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Journal for Geometry and Graphics 26 (2022), No. 1, 101--114
Copyright Heldermann Verlag 2022

Shape Computing: A New Geometric Computing Mechanism

Yuanjun He
Shanghai Jiao Tong University, Shanghai, China

Haiyan Yu
Donghua University, Shanghai, China

Hongming Cai
Shanghai Jiao Tong University, Shanghai, China

Zhenghong Peng
Wuhan University, Wuhan, Hubei, China

Wei Liu
Shanghai Jiao Tong University, Shanghai, China

Zhiping Hu
Shanghai Customs College, Shanghai, China

Graph/image has become an important computing source, object and representing result, and it is also pursued as a representing form for the solution. The processing work of graph/image is mainly geometric computing. A geometrized computing mechanism named “Shape Computing” is proposed. It considers the representation of shape and the generation of graph more from the perspective of geometry itself, which is more conducive to the processing of geometric relations. Hence the algorithm framework can be built from a more macroscopic view, and the computing process is more structured, intuitive and simplified. The general ideas and main strategies of this mechanism are expounded, the framework and implementing strategies are then constructed, application examples along with comparative analysis of computing performance are also given. Compared with current “numeric computing”, Shape Computing is better designed for the fusion of multi-dimensional spaces of “three-dimensional conceptual thinking, two-dimensional graphic construction, one-dimensional numerical calculation”. Theoretical analysis and application examples demonstrate that the proposed Shape Computing contributes to improve the readability, to reduce computational complexity, and to deal with computing robustness.

Keywords: Shape computing, geometry, geometric computing, algebraic computing, graphic construction.

MSC: 68U05

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