Construction of blend surfaces in surface modelling

Abstract

Blending is one of very important issues in geometric modelling. Developed in this thesis are algorithms for constructing edge and corner blend surfaces among rectangular parametric surface patches. A blend surface connects base surfaces with position and gradient continuity. Any rectangular parametric surface patches can be blended as long as their offset surfaces (with offset distance equal to the blending radius) are smooth so that intersections between offset surfaces can be well defined. Two types of edge blends are considered. One is the constant radius edge blend, the other is the variable radius edge blend. The first may be regarded as a special case of the second. The edge blends are constructed mathematically be sweeping a rational quadratic curve along an offset surface intersection curve. Corner blend is divided into C-type (convex combination type) and E-type (edge blending type). The C-type corner blend is represented by a convex combination of linear Taylor interpolants defined on edge blends and it may have more than three edge boundaries having different radius values. On the other hand, the E-type corner blend is obtained by applying the edge blending method on edge blend surfaces. The fullness of edge and corner blends can be easily be controlled. Many examples are provided in order to illustrate the blend surfaces.