A GEOMETRIC METHOD TO CONSTRUCT SMOOTH CONNECTING SURFACES FOR POLYHEDRON CORNER RENDERING

摘要

In CAD/CAM and surface modeling, it is an essential and important function to build the smooth connecting surface for the polyhedron vertex and edge rendering. The general method for polishing the polyhedron vertex and edges with the spherical and cylindrical surfaces do not possess the continuity of geometry. While the algorithm for constructing connection surface with high order geometric continuity is very complicated, this paper proposed a new geometric method to construct the smooth connecting surfaces for the polyhedron corner rendering with high order geometry continuity. The proposed method is based on the principle of the theory of geometry continuity. Through a simple geometry drawing algorithm, we constructed the smooth connection surfaces with high order geometry continuity with their neighboring surfaces. The algorithm does not need complex computation. The method can be popularized to the situation of the higher order geometry continuity connection. The results show that the generated surfaces can polish and render the polyhedron corners with good geometry property. The method can be applied to CAD/CAM system directly.