Solid Modeling by Computers pp 211-236 | Cite as

# Design Methods of Free-Form Surfaces and their Integration into the Solid Modeling Package GEOMAP-III

## Abstract

Two powerful methods are shown for the construction of complex solid shapes with free-form surfaces: local modification operations for constructing rough shapes and their smoothing, and complete set operations among curved objects. For actually realizing these methods, it is necessary to develop a basic theory for treating problems which cannot be solved thoroughly by the conventional theories, such as smooth connection of surface patches under various restrictive conditions, and generation of irregular (nonrectangular) surface patches. Some theoretical results are described which are based on the control point approach of Bezier and which are useful for these problems. The two methods are integrated into our comprehensive solid modeling package GEOMAP-III which is soon to be operational and which will serve as a basis for sophisticated shape design and integrated CAD/CAM systems.

## Keywords

Control Point Surface Patch Bezier Curve IEEE Computer Graphic Bezier Surface## Preview

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