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Isosurfaces are an appropriate approach to visualize scalar fields or the absolute value of vector fields in three dimensions. The nodes of the corresponding isosurface mesh are determined using an efficient and accurate isovalue search method. Then, these nodes are typically connected by triangular elements, which are obtained with the help of an adapted advancing front algorithm. An important prerequisite of an isovalue search method is that volume data of the examined field is available in total space. That means, the field values are precomputed in the nodes of an auxiliary post-processing volume mesh or a novel meshfree method is developed that enables both efficient computations of field values in arbitrary points and fast determination of domains with a defined range of field values. If the first approach is applied, a classical isovalue search method is to use an octree scheme to find relevant volume elements, which are intersected by the isosurface. Finally, the surface elements of the isosurface are constructed based on the intersection points of the isosurface with the volume elements. In that case, the accuracy and the computational costs are mainly influenced by the density of the post-processing volume mesh. In contrast, an innovative coupling of established isovalue search methods, fast boundary element method (BEM) techniques, and advancing front meshing algorithms is here presented to compute isosurfaces with high accuracy only using the original BEM model. This novel meshfree method enables very accurate isovalue search methods along with nearly arbitrarily adjustable resolution of the computed isosurface. Furthermore, refinements of the isosurface are also possible, for instance in dependency of the current viewing position. The main idea to realize this meshfree method is to directly combine an octree-based isovalue search method with the octree-based fast multipole method (FMM).

A meshfree isosurface computation method for boundary element methods