Visualization of implicit surfaces

We discuss the polygonization and rendering of implicit surfaces through the adaptive subdivision of octree nodes. Three new algorithms which form part of this process, are discussed. The first algorithm removes the cracks that form on the surfaces between adjacent nodes that are subdivided to different depths in the octree. This algorithm fixes the cracks for arbitrary differences in depth between the adjacent nodes. The second algorithm allows user specified selected polygon outlines to be drawn on the surfaces, instead of drawing all the outlines, or no outlines. The third algorithm fixes 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