Constant-ratio blended models of curves and surfaces in euclidean 3-space

Abstract

We consider a simple blending method for parametric curves and surfaces. The described blending method offers a systematic approach to creating smooth transitions between parametric curves and surfaces while maintaining Cn-continuity. It utilizes the parametrizations of the original objects to achieve predictable variations in shape and enables the generation of families of blending curves and surfaces with controlled characteristics. Therefore, considering the blending of the curves/surfaces to be constant-ratio objects, some results on the blending functions are obtained.