Methods for implicit surfaces polygonization: technical report no. DCSE/TR-2003-01

Both object modeling and visualization belong to the fundamental tasks of the computer graphics. In recent years, implicit modeling has become attractive. Because of the fact that the implicit surfaces conveniently define volumes, they are frequently used in CSG-based solid modelers. The visualization of objects defined in such way is possible either by direct rendering based on Ray-tracing principle or by approximation of the implicit models by polygons, triangular mesh usually. Such approximation process is called polygonization. The polygonal (triangular) meshes are supported by a wide range of graphics hardware and, therefore, working with them is very fast as well as their arbitrarily transformations are possible without repeated solution of the implicit function. Programs for 3D graphics support polygonal meshes as well. It is not complicated to import such object and also its additional modification is possible with these professional tools. The offered work contains an overview of commonly used principles for polygonization of implicit objects as well as information about our previous research in this field. Advantages and disadvantages of presented algorithms are discussed. The outlook of our future work is presented in conclusion