Point rendering of non-manifold surfaces with features

We are concerned with producing high quality images of implicit surfaces, in particular those with non-manifold features. In this work we present a point based technique that improves the rendering of non-manifold implicit surfaces by using point and gradient information to prune plotting nodes resulting from using octree spatial subdivision based on the natural interval extension of the surface’s function. The use of intervals guarantees that no parts of the surfaces are missed in the view volume and the combination of point and gradient sampling preserves this feature while greatly enhacing the quality of point based rendering of implicit surfaces. We also sucessfully render non-manifold features of implicit surfaces such as rays and thin sections. We illustrate the technique with a number of example surfaces.