A triangulation method of an arbitrary point set for biomagnetic problems

A new triangulation method has been developed for extracting isosurface from volume data. The nodes for triangulation can be selected arbitrarily from the surface of the object of interest. The Voronoi polygons for nodes are searched on the surface and triangulation is accomplished by connecting the neighboring Voronoi areas. The method is basically Delaunay triangulation using geodesic distances instead of Euclidean ones. In areas where the curvature of the surface is low, the Delaunay criteria are fulfilled. When the curvature is high, the geometry of the object is described more accurately than in Euclidean Delaunay methods. Since geodesic distances are utilized, i.e., the surface information is used in triangulation, the topology of the object can be preserved more easily than in the Euclidean cases. Our fully automatic method has been developed for boundary element modeling and it has been successfully applied in magnetocardiographic and electrocardiographic forward and inverse studies. However, the method can be utilized in any triangulation problem if the surface description is provided.