Point hierarchies are suitable for creating frame-coherent animations of 3D models in non-photorealistic styles such as stippling, painterly and other artistic rendering. In this paper, we present a new approach to produce regular point distributions on the surface of a polygonal mesh. We propose a graph-based token distribution approach, where a graph that extends over the surface of the polygonal model is used as the playing field for the distribution of points. This graph-based approach eliminates the need of using geometrical operations to distribute points over the surface of a polygonal mesh. The graph exists at several levels of detail that are easily created using iterative patch fusion, and which are used to create a point hierarchy. In addition, we show how 3D stippling is used to render transparent surfaces and illustrate complex animations.