Abstract
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.
Highlights
Along with the development of surface construction and reconstruction, many researchers have realized that mesh models may be constructed initially with some flaws because of the complex geometrical and topological structures of surfaces, and the limitations of scanning technologies and modeling schemes [1]-[10]
This paper presents a new scheme of flaw searching in surface modeling based on Euler Characteristic
Two propositions in algebraic topology are presented, which are the foundation of the Euler Accompanying Test (EAT) algorithm
Summary
Along with the development of surface construction and reconstruction, many researchers have realized that mesh models may be constructed initially with some flaws because of the complex geometrical and topological structures of surfaces, and the limitations of scanning technologies and modeling schemes [1]-[10]. Be seen when the character raises the right arm Another example is a case in fashion design, in which two adjoining cloth patches are not defined to fit together mistakenly. This paper presents a new scheme to globally search a mesh model for and locate the flaws. The first reason is that it is more efficient and tractable to search for, locate and correct a flaw during modeling than post-processing after the whole mesh model has been constructed. It is why the new scheme is named Euler. The rest of this paper is arranged as follows: Section 2 introduces related studies; Section 3 details the EAT algorithm and the related propositions; Section 4 presents the searching cases of EAT on the PAMA stamp model; Section 5 is for the final conclusions
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