Anisotropic diffusion in vector field visualization on Euclideandomains and surfaces

摘要

Vector field visualization is an important topic in scientificnvisualization. Its aim is to graphically represent field data on two andnthree-dimensional domains and on surfaces in an intuitivelynunderstandable way. Here, a new approach based on anisotropic nonlinearndiffusion is introduced. It enables an easy perception of vector fieldndata and serves as an appropriate scale space method for thenvisualization of complicated flow pattern. The approach is closelynrelated to nonlinear diffusion methods in image analysis where imagesnare smoothed while still retaining and enhancing edges. Here, an initialnnoisy image intensity is smoothed along integral lines, whereas thenimage is sharpened in the orthogonal direction. The method is based on ancontinuous model and requires the solution of a parabolic PDE problem.nIt is discretized only in the final implementational step. Therefore,nmany important qualitative aspects can already be discussed on ancontinuous level. Applications are shown for flow fields in 2D and 3D,nas well as for principal directions of curvature on general triangulatednsurfaces. Furthermore, the provisions for flow segmentation are outlined