Multi-resolution hierarchies of polygons and more recently of points are familiar and useful tools for achieving interactive rendering rates. We present an algorithm for tightly integrating the two into a single hierarchical data structure. The trade-off between rendering portions of a model with points or with polygons is made automatically. Our approach to this problem is to apply a bottom-up simplification process involving not only polygon simplification operations, but point replacement and point simplification operations as well. Given one or more surface meshes, our algorithm produces a hybrid hierarchy comprising both polygon and point primitives. This hierarchy may be optimized according to the relative performance characteristics of these primitive types on the intended rendering platform. We also provide a range of aggressiveness for performing point replacement operations. The most conservative approach produces a hierarchy that is better than a purely polygonal hierarchy in some places, and roughly equal in others, A less conservative approach can trade reduced complexity at the far viewing ranges for some increased complexity at the near viewing ranges. We demonstrate our approach on a number of input models, achieving primitive counts that are 1.3 to 4.7 times smaller than those of triangle-only simplification.
