle the case where tmin or tmax is NaN
		// (result of 0 * Infinity). x !== x returns true if x is NaN

		if ( tymin > tmin || tmin !== tmin ) tmin = tymin;

		if ( tymax < tmax || tmax !== tmax ) tmax = tymax;

		if ( invdirz >= 0 ) {

			tzmin = ( box.min.z - origin.z ) * invdirz;
			tzmax = ( box.max.z - origin.z ) * invdirz;

		} else {

			tzmin = ( box.max.z - origin.z ) * invdirz;
			tzmax = ( box.min.z - origin.z ) * invdirz;

		}

		if ( ( tmin > tzmax ) || ( tzmin > tmax ) ) return null;

		if ( tzmin > tmin || tmin !== tmin ) tmin = tzmin;

		if ( tzmax < tmax || tmax !== tmax ) tmax = tzmax;

		//return point closest to the ray (positive side)

		if ( tmax < 0 ) return null;

		return this.at( tmin >= 0 ? tmin : tmax, optionalTarget );

	},

	intersectTriangle: function () {

		// Compute the offset origin, edges, and normal.
		var diff = new THREE.Vector3();
		var edge1 = new THREE.Vector3();
		var edge2 = new THREE.Vector3();
		var normal = new THREE.Vector3();

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

			// from http://www.geometrictools.com/LibMathematics/Intersection/Wm5IntrRay3Triangle3.cpp

			edge1.subVectors( b, a );
			edge2.subVectors( c, a );
			normal.crossVectors( edge1, edge2 );

			// Solve Q + t*D = b1*E1 + b2*E2 (Q = kDiff, D = ray direction,
			// E1 = kEdge1, E2 = kEdge2, N = Cross(E1,E2)) by
			//   |Dot(D,N)|*b1 = sign(Dot(D,N))*Dot(D,Cross(Q,E2))
			//   |Dot(D,N)|*b2 = sign(Dot(D,N))*Dot(D,Cross(E1,Q))
			//   |Dot(D,N)|*t = -sign(Dot(D,N))*Dot(Q,N)
			var DdN = this.direction.dot( normal );
			var sign;

			if ( DdN > 0 ) {

				if ( backfaceCulling ) return null;
				sign = 1;

			} else if ( DdN < 0 ) {

				sign = - 1;
				DdN = - DdN;

			} else {

				return null;

			}

			diff.subVectors( this.origin, a );
			var DdQxE2 = sign * this.direction.dot( edge2.crossVectors( diff, edge2 ) );

			// b1 < 0, no intersection
			if ( DdQxE2 < 0 ) {

				return null;

			}

			var DdE1xQ = sign * this.direction.dot( edge1.cross( diff ) );

			// b2 < 0, no intersection
			if ( DdE1xQ < 0 ) {

				return null;

			}

			// b1+b2 > 1, no intersection
			if ( DdQxE2 + DdE1xQ > DdN ) {

				return null;

			}

			// Line intersects triangle, check if ray does.
			var QdN = - sign * diff.dot( normal );

			// t < 0, no intersection
			if ( QdN < 0 ) {

				return null;

			}

			// Ray intersects triangle.
			return this.at( QdN / DdN, optionalTarget );

		};

	}(),

	applyMatrix4: function ( matrix4 ) {

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

		return this;

	},

	equals: function ( ray ) {

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

	}

};