Which geometrical calculations can be accelerated using OpenGL

Question

I need to accelerate some programs that use intensive calculations where surface calculations from the intersection between cubes, spheres and similar are needed. Using CUDA I need to specify all the formuale I need, of course, in order to analytically calculate information related to intersections. But since I only need a good approximation of the resulting surface, I read about OpenGL can calculate or estimate such surfaces. I wonder if you could give me your opinion or point me to relevant references

Answer 1

If you just need to render those objects, you could use the stencil buffer to evaluate whatever boolean operations you need: http://www.opengl.org/resources/code/samples/advanced/advanced97/notes/node11.html

Any quantities that could be computed from either a perspective or orthographic projection of the intersection surface could be deduced from such a rendering together with its depth buffer. If you need to extract the whole intersection, you can try using depth peeling together with stencilled CSG to extract a layered representation of the complete intersection, though it can be very inaccurate on the parts of the surface which are parallel to the viewing direction and you will need to do some extra work to stitch the layers back together: http://developer.download.nvidia.com/SDK/10/opengl/src/dual_depth_peeling/doc/DualDepthPeeling.pdf

EDIT: This will work for arbitrary, free form surfaces and is a fairly standard technique. But it does have its limitations, in that the accuracy you get will be fairly poor and you may have to project onto multiple views in order to get some adequate covering of your object. As an example, here is an application to collision detection: http://www.cs.ucl.ac.uk/staff/b.spanlang/ISBCICSOWH.pdf

Answer 2

OpenGL is of even less use here than CUDA or OpenCL, since it's primarily targeted at drawing triangular tesselated meshes. Of course you can do sophisticated geometrical computations in the various shader stages of modern OpenGL. The problem is, that the result of all those computations is a pixel based picture. There is a feedback mechanism to retrieve the processed vertex data, but that only gives you a mesh.

Intersections of anything planar or/and with spheres is actually quite easy and can be done analytically. The real hard stuff is intersecting freeform curved surfaces (Bezìer or NURBS). Those usually don't have a closed solution, so what you need to do is numerically aproximating a trim curve that best fits the intersection.