Calc reflection/re-bounce Vector in SceneKit Swift - ios

Question

I try to calculate the bounce-vector or reflection-vector to a given direction at a specific intersection point/surface in 3D SceneKit space within a AR Session.
To do this, I send out a hittest from the exact center of the screen straight forward. There is i.Ex a cube positioned let’s say 2 meter in front of me. Now I’d like to continue this hittest in the logical re-bounce/reflection direction, just as a light-ray on a mirror would do. Of course the hittest is ended at its intersection point, but from there I would like to draw like a line or small and long SCNTube node to visualise the direction in which this hittest would continue if it was reflected by one of the faces of the cube. And this from any particular direction.
Lets say, I have the direction vector in which I send the hittest. I also have the intersection point given by the hittest result. And I have the normal of the surface at the intersection point.
Regarding to some Answers I found about this issue on Linear Algebra Forums:
https://math.stackexchange.com/questions/2235997/reflecting-ray-on-triangle-in-3d-space
https://math.stackexchange.com/questions/13261/how-to-get-a-reflection-vector
the following Formula should do, and this in 3D space:
(and it should give me the re-bounce/reflection vector)
r = d − 2(d⋅n)n
(where d⋅n is the dot product, and n must be normalised. r is the reflection vector.)
I tried to make a kind of Swift implementation of that resulting in nonsense. Here is my code:
let location: CGPoint = screenCenter
let hits = self.sceneView.hitTest(location, options: [SCNHitTestOption.categoryBitMask: NodeCategory.catCube.rawValue, SCNHitTestOption.searchMode: SCNHitTestSearchMode.any.rawValue as NSNumber])
if !hits.isEmpty {
print("we have a hittest")
let d = currentDirection
let p = hits.first?.worldCoordinates // Hit Location
let n = hits.first?.worldNormal // Normal of Hit Location
print("D = \(d)")
print("P = \(p)")
print("N = \(n)")
// r = d - 2*(d*n).normalized // the Formula
let r : SCNVector3 = d - (d.crossProduct(n!).crossProduct(d.crossProduct(n!))).normalized
// let r : SCNVector3 = d - (2 * d.crossProduct(n!).normalized) // I also tried this, but that gives me errors in Xcode
print("R = \(r)")
// This Function should setup then the node aligned to that new vector
setupRay(position: p!, euler: r)
}
All this results in nonsense. I get the following console output:
we are in gesture TAP recognizer
we have a hittest
D = SCNVector3(x: -0.29870644, y: 0.5494926, z: -0.7802771)
P = Optional(__C.SCNVector3(x: -0.111141175, y: 0.034069262, z: -0.62390435))
N = Optional(__C.SCNVector3(x: 2.672451e-08, y: 1.0, z: 5.3277716e-08))
R = SCNVector3(x: nan, y: nan, z: nan)
My Euler Angle: SCNVector3(x: nan, y: nan, z: nan)
(D is the direction of the hittest, P is the Point of intersetion, N is the Normal at the Point of intersection, R should be the reflection Vector but is always just nan, not a number)
I also tried the extension dotProduct instead of crossProduct, but dotProduct gives me a Float value, which I cannot calc with a SCNVector3
How can I calculate this re-bounce vector and align a SCNNode facing in that direction (with the Pivot at the start Point, the point of intersection from the hittest)
What am I doing wrong? Can anyone show me a working Swift implementation of that calculation?
Any Help would be so helpful. (Linear Algebra belongs not to my powers)
PS: I use standard SCNVector 3 math extensions as available from GitHub

Answer 1

Finally this Solution should work as far as I can say for iOS 12 (successfully tested). It gives you the reflection Vector from any surface and any Point of view.
let location: CGPoint = screenCenter
let hits = self.sceneView.hitTest(location, options: [SCNHitTestOption.categoryBitMask: NodeCategory.catCube.rawValue, SCNHitTestOption.searchMode: SCNHitTestSearchMode.any.rawValue as NSNumber])
if let hitResult = hits.first {
let direction = normalize(double3(sceneView.pointOfView!.worldFront))
// let reflectedDirection = reflect(direction, n: double3(hitResult.worldNormal))
let reflectedDirection = simd_reflect(direction, double3(hitResult.worldNormal))
print(reflectedDirection)
// Use the Result for whatever purpose
setupRay(position: hitResult.worldCoordinates, reflectDirection: SCNVector3(reflectedDirection))
}

Answer 2

the SIMD library is really useful for thing like that:
if let hitResult = hitResults.first {
let direction = normalize(scnView.pointOfView!.simdPosition - hitResult.simdWorldCoordinates)
let reflectedDirection = reflect(direction, n: hitResult.simdWorldNormal)
print(reflectedDirection)
}