public override void FindClosestPointOnSurface(Vector3 pos,
out Vector3 surfacePos, out Vector3 surfaceNorm)
{
// The closest-point functions operate on an unrotated ellipsoid at the origin.
// I'll call that coordinate system "ellipse space (ES)".
// "object space (OS)" is the true scale-compensated object-space coordinate system.
// Take (uniform) scale from parent, but no scale from this object.
// Our local scale is instead treated as Extents
TrTransform xfWorldFromEllipse =
TrTransform.FromTransform(transform.parent) *
TrTransform.TR(transform.localPosition, transform.localRotation);
TrTransform xfEllipseFromWorld = xfWorldFromEllipse.inverse;
Vector3 halfExtent = Extents * .5f;
Vector3 pos_OS = transform.InverseTransformPoint(pos);
Vector3 pos_ES = xfEllipseFromWorld * pos;
Vector3 closest_ES = MathEllipsoidAnton.ClosestPointEllipsoid(halfExtent, pos_ES);
// Transform from ES -> OS, get the OS normal, then transform OS -> WS.
// Normals are axial, so OS -> WS uses the inv-transpose. That all ends
// up simplifying to this:
surfaceNorm = transform.rotation *
CDiv(closest_ES,
CMul(halfExtent, halfExtent)).normalized;
surfacePos = xfWorldFromEllipse * closest_ES;
}
public void TestEllipsoidInOctant_Anton()
{
TestEllipsoidInOctant((a, b) => MathEllipsoidAnton.ClosestPointEllipsoid(a, b));
}
public void TestEllipsoidTangent_Anton()
{
TestEllipsoidRandomPoints((a, b) => MathEllipsoidAnton.ClosestPointEllipsoid(a, b));
}