Per-Pixel Divisions

We describe a method to perform per pixel divisions using graph ics hardware with a simple iterative algorithm In the worst case the number of rendering passes is for approximate divisions and for accurate divisions The algorithm can be used for D vec tor normalization evaluating complex lighting models and image reconstruction Introduction and Previous Work Graphics hardware can act as a powerful SIMD data processing unit However the numerical precision is limited to the available number of bits per color channel of a pixel and only fairly simple operations are available in the hardware In particular the OpenGL standard contains no operation for a single per pixel division operation This paper presents an algorithm for computing division using multiple rendering passes Alternatives to our division algorithm described below could be using look up tables storing Alpha values or using pixel textures to perform R G B A to R G B look up s Unfortunately even bit look up tables result in considerable loss of precision when set up to evaluate x Pixel textures are not widely supported by the graphics hardware and have an additional drawback of consuming too much memory One of our applications of the division algorithm is image reconstruc tion from non uniformly distributed samples which requires the compu tation of a weighted average of the form P