
Journal for Geometry and Graphics 26 (2022), No. 1, 101114 Copyright Heldermann Verlag 2022 Shape Computing: A New Geometric Computing Mechanism Yuanjun He Shanghai Jiao Tong University, Shanghai, China yjhe@sjtu.edu.cn Haiyan Yu Donghua University, Shanghai, China yuhy@dhu.edu.cn Hongming Cai Shanghai Jiao Tong University, Shanghai, China hmcai@sjtu.edu.cn Zhenghong Peng Wuhan University, Wuhan, Hubei, China laopeng129@vip.sina.com Wei Liu Shanghai Jiao Tong University, Shanghai, China liuwei@sjtu.edu.cn Zhiping Hu Shanghai Customs College, Shanghai, China zhiping_hu@163.com 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 multidimensional spaces of “threedimensional conceptual thinking, twodimensional graphic construction, onedimensional 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 [ Fulltextpdf (1642 KB)] 