Fast contouring of solutions to partial differential equations
The application of Differential Equation Interpolants (DEIs) to the visualization of the solutions to Partial Differential Equations (PDEs) is investigated. In particular, we describe how a DEI can be used to generate a fine mesh approximation from a coarse mesh approximation; this fine mesh approximation can then be used by a standard contouring function to render an accurate contour plot of the surface. However, the standard approach has a time complexity equivalent to that of rendering a surface plot, O(fm(2)) for each element of the coarse mesh, (where fm is the ratio of the width of the coarse mesh to the fine mesh). To address this concern three fast contouring algorithms are proposed that compute accurate contour lines directly from the DEI, and have time complexity at most O(fm) for each coarse mesh element.
contour interpolation visualization pdes rendering algorithms performance