Interpolation-Induced Numerical Uncertainties in Curvilinear Grid-Based Visualization

摘要

Bilinear and trilinear interpolations are two of the most popular techniques for interpolating scientific data specified on a curvilinear grid in two and three dimensions respectively. These interpolation techniques result in a system of nonlinear equations. Iterative numerical solution is a standard technique used in visualization softwares to solve this system of non-linear equations. In this work, we utilize resultant methods to compute these interpolants using a direct non-iterative procedure. The two techniques are contrasted by presenting examples of interpolation in concave cells. Errors resulting from bilinear and trilinear interpolation schemes have important implications for visualizing uncertainty in scientific data prescribed on curvilinear grids.