Anisotropic nonlinear diffusion in flow visualization

Many applications produce three-dimensional points that must be further processed to generate a surface. Surface reconstruction algorithms that start with a set of unorganized points are extremely time-consuming. Sometimes, however, points are generated such that there is additional information available to the reconstruction algorithm. We present Spiraling Edge, a specialized algorithm for surface reconstruction that is three orders of magnitude faster than algorithms for the general case. In addition to sample point locations, our algorithm starts with normal information and knowledge of each point's neighbors. Our algorithm produces a localized approximation to the surface by creating a star-shaped triangulation between a point and a subset of its nearest neighbors. This surface patch is extended by locally triangulating each of the points along the edge of the patch. As each edge point is triangulated, it is removed from the edge and new edge points along the patch's edge are inserted in its place. The updated edge spirals out over the surface until the edge encounters a surface boundary and stops growing in that direction, or until the edge reduces to a small hole that is filled by the final triangle.