**Compression of Dense and Regular Point Clouds**

We present a simple technique for single-rate compression of point clouds sampled from a surface, based on a spanning tree of the points. Unlike previous methods, we predict future vertices using both a linear predictor, which uses the previous edge as a predictor for the current edge, and lateral predictors that rotate the previous edge 90 degrees left or right about an estimated normal. By careful construction of the spanning tree and choice of prediction rules, our method improves upon existing compression rates when applied to regularly sampled point sets, such as those produced by laser range scanning or uniform tesselation of higherorder surfaces. For less regular sets of points, the compression rate is still generally within 1.5 bits per point of other compression algorithms.