Special Issue on The First Korea-UK Workshop on Geometric Modeling and Computer Graphics; Guest Editors: M.-S. Kim & R. MartinNo Access

POINT-SETS AND CELL STRUCTURES RELEVANT TO COMPUTER AIDED DESIGN

A. E. MIDDLEDITCH

Centre for Geometric Modelling and Design, Brunei University, Kingston Lane, Uxbridge, Middlesex, UB10 3PH, UK

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C. M. P. READE

School of Business Information Management, Kingston University, Kingston Hill, Kingston, Surrey KT2 7LB, UK

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, and

A. J. GOMES

Centre for Geometric Modelling and Design, Brunei University, Kingston Lane, Uxbridge, Middlesex, UB10 3PH, UK

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https://doi.org/10.1142/S0218654300000132Cited by:6 (Source: Crossref)

Abstract

Several fields of mathematics are relevant to computer aided design and other software systems involving solid object geometry, topology, differential and algebraic geometry being particularly important. This paper discusses some of this mathematics in order to provide a theoretical foundation for geometric modelling kernels that support non-manifold objects with an internal cellular structure and subsets of different dimensions.

The paper shows relationships between relevant concepts from topology, differential geometry and computer aided geometric design that are not widely known in the CAD community. It also discusses semialgebraic, semianalytic and subanalytic sets as candidates for object representation. Stratifications of such sets are proposed for an object's cellular structure and new stratification concepts are introduced to support candidate applications.

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