/**
* @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 result.copy( this.origin );
}
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 );
};
}(),
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 );
},
clone: function () {
return new THREE.Ray().copy( this );
}
};