Topological graph theory
Introduction to Solid Modeling
Introduction to Solid Modeling
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Topological design of sculptured surfaces
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
The simplest subdivision scheme for smoothing polyhedra
ACM Transactions on Graphics (TOG)
A feature-based approach for smooth surfaces
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
A Corner-Cutting Scheme for Hexagonal Subdivision Surfaces
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Semiregular Pentagonal Subdivisions
SMI '04 Proceedings of the Shape Modeling International 2004
Local Mesh Operators: Extrusions Revisited
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Connected & manifold Sierpinsky polyhedra
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
A unified framework for primal/dual quadrilateral subdivision schemes
Computer Aided Geometric Design
Discrete Distortion for Surface Meshes
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
SMI 2012: Short Sketch based 3D modeling with curvature classification
Computers and Graphics
Concentrated curvature for mean curvature estimation in triangulated surfaces
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
SMI 2013: Towards building smart self-folding structures
Computers and Graphics
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In this paper, we introduce an insight for practical subdivision modeling to improve the quality of control mesh structures. Our approach is based on a discrete version of Gaussian-Bonnet theorem on piecewise planar manifold meshes and vertex angle deflections that determines local geometric behavior. Based on discrete Gaussian-Bonnet theorem, summation of angle deflections of all vertices is independent of mesh structure and it depends on only the topology of the mesh surface. Based on this result, it can be possible to improve organization of mesh structure of a shape according to its intended geometric structure.