Efficient contouring on unstructured meshes for partial differential equations
We introduce three fast contouring algorithms for visualizing the solution of partial differential equations based on the PCI (pure cubic interpolant). The PCI is a particular piecewise bicubic polynomial interpolant defined over an unstructured mesh. Unlike standard contouring approaches, our contouring algorithms do not need a fine-structured approximation and work efficiently with the original scattered data. The basic idea is to first identify the intersection points between contour curves and the sides of each triangle and then draw smooth contour curves connecting these points. We compare these contouring algorithms with the built-in Matlab contour procedure and other contouring algorithms. We demonstrate that our algorithms are both more accurate and faster than the others.
contour unstructured mesh algorithms visualization scattered data performance pde