FILLING HOLES WITH PIECEWISE ALGEBRAIC SURFACES

Abstract

To construct a smooth transition surface for mending holes intersected by given surfaces is called lling holes Filling holes widely appears in mechanical design geometrical modeling computer graphics and animation Implicit algebraic surfaces play an important role in such area Early in G lling holes was drawn out Coons surface mends four side hole formed of two pairs of B ezier curves Filling n side polygonal holes with smooth parametric surfaces get much research in these years Gregory et al gave a tutorial report on bicubic method and some further research was proposed in later years While few reseach on lling holes with algebraic surfaces was done Sederberg used algebraic surfaces to C interpolate points and curves and Bajaj extended the result to C continuity In blending corner of table Bajaj smoothed out the three edges with three quadratic surfaces and formed a side hole then he construct a quintic surfaces to mend the hole However algebraic surfaces generally have multiple sheets and singular ities especially when the degree of the surface is relatively high Therefore many researchers suggest to use low degree algebraic surfaces We made our rst attempt to tangentially blend three cylinders using piecewise algebraic surface The results show one of the most important advantages of blend ing algebraic surfaces with piecewise algebraic surfaces the degree of the piecewise algebraic blending surface is relatively low compared with a single algebraic blending surface In this paper we use piecewise algebraic surfaces instead of a single surface for lling holes ought to decrease the degree of blending surfaces x gives some preliminary knowledges about geometric continuity of algebraic surfaces and the geometric continuity conditions for several algebraic surface patches meeting at a common vertex x presents a general algorithm of lling holes