3D Line Segment and Plane Intersection - Contd - c++

Question

After advice from krlzlx I have posted it as a new question.
From here:
3D Line Segment and Plane Intersection
I have a problem with this algorithm, I have implemented it like so:
template <class T>
class AnyCollision {
public:
std::pair<bool, T> operator()(Point3d &ray, Point3d &rayOrigin, Point3d &normal, Point3d &coord) const {
// get d value
float d = (normal.x * coord.x) + (normal.y * coord.y) + (normal.z * coord.z);
if (((normal.x * ray.x) + (normal.y * ray.y) + (normal.z * ray.z)) == 0) {
return std::make_pair(false, T());
}
// Compute the X value for the directed line ray intersecting the plane
float a = (d - ((normal.x * rayOrigin.x) + (normal.y * rayOrigin.y) + (normal.z * rayOrigin.z)) / ((normal.x * ray.x) + (normal.y * ray.y) + (normal.z * ray.z)));
// output contact point
float rayMagnitude = (sqrt(pow(ray.x, 2) + pow(ray.y, 2) + pow(ray.z, 2)));
Point3d rayNormalised((ray.x / rayMagnitude), (ray.y / rayMagnitude), (ray.z / rayMagnitude));
Point3d contact((rayOrigin.x + (rayNormalised.x * a)), (rayOrigin.y + (rayNormalised.y * a)), (rayOrigin.z + (rayNormalised.z * a))); //Make sure the ray vector is normalized
return std::make_pair(true, contact);
};
Point3d is defined as:
class Point3d {
public:
double x;
double y;
double z;
/**
* constructor
*
* 0 all elements
*/
Point3d() {
x = 0.0;
y = 0.0;
z = 0.0;
}
I am forced to use this structure, because in the larger system my component runs in it is defined like this and it cannot be changed.
My code compiles fine, but testing I get incorrect values for the point. The ratio of x, y, z is correct but the magnitude is wrong.
For example if:
rayOrigin.x = 0;
rayOrigin.y = 0;
rayOrigin.z = 0;
ray.x = 3;
ray.y = -5;
ray.z = 12;
normal.x = -3;
normal.y = 12;
normal.z = 0;
coord.x = 7;
coord.y = -5;
coord.z = 10;
I expect the point to be:
(0.63, 1.26, 1.89)
However, it is:
(3.52, -5.87, 14.09)
A magnitude of 5.09 too big.
And I also tested:
rayOrigin.x = 0;
rayOrigin.y = 0;
rayOrigin.z = 0;
ray.x = 2;
ray.y = 3;
ray.z = 3;
normal.x = 4;
normal.y = 1;
normal.z = 0;
p0.x = 2;
p0.y = 1;
p0.z = 5;
I expect the point to be:
(1.64, 2.45, 2.45)
However, it is:
(3.83761, 5.75642, 5.75642)
A magnitude of 2.34 too big?

Answer 1

Pseudocode (does not require vector normalization):
Diff = PlaneBaseCoordinate - RayOrigin
d = Normal.dot.Diff
e = Normal.dot.RayVector
if (e)
IntersectionPoint = RayOrigin + RayVector * d / e
otherwise
ray belongs to the plane or is parallel
Quick check:
Ray (0,0,0) (2,2,2) //to catch possible scale issues
Plane (0,1,0) (0,3,0) //plane y=1
Diff = (0,1,0)
d = 3
e = 6
IntersectionPoint = (0,0,0) + (2,2,2) * 3 / 6 = (1, 1, 1)