期刊
GRAPHICAL MODELS
卷 82, 期 -, 页码 1-12出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.gmod.2015.09.004
关键词
3D MAT; Moving frame; Differential form; Invariants; Moulding surfaces
资金
- National Natural Science Foundation of China [61502148, 51175065]
This paper investigates the differential geometry of 3D MAT (medial axis transform) using the moving frame and differential form. After constructing the mapping relation and moving frames around both the MA (medial axis) point and the associated boundary points, various curves are defined to serve as carriers for the study. Based on analysis of the infinitesimal translation and rotation of the moving frames, the relations of distance differentials, rotation vectors and differential invariants are derived. Furthermore, a special case in the 3D MAT, the normal form, is defined for the moulding surfaces, where the 3D problem can be converted into a 2D one. (C) 2015 Elsevier Inc. All rights reserved.
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