Author(s)

Yukun Liu¹, Yong Yue², Dongwen Zhang¹, Chunhua Li¹

¹School of Information Science and Engineering, Hebei University of Science and Technology, Shijiazhuang, China.
²Department of Computer Science and Software Engineering, Xi’an Jiaotong-Liverpool University, Suzhou, China.

This paper presents a new scheme of flaw searching in surface modeling based on Euler Characteristic. This scheme can be applied to surface construction or reconstruction in computer. It is referred to as Euler Accompanying Test (EAT) algorithm in this paper. Two propositions in algebraic topology are presented, which are the foundation of the EAT algorithm. As the modeling is the first step for rendering in the animation and visualization, or computer-aided design (CAD) in related applications, the flaws can bring some serious problems in the final image or product, such as an artificial sense in animation rendering or a mistaken product in industry. To verify the EAT progressive procedure, a three-dimensional (3D) stamp model is constructed. The modeling process is accompanied by the EAT procedure. The EAT scheme is verified as the flaws in the stamp model are found and modified.

Algebraic Topology, Euler Characteristic, Flaw Searching, Surface Modeling, Topologic Consistence

Liu, Y. , Yue, Y. , Zhang, D. and Li, C. (2020) Euler Characteristic Scheme of Globally Searching for Flaws in Surface Modeling. Advances in Pure Mathematics, 10, 57-85. doi: 10.4236/apm.2020.102005.