A ray can now compute its minimal distance to a segment

We can give optional targets to compute the points on the ray and the other on the segment (defining the minimal distance...)

src/math/Ray.js

@@ -78,6 +78,66 @@ THREE.Ray.prototype = {
 
 	}(),
 
+	distanceSqAndPointToSegment: function( v0, v1, optionalPointOnLine, optionalPointOnSegment ) {
+		// from http://www.geometrictools.com/LibMathematics/Distance/Wm5DistLine3Segment3.cpp
+		// It returns the min distance between the ray (actually... the line) and the segment
+		// defined by v0 and v1
+		// It can also set two optional targets :
+		// - The closest point on the ray (...line)
+		// - 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 c = diff.lengthSq();
+		var det = Math.abs( 1 - a01 * a01 );
+		var b1, s0, s1, sqrDist, extDet;
+		if( det >= 0 ) {
+			// The line and segment are not parallel.
+			b1 = -diff.dot( segDir );
+			s1 = a01 * b0 - b1;
+			extDet = segExtent * det;
+			if( s1 >= -extDet ) {
+				if( s1 <= extDet ) {
+					// Two interior points are closest, one on the line and one
+					// on the segment.
+					var invDet = 1 / det;
+					s0 = ( a01 * b1 - b0 ) * invDet;
+					s1 *= invDet;
+					sqrDist = s0 * ( s0 + a01 * s1 + 2 * b0 ) + s1 * ( a01 * s0 + s1 + 2 * b1 ) + c;
+				}
+				else {
+					// The endpoint e1 of the segment and an interior point of
+					// the line are closest.
+					s1 = segExtent;
+					s0 = - ( a01 * s1 + b0 );
+					sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c;
+				}
+			}
+			else {
+				// The end point e0 of the segment and an interior point of the
+				// line are closest.
+				s1 = - segExtent;
+				s0 = - ( a01 * s1 + b0 );
+				sqrDist = - s0 * s0 + s1 * ( s1 + 2 * b1 ) + c;
+			}
+		}
+		else {
+			// The line and segment are parallel.  Choose the closest pair so that
+			// one point is at segment center.
+			s1 = 0;
+			s0 = - b0;
+			sqrDist = b0 * s0 + c;
+		}
+		if(optionalPointOnLine)
+			optionalPointOnLine.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 );