A design scheme using coons surfaces with nonuniform basis B-spline curves

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A design scheme using coons surfaces with nonuniform basis B-spline curves

Knapp, L.C.

A computer based system for design of physical objects must be able to represent objects in siffucient richness and detail that a designer may benefit by becoming fluent in its use. Mathematically based forms of surface description and their implementation on a computer show promise as a means of representing 'free form' or 'sculptured' surfaces with greater accuracy than with conventional drafting techniques. This dissertation develops several such mathematical forms and investigates their suitability as tools for CAD. The recent application of B-spline approximation as a basis for representation of curves and surfaces is developed to include a form of curve representation which uses a non-uniform basis B-spline curve. This form has properties which are conducive to providing a stable designer interface. Several surface definition methods are surveyed, including some based on restricted forms of the Coons surface (the bicubic and biquintic surface patches). The general Coons surface is a surface defined by boundary conditions of very general form. A Coons surface defined by boundary conditions represented by nonuniform basis B-splines is described. (DePo)