public static LinearIntersection RaySphere(ref Vector3d rayOrigin, ref Vector3d rayDirection, ref Vector3d sphereCenter, double sphereRadius)
{
LinearIntersection result = new LinearIntersection();
LineSphere(ref rayOrigin, ref rayDirection, ref sphereCenter, sphereRadius, ref result);
return(result);
}
public static LinearIntersection LineSphere(ref Vector3d lineOrigin, ref Vector3d lineDirection, ref Vector3d sphereCenter, double sphereRadius)
{
var result = new LinearIntersection();
LineSphere(ref lineOrigin, ref lineDirection, ref sphereCenter, sphereRadius, ref result);
return(result);
}
/// <summary>
/// Intersect ray with sphere and return intersection info (# hits, ray parameters)
/// </summary>
public static bool RaySphere(ref Vector3d rayOrigin, ref Vector3d rayDirection, ref Vector3d sphereCenter, double sphereRadius, ref LinearIntersection result)
{
// [RMS] adapted from GeometricTools GTEngine
// https://www.geometrictools.com/GTEngine/Include/Mathematics/GteIntrRay3Sphere3.h
LineSphere(ref rayOrigin, ref rayDirection, ref sphereCenter, sphereRadius, ref result);
if (result.intersects)
{
// The line containing the ray intersects the sphere; the t-interval
// is [t0,t1]. The ray intersects the sphere as long as [t0,t1]
// overlaps the ray t-interval [0,+infinity).
if (result.parameter.b < 0)
{
result.intersects = false;
result.numIntersections = 0;
}
else if (result.parameter.a < 0)
{
result.numIntersections--;
result.parameter.a = result.parameter.b;
}
}
return(result.intersects);
}
/// <summary>
/// Intersect ray with sphere and return intersection info (# hits, ray parameters)
/// </summary>
public static bool LineSphere(ref Vector3d lineOrigin, ref Vector3d lineDirection, ref Vector3d sphereCenter, double sphereRadius, ref LinearIntersection result)
{
// [RMS] adapted from GeometricTools GTEngine
// https://www.geometrictools.com/GTEngine/Include/Mathematics/GteIntrLine3Sphere3.h
// The sphere is (X-C)^T*(X-C)-1 = 0 and the line is X = P+t*D.
// Substitute the line equation into the sphere equation to obtain a
// quadratic equation Q(t) = t^2 + 2*a1*t + a0 = 0, where a1 = D^T*(P-C),
// and a0 = (P-C)^T*(P-C)-1.
Vector3d diff = lineOrigin - sphereCenter;
double a0 = diff.LengthSquared - sphereRadius * sphereRadius;
double a1 = lineDirection.Dot(diff);
// Intersection occurs when Q(t) has real roots.
double discr = a1 * a1 - a0;
if (discr > 0)
{
result.intersects = true;
result.numIntersections = 2;
double root = Math.Sqrt(discr);
result.parameter.a = -a1 - root;
result.parameter.b = -a1 + root;
}
else if (discr < 0)
{
result.intersects = false;
result.numIntersections = 0;
}
else
{
result.intersects = true;
result.numIntersections = 1;
result.parameter.a = -a1;
result.parameter.b = -a1;
}
return(result.intersects);
}
