Fast Contouring of Solutions to

The application of Diierential Equation Interpolants (DEIs) to the visualization of the solutions to Partial Diierential Equations (PDEs) is investigated. In particular, we describe how a DEI can be used to generate a ne mesh approximation from a coarse mesh approximation; this ne 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 ne mesh). To address this concern three fast contouring algorithms are proposed which compute accurate contour lines directly from the DEI, and have time complexity at most O(fm) for each coarse mesh element.