Computer Modeling of Surfaces with Arbitrary Shapes

Abstract

This article describes in detail a local mathematical procedure for constructing a geometrically C1 surface by interpolating a grid of cubic Bezier curves that meet in a quite general fashion (for example, they need not meet rectangularly). The constructed surface is a composite mosaic of independently parameterized tensor-product Bezier patches of different degrees (maximum of 6 + 6). Adjacent patches can be made either C1 or C0 continuous, as desired. The overall surface can have almost any shape that arises in practice, including the closed surfaces used in solid modeling. Because of its locality, the procedure can be applied at different times in different locations of a surface-to-be; for example, it can be used to combine preexisting smaller surfaces. © 1990 IEEE