I want to do some basic view frustum culling, using bounding spheres for my objects.

The spheres are positioned in world space and I am constructing planes for my frustum.

I then calculate the distance between my spheres centers and each plane and if it is bigger than the radius and on the wrong side, the object is culled. This can be optimized by first culling with a sphere around the frustum and maybe some caching for the plane that culled an object in the previous frame and generally works great. Something like this can be found easily online and is most probably good enough for most cases.

A problematic case looks like this:

where "View" is the visible area, "PL" the left plane, "PB" the bottom plane and "P" the center of the sphere to cull.

It is obviously inside the top and right plane (where ever those are) and while the point is clearly on the wrong side of PL and PB, the distance to each minus the radius is inside the both planes, but still the sphere would not be visible.

This usually shouldn´t be a problem, but I am using it to cull lights for tiled shading, so I´ve got many small frustums and many in comparison big spheres, so this is a big issue.

The solution I came up with is simple, all I do is (additional to the culling above) storing the distances to the planes and using pythagoras to get the squared distance to the frustums corner which means for example for the case above: distToPL*distToPL+distToPB*distToPB

For visibility, the result can be compared to the squared radius.

Now I am wondering if this makes sense (I am not completely sure if maybe the perspective frustum breaks it? From my understanding it shuldn´t, but that doesn´t have to mean much...) and if there is any better alternative?

IgnatusZuk, thanks, but your code has the exact same problem I am trying to solve: There are some cases, where the function return visibility, while the object is actually outside the view frustum. In most cases I expect this to be just very few objects, so anything more complicated for culling is not worth it.

TMarques, I may should have mentioned that I am culling spheres in a 3D frustum, so those corners are actually lines and not points, but my approach to get that V as the distance to the planes should be fine, except the thing you mentioned, where I have to check which side of the planes the center is on, which explains why now in my implementation too many lights are culled.

Thank you very much for that hint :)

If there are any more ideas, please post them, as I´d love to find a better way if there is one :)

For now it is just a list, later they will probably be sorted into an octree or something similar, which should of course be an improvement but for now it is good enough to optimize the culling itself a little (for less than 1000 lights, it performs very well, using multithreading and some basic code optimizations).

My code seems to work well and looks like this now:

#define Distance(plane, op, r) { \
	float dot = (position.x * plane.normal.x + position.y * plane.normal.y + position.z * plane.normal.z);\
	distance = dot - plane.d; \
	if(distance op r) \
		continue; \
	}


const Vector3& position = light->_worldPosition;
const float range = light->_range;
float distance, dr, dl, dt, db;
Distance(plright, >, range);
dr = distance;
Distance(plleft, <, -range);
dl = distance;
Distance(plbottom, <, -range);
db = distance;
Distance(pltop, >, range);
dt = distance;

float sqrange = range*range;
if(dr > 0.0f && db < 0.0f && dr*dr+db*db > sqrange)
	continue;
if(dr > 0.0f && dt > 0.0f && dr*dr+dt*dt > sqrange)
	continue;
if(dl < 0.0f && db < 0.0f && dl*dl+db*db > sqrange)
	continue;
if(dl < 0.0f && dt > 0.0f && dl*dl+dt*dt > sqrange)
	continue;

It´s not pretty, but I have to fix some other things before cleaning up and while my planes have a function to get it´s distance to a point, at 32*24*1024*4 calls, the function call overhead was the biggest performance hit ;)