distanceSqToSegment method
Implementation
num distanceSqToSegment(Vector3 v0, Vector3 v1,
[Vector3? optionalPointOnRay, Vector3? optionalPointOnSegment]) {
// from http://www.geometrictools.com/GTEngine/Include/Mathematics/GteDistRaySegment.h
// 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(origin).sub(_segCenter);
var segExtent = v0.distanceTo(v1) * 0.5;
num a01 = -direction.dot(_segDir);
var b0 = _diff.dot(direction);
var b1 = -_diff.dot(_segDir);
var c = _diff.lengthSq();
var det = Math.abs(1 - a01 * a01);
num 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 != null) {
optionalPointOnRay.copy(direction).multiplyScalar(s0).add(origin);
}
if (optionalPointOnSegment != null) {
optionalPointOnSegment.copy(_segDir).multiplyScalar(s1).add(_segCenter);
}
return sqrDist;
}