Technical note

Well known implementations for perspective correct rendering of planar polygons require a division per rendered pixel. Such a division is better to be avoided as it is an expensive operation in terms of silicon gates and clock cycles. In this paper we present a family of efficient midpoint algorithms that can be used to avoid division operators. These algorithms do not require more than a small number of additions per pixel. We show how these can be embedded in scan line algorithms and in algorithms that use mipmaps. Experiments with software implementations show that the division free algorithms are a factor of two faster, provided that the polygons are not too small. These algorithms are however most profitable when realised in hardware. CR Categories: I.3.3 [Computer Graphics]: picture/image generation − Display algorithms; I.3.7 [Computer Graphics]: three dimensional graphics and realism − color, shading, shadowing and texture