Internet-Based Visualization of Basin Boundaries for Three-Dimensional Dynamical Systems
Bernd Wallisch · 2000
One a pplication of surface-oriented visualization of volume data is the c onstruction of surfaces between two different regions of the volume (e.g. iso-surfaces). For some a pplications, a binary subdivision of the volume is not sufficient, for instance for the representation of basin boundaries in the phase space of dynamical systems. Basins describe regions with the same long-time behaviour. An extension of the known Marching Cubes algorithm is introduced, which works both with binary and g enerally classified (at least t hree different classifications within a cell) data sets. For faster surface c onstruction the original look-up table of the Marching Cubes algorithm is used. The algorithm supports both progressive refinement of surfaces by binary subdivision of data cells and smooth transitions between models, which are differently refined. The adaptive subdivision depends on the local properties of the surface. Binary subdivision for refinement of regions leads to a coarse representation of the surface, therefore the vertices of the triangles are relocated after the surface construction depending on the classifications of adjacent cells, in order to smooth the surface.