Patch Interpolation Using Edge-based Blending Function

Abstract

By introducing the edge-based blending function derived from the surface-based one, we can capture the effects of the edges on the shape of the n-sided patch more directly. Because of the good natures of the edge-based blending function, the designers can manipulate it as well as the geometry of the boundary curves to design and modify the patch shape. In this paper, we have discussed the derivation of the edge-based blending function, its properties, especially the differences between ones for odd-sided and for even-sided patches, and easiness of designing it by the users. We have demonstrated its validty by showing several triangular, rectangular, and pentagonal patchs using the modifiable blending functions. 1. Introduction The need for the surface representation scheme to cover n-sided faces was pointed out during the first half of 1980's by several pioneers, for example, Gregory 3 , Sabin 6 , and Hosaka and Kimura 5 . Recent researches done by Loop and DeRose, Grim and Hug..