Visualisation of non-manifold implicit surfaces

This thesis addresses several visualisation problems for non-manifold and singular implicit algebraic surfaces and proposes algorithms for fast and correct rendering of many such surfaces. It is well known that non-manifold surfaces are particularly difficult to render and hence these algorithms provide interesting perspectives in rendering these surfaces. A main contribution is a GPU algorithm for point-based rendering of implicit surfaces. This algorithm is based on a hierarchical decomposition of the bounding volume using an octree spatial data structure and testing the occupied cells of the octree through interval arithmetic. Previous work had difficulty in rendering the non-manifold and singular features. The work also presents point-based anti-aliasing of silhouette and contour edges. The second contribution is a GPU hybrid polygon and point-based rendering algorithm. Previous work using polygons alone could not represent the non-manifold and singular features. The third contribution is an algorithm for visualisation of curvature surfaces of implicit surfaces. A robust visualisation of curvature surfaces is presented here for the first time. A DVD is enclosed showing animations created using the discussed methods. Even though Computer Aided geometric Design (CAD) uses predominately parametric surfaces, implicit surfaces are also used in this area as blending and offset surfaces in CAD are often implicit surfaces. Curvature analysis is also used extensively in the aeronautical and automotive manufacturing industries.