An efficient 3-D visualization technique for finite element models and other coarse volumes

We have developed a technique that extends existing 3-D result visualization methods for use with discretized volumes such as finite element models, where result values are only available at coarsely spaced points throughout the volume. It represents results as smooth isosurfaces within the volume for one or more result values, using visually continuous, bi-cubic polynomials.At each of the points where results are available, result gradients are calculated by a finite difference procedure. The result values and result gradients are used to obtain the location of and the tangents to the isosurfaces on lines connecting the result points. Continuous doubly curved surfaces and surface normals are constructed separately between these discrete isosurface points using bi-cubic polynomials. The isosurfaces are rendered with standard light-source shading and optional levels of translucency, surrounded by translucent free faces of the structure.The method generates isosurfaces on an element-by-element basis, without reference at display time to the behavior of neighboring elements. It is intended for high speed display-time processing of either static or varying isosurface values.