Scale-aware shape manipulation

A novel representation of a triangular mesh surface using a set of scale-inva~iant measures is proposed. The measures consist of angles of the triangles （triangle angles） and dihedral angles along the edges （edge angles） which are scale and rigidity independent. The vertex coordinates for a mesh giv...

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Bibliographic Details
Published in:Frontiers of information technology & electronic engineering 2014-09, Vol.15 (9), p.764-775
Main Authors: Liu, Zheng, Wang, Wei-ming, Liu, Xiu-ping, Liu, Li-gang
Format: Article
Language:English
Subjects:
Algorithms
Angles (geometry)
Communications Engineering
Computer Hardware
Computer Science
Computer Systems Organization and Communication Networks
Electrical Engineering
Electronics and Microelectronics
Graph theory
Instrumentation
Invariants
Networks
Representations
Rotation
Shearing
Triangles
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Summary:A novel representation of a triangular mesh surface using a set of scale-inva~iant measures is proposed. The measures consist of angles of the triangles （triangle angles） and dihedral angles along the edges （edge angles） which are scale and rigidity independent. The vertex coordinates for a mesh give its scale-invariant measures, unique up to scale, rotation, and translation. Based on the representation of mesh using scale-invariant measures, a two-step iterative deformation algorithm is proposed, which can arbitrarily edit the mesh through simple handles interaction. The algorithm can explicitly preserve the local geometric details as much as possible in different scales even under severe editing operations including rotation, scaling, and shearing. The efficiency and robustness of the proposed algorithm are demonstrated by examples.
ISSN:1869-1951
2095-9184
1869-196X
2095-9230
DOI:10.1631/jzus.C1400122