Sphere-cone intersection test fails

[Leadwerks]

If you use this code with a very wide angle cone it can fail when the camera gets near the apex.

The problem is with this line of code:

/* Point - cone test */
if ((diff - sphereRadius * sinAngle * coneNormal).Dot(coneNormal) > 0.0f)
{

I don't understand the exact math here but that statement is causing some valid intersections to get discarded.

I worked around this by adding my own checks for when the camera is above or below the cone, or within the radius of the apex.

[Squareys]

template<class T> bool sphereConeNotFast(
    const Vector3<T> sphereCenter, const T sphereRadius,
    const Vector3<T>& origin, const Vector3<T>& normal, const Rad<T> angle)
{
    const Vector3<T> diff = sphereCenter - origin;
    const Vector3<T> dir = diff.normalized();
    const Rad<T> halfAngle = angle/T(2);
    /* Compute angle between normal and point */
    const Rad<T> actual = Math::acos(dot(normal, dir));
    /* Distance from cone surface */
    const T distanceFromCone = Math::sin(actual - halfAngle)*diff.length();
    /* Either the sphere center lies in cone, or cone is max radius away from
       the cone */
    return actual <= halfAngle || distanceFromCone <= sphereRadius;
}

@mosra This is the code from my bachelor's thesis if that helps.