Summary: We introduce planar grouping, a technique where planar relationship information is gathered for a set of rigid points. This information is used to accelerate affine transformations and clipping. The planar grouping technique is an optimization problem, implemented in a best-first greedy search. We present two error metrics, one simple and fast, one based on the quadric error metric (QEM) to achieve higher quality planar grouping. We also apply the quadric error metric to linear grouping.