Visualisation of implicit surfaces

We discuss the polygonisation and rendering of implicit surfaces through the adaptive subdivision of octree nodes. Three new algorithms which form part of this process, are discussed. The "rst algorithm removes the cracks that form on the surfaces between adjacent nodes that are subdivided to di!erent depths in the octree. This algorithm "xes the cracks for arbitrary di!erences in depth between the adjacent nodes. The second algorithm allows user speci"ed selected polygon outlines to be drawn on the surfaces, instead of drawing all the outlines, or no outlines. The third algorithm "xes the gaps that can appear in the polygon outlines when only selected outlines are drawn. We also investigated the use of an exact calculation of the curvature of the implicit surfaces to drive the adaptive subdivision. We conclude that this is not worthwhile doing, and give reasons.