Adaptive polygonisation of non-manifold implicit surfaces

We discuss the polygonisation and rendering of non-manifold implicit surfaces using adaptive octree subdivision and interval arithmetic for surface exclusion in octree nodes. We present a new algorithm that polygonises some surfaces that self intersect, or have other non-manifold features such as separate sections that meet at points. Gradient information is used to resolve ambiguous polygonisations in plotting nodes. A line-stitching algorithm is discussed that allows for multiple polygons to be in a plotting node. We illustrate the algorithm with a number of surfaces that demonstrate its capabilities and limitations.