Hybrid Polygon-Point Rendering of Singular and Non-Manifold Implicit Surfaces

A hybrid polygons-points algorithm based on a hierarchical decomposition of the bounding volume using an octree spatial data structure, and testing cell occupation with interval arithmetic is given. Polygons are produced where curvature in occupied cells is low and points are used where curvature is high. As a result, points are rendered around extreme features and polygons around regular features. Using this approach implicit surfaces of high complexity, such as recursively defined curvature surfaces, are rendered. A discussion of the implementation is given for a GPU version of the algorithm and a comparison with GPU ray-casting is made. As the approach uses subdivision and it can be used for surface modelling. An advantage of the approach is the few artefacts that occur with singular points, cusps, rays and curves of self intersection. Production of antialiased animations and multiple views of the surface can be faster than in ray-casting. The algorithm is robust, renders singular and non-manifold surface and the algorithm works for algebraic and non-algebraic surfaces.