Fast contouring of solutions to partial differential equations

The application of Differential Equation Interpolants (DEI) to the visualization of the solutions to Partial Differential Equations (PDE) 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(fm2) (where fm is the refinement requested). Finally, three fast contouring algorithms are proposed which compute accurate contour lines directly from the DEI, and have time complexity at most O(fm).