Visualizing flow over curvilinear grid surfaces using line integral convolution

Line integral convolution (LIC), introduced by B. Cabral and C. Leedom (1993), is a powerful technique for imaging and animating vector fields. We extend the LIC paradigm in three ways: the existing technique is limited to vector fields over a regular Cartesian grid and we extend it to vector fields over parametric surfaces, specifically those found in curvilinear grids, used in computational fluid dynamics simulations; periodic motion filters can be used to animate the flow visualization, but when the flow lies on a parametric surface, the motion appears misleading, and we explain why this problem arises and show how to adjust the LIC algorithm to handle it; we introduce a technique to visualize vector magnitude as well as vector direction, which is based on varying the frequency of the filter function and we develop a different technique based on kernel phase shifts which we have found to show substantially better results. Implementation of these algorithms utilizes texture-mapping hardware to run in real time, which allows them to be included in interactive applications