Polishing Vertex with Rational Triangular Bézier Surface

The joining vertexes between three or several adjacent surfaces are generally required to be polished smoothly to express a whole surface in multi-surfaces geometric modeling. This paper proposed a new method of polishing the vertexes with the rational triangular Bezier surface in G¹ continuous conditions The method of polishing triangular Bezier surface are conducted from the share common plane judgment condition which is based on the general necessary and sufficient G^k continuous connection condition in the geometric continuity theory. By the share common plane condition, the second layer control points of triangular Bezier are calculated with a simple algorithm to keep the generated polishing triangular Bezier surface connected with adjacent surfaces in G¹ continuity. The numerical experimental result shows that the method is reliable and meets the requirements of vertexes polishing in surface modeling and processing. The method can be directly applied to the higher order geometric continuous connection in polishing the joining vertexes