Visualizing Flow Over Parametric Surfaces Using Line Integral Convolution

Line Integral Convolution (LIC) is a powerful technique for imaging and animating vector fields. We extend the LIC paradigm in three ways: (1) The existing technique is limited to vector fields over a regular Cartesian grid. We extend it to vector fields over parametric surfaces, such as those found in curvilinear grids, used in computational fluid dynamics simulations; (2) Periodic motion filters can be used to animate the flow visualization. When the flow lies on a parametric surface, however, the motion appears misleading. We explain why this problem arises and show how to adjust the LIC algorithm to handle it; (3) We introduce a technique to visualize vector magnitudes as well as vector direction. Cabral and Leedom have suggested a method for variable-speed animation, which is based on varying the frequency of the filter function. We develop a different technique based on kernel phase shifts which we have found to show substantially better results. Our implementation of these algorithms utilizes texture-mapping hardware to run in real time, which allows them to be included in interactive applications.