Point based rendering of non manifold surfaces

We are concerned with producing high quality images of parametric and implicit surfaces, in particular those with non-manifold features. We present a point based technique for rendering implicit surfaces that uses octree spatial subdivision with a natural interval exclusion test that guarantees that no parts of the surface are missed. This allows us to render non-manifold implicit surfaces at speeds comparable to parametric surfaces. We also derive criteria that guarantee complete pixel coverage of the surface. The point based method allows for hidden surface elimination using a z-buffer, and shadow casting using a shadow buffer. We illustrate the techniques with a number of surfaces, and discuss their advantages and disadvantages.