Blending Of Convex N-hedral Angles Based On B-net Method

Blending of implicit algebraic surface is an important issue in Computer Aided Design.We introduce an approach to blend convex n-hedral angles based on B-net mothed with quardric algebraic spline and order one continuity.It is practical and convenient,and provides n+1 parameters to control the blending region separately.Based on the potential method,this paper introduces an approach to blend a combination of n surfaces with order one contiunuity.Also n+1 parameters are presented to control the blending region separately.The thesis is organized as follows.In chapter 1,some existing methods of constructing blending surfaces are reviewed, especially some approaches using algebraic splines.In chapter 2,some preliminary knowledge about the B-net method,mutivariate splines and geometric continuity is provided.In chapter 3,quadric algebraic splines of blending convex comers with order one continuity are constructed,which are based on the B-net method and the refinement of Morgan-Scott partition.N+1 parameters are provided to control the blending region separately.Examples of blending are alse provided in this chapter.In chapter 4,combining the potential method and the method provided in chapter 3.this paper introduces a method to blend a combination of n surfaces with order one contiunuity. Also,n+1 parameters are provided to control the blending region separately and examples of blending are provided in the end of this chapter.