public static void GetIntersections(ColoredRay3D ray, RESphere sphere, NearestIntersection intersections)
{
/*
* __ ___ ___
* Ro, Dir - the ray, |Dir| = 1
* __
* So, R - Sphere
*
* Equations
* _ ___
* Ray: P = Ro + t * Dir
* __ _ __ _
* Sphere: (So - P)*(So - P) = R*R
* __ __ ___ __ __ ___
* (So - (Ro + t*Dir))*(So - (Ro + t*Dir)) = R*R
* __ __ ___ __ __ ___
* ((So - Ro) - t*Dir)*((So - Ro) - t*Dir) = R*R
* _ _ _ ___ ___ ___ _ __ __
* C*C - 2*C*Dir*t + Dir*Dir*t*t = R*R, C = (So - Ro)
* _ _ ___ _ ___
* t*t - 2*k*t + C*C - R*R = 0, |Dir| = 1, k = C*Dir
* _ _
* det' = 4*k*k - 4*(C*C - R*R)
* _ _
* det = k*k - (C*C - R*R)
*
* 2*k +/- sqrt(det')
* t1,2 = -------------------------
* 2
*
* t1,2 = k +/- sqrt(det)
*
* */
//Vector3D ro = ray.CoordinateSystem.TransformVector(ray.Start, flatShape.Origin.CoordinateSystem);
//Vector3D re = ray.CoordinateSystem.TransformVector(ray.End, flatShape.Origin.CoordinateSystem);
Vector3D ro = ray.Start;
Vector3D re = ray.End;
Vector3D c = sphere.Position - ro;
Vector3D dir = re - ro;
float k = Vector3D.Scalar(dir, c);
float det = k * k - Vector3D.Scalar(c, c) + sphere.Radius2;
if (det > 0) {
det = (float)System.Math.Sqrt(det);
float t1 = k - det;
float t2 = k + det;
if (t1 > 0) {
var first = new Intersection(0, 0, 0) {
Shape3D = sphere,
Ray = ray,
Length = t1,
Point = ro + dir * t1
};
first.Normal = (first.Point - sphere.Position) / sphere.Radius;
intersections.Set(first);
}
if (t2 > 0) {
var second = new Intersection(0, 0, 0) {
Shape3D = sphere,
Ray = ray,
Length = t2,
Point = ro + dir * t2
};
second.Normal = (second.Point - sphere.Position) / sphere.Radius;
intersections.Set(second);
}
}
}
public static void GetIntersections(ColoredRay3D ray, REFlatShape flatShape, NearestIntersection intersections)
{
/* Math for float shapes like triangle or rectangle
* __ ___ ___
* Ro, Dir - the ray, |Dir| = 1
_ _ _
* A, B, C - the triangle
*
* Equations
* _ ___
* Ray: P = Ro + t * Dir
* _ _ _ _ _
* Triangle: P = U * u + V * v + W * w + A, _ _ _
* U = (B - A)
* _ _ _
* V = (C - A)
* _ _ _
* W = U x V
*
* w = 0
* _ _ _
* D = P - A
* D.x = U.x * u + V.x * v + W.x * w
* D.y = U.y * u + V.y * v + W.y * w
* D.z = U.z * u + V.z * v + W.z * w
*
* | U.x V.x W.x |
* det = | U.y V.y W.y |
* | U.z V.z W.z |
*
* | D.x V.x W.x | _ _ _
* detU = | D.y V.y W.y | = D * (V x W)
* | D.z V.z W.z |
*
* | U.x D.x W.x | _ _ _
* detV = | U.y D.y W.y | = D * (W x U)
* | U.z D.z W.z |
*
* | U.x V.x D.x | _ _ _ _ _
* detW = | U.y V.y D.y | = D * (U x V) = D * W
* | U.z V.z D.z |
* _ _ _ _ _
* detU D * (V x W) _ V x W _ __
* u = ---- = ----------- = D * (-----) = D * Tu
* det det det
* _ _ _ _ _
* detV D * (W x U) _ W x U _ __
* v = ---- = ----------- = D * (-----) = D * Tv
* det det det
* _ _ _ _ _
* detW D * (U x V) _ U x V _ __
* w = ---- = ----------- = D * (-----) = D * Tw
* det det det
*
* w = 0
* _ __
* D * Tw = 0
* _ _ __
* (P - A) * Tw = 0
* _ __ _ __
* P * Tw = A * Tw
* __ ___ __ _ __
* (Ro + t * Dir) * Tw = A * Tw
* ___ __ _ __ __
* t * Dir * Tw = (A - Ro) * Tw
* _ __ __
* (A - Ro) * Tw
* t = -===---==----
* Dir * Tw
* */
//Vector3D ro = ray.CoordinateSystem.TransformVector(ray.Start, flatShape.Origin.CoordinateSystem);
//Vector3D re = ray.CoordinateSystem.TransformVector(ray.End, flatShape.Origin.CoordinateSystem);
Vector3D ro = ray.Start;
Vector3D re = ray.End;
Vector3D dir = re - ro;
float k = Vector3D.Scalar(dir, flatShape.Tw);
if (k == 0) return;
float t = Vector3D.Scalar(flatShape.A - ro, flatShape.Tw) / k;
if (t < 0) return;
var point = ro + dir*t;
Vector3D d = point - flatShape.A;
float u = Vector3D.Scalar(d, flatShape.Tu);
float v = Vector3D.Scalar(d, flatShape.Tv);
if (!flatShape.ValidateTexture(u, v)) return;
var intersection = new Intersection(u, v, 0) {
Length = t,
Normal = k < 0 ? flatShape.Normal : flatShape.Normal * -1,
Shape3D = flatShape,
Point = point,
Ray = ray
};
intersections.Set(intersection);
}