Abstract: This paper introduces linear grouping, a slightly lossy optimization technique for affine transformation of rigid vertex data. This technique is beneficial when vertex transformation is of notable cost, such as in software rendering systems and applications and where visual correctness is sufficient, for example games, simulators, and other real-time applications. In practice, linear grouping (nearly visually lossless) eliminates approximately 55% of the vertices in an average polygonal mesh, reducing transform overhead by about 50% and clipping overhead by about 32%.