// Returns 'true' if the OBB intersects (or is inside) the frustum, 'false' otherwise.
// 'cameraRelativeOffset' can be used to intersect a world-space OBB with a camera-relative frustum.
public static bool Overlap(OrientedBBox obb, Vector3 cameraRelativeOffset,
Frustum frustum, int numPlanes, int numCorners)
{
Vector3 center = obb.center + cameraRelativeOffset;
Vector3 forward = Vector3.Cross(obb.up, obb.right);
bool overlap = true;
// Test the OBB against frustum planes. Frustum planes have inward-facing.
// The OBB is outside if it's entirely behind one of the frustum planes.
// See "Real-Time Rendering", 3rd Edition, 16.10.2.
for (int i = 0; overlap && i < numPlanes; i++)
{
Vector3 n = frustum.planes[i].normal;
float d = frustum.planes[i].distance;
// Max projection of the half-diagonal onto the normal (always positive).
float maxHalfDiagProj = obb.extentX * Mathf.Abs(Vector3.Dot(n, obb.right))
+ obb.extentY * Mathf.Abs(Vector3.Dot(n, obb.up))
+ obb.extentZ * Mathf.Abs(Vector3.Dot(n, forward));
// Negative distance -> center behind the plane (outside).
float centerToPlaneDist = Vector3.Dot(n, center) + d;
// outside = maxHalfDiagProj < -centerToPlaneDist
// outside = maxHalfDiagProj + centerToPlaneDist < 0
// overlap = overlap && !outside
overlap = overlap && (maxHalfDiagProj + centerToPlaneDist >= 0);
}
if (numCorners == 0)
{
return(overlap);
}
// Test the frustum corners against OBB planes. The OBB planes are outward-facing.
// The frustum is outside if all of its corners are entirely in front of one of the OBB planes.
// See "Correct Frustum Culling" by Inigo Quilez.
// We can exploit the symmetry of the box by only testing against 3 planes rather than 6.
Plane[] planes = new Plane[3];
planes[0].normal = obb.right;
planes[0].distance = obb.extentX;
planes[1].normal = obb.up;
planes[1].distance = obb.extentY;
planes[2].normal = forward;
planes[2].distance = obb.extentZ;
for (int i = 0; overlap && i < 3; i++)
{
Plane plane = planes[i];
// We need a separate counter for the "box fully inside frustum" case.
bool outsidePos = true; // Positive normal
bool outsideNeg = true; // Reversed normal
// Merge 2 loops. Continue as long as all points are outside either plane.
for (int j = 0; j < numCorners; j++)
{
float proj = Vector3.Dot(plane.normal, frustum.corners[j] - center);
outsidePos = outsidePos && (proj > plane.distance);
outsideNeg = outsideNeg && (-proj > plane.distance);
}
overlap = overlap && !(outsidePos || outsideNeg);
}
return(overlap);
}