Issue No. 06 - November/December (2007 vol. 13)
Miriah Meyer , IEEE
Robert M. Kirby , IEEE
Ross Whitaker , IEEE
This paper describes a method for constructing isosurface triangulations of sampled, volumetric, three-dimensional scalar fields. The resulting meshes consist of triangles that are of consistently high quality, making them well suited for accurate interpolation of scalar and vector-valued quantities, as required for numerous applications in visualization and numerical simulation. The proposed method does not rely on a local construction or adjustment of triangles as is done, for instance, in advancing wavefront or adaptive refinement methods. Instead, a system of dynamic particles optimally samples an implicit function such that the particles' relative positions can produce a topologically correct Delaunay triangulation. Thus, the proposed method relies on a global placement of triangle vertices. The main contributions of the paper are the integration of dynamic particles systems with surface sampling theory and PDE-based methods for controlling the local variability of particle densities, as well as detailing a practical method that accommodates Delaunay sampling requirements to generate sparse sets of points for the production of high-quality tessellations.
Isosurface extraction, particle systems, Delaunay triangulation.
M. Meyer, R. Whitaker and R. M. Kirby, "Topology, Accuracy, and Quality of Isosurface Meshes Using Dynamic Particles," in IEEE Transactions on Visualization & Computer Graphics, vol. 13, no. , pp. 1704-1711, 2007.