Space Subdivision for Fast Polygonization of Implicit Surfaces

Abstract

This paper presents the basic principles for the visualization of objects which are defined by implicit functions and CSG trees. The basic principles (Marching cubes, Marching tetrahedra and Marching triangles) for iso-surfaces rendering of such objects are compared. A new fast modification of the Marching triangles algorithm is presented and compared with others algorithms. It is based on the space subdivision technique that enabled a significant speed-up of the Marching triangles algorithm. The speed-up grows with the grid resolution in which the object is represented. The presented algorithm is convenient for objects with large smooth and complex surfaces. The method produces a triangular mesh that consists of well-shaped triangles.