Borders, Semi-Sharp Edges and Adaptivity for Hexagonal Subdivision Surface Schemes

In recent research, hexagonal subdivision schemes for meshes with an arbitrary topology have been introduced. They can either be viewed on their own or be combined with their dual triangular counterparts to generate surfaces with high degrees of continuity, similar to the earlier approaches with quadrilateral schemes. For practical applications, however, a major obstacle is the lack of good algorithms to generate borders and to adaptively subdivide meshes up to user-controlled criteria.

[1]  N. Dyn,et al.  A butterfly subdivision scheme for surface interpolation with tension control , 1990, TOGS.

[2]  Richard F. Riesenfeld,et al.  A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Jean Schweitzer,et al.  Analysis and application of subdivision surfaces , 1996 .

[4]  Ahmad H. Nasri,et al.  Interpolating meshes of boundary intersecting curves by subdivision surfaces , 2000, The Visual Computer.

[5]  M. Sabin,et al.  Behaviour of recursive division surfaces near extraordinary points , 1978 .

[6]  Peter Schröder,et al.  Wavelets in computer graphics , 1996, Proc. IEEE.

[7]  Henning Biermann,et al.  Piecewise smooth subdivision surfaces with normal control , 2000, SIGGRAPH.

[8]  D. Zorin,et al.  4-8 Subdivision , 2001 .

[9]  Kunio Kondo,et al.  Adaptive Refinements in Subdivision Surfaces? , 1999, Eurographics.

[10]  Malcolm A. Sabin,et al.  Non-uniform recursive subdivision surfaces , 1998, SIGGRAPH.

[11]  D. Zorin,et al.  A unified framework for primal/dual quadrilateral subdivision schemes , 2001 .

[12]  Tony DeRose,et al.  Subdivision surfaces in character animation , 1998, SIGGRAPH.

[13]  Ahmad H. Nasri.  Constructing polygonal complexes with shape handles for curve interpolation by subdivision surfaces , 2001, Comput. Aided Des..

[14]  Heinrich Müller,et al.  Adaptive subdivision curves and surfaces , 1998, Proceedings. Computer Graphics International (Cat. No.98EX149).

[15]  Adi Levin.  Combined subdivision schemes for the design of surfaces satisfying boundary conditions , 1999, Comput. Aided Geom. Des..

[16]  J. Stam.  On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree , 2001 .

[17]  Tony DeRose,et al.  Piecewise smooth surface reconstruction , 1994, SIGGRAPH.

[18]  E. Catmull,et al.  Recursively generated B-spline surfaces on arbitrary topological meshes , 1978 .

[19]  George Merrill Chaikin,et al.  An algorithm for high-speed curve generation , 1974, Comput. Graph. Image Process..

[20]  Charles T. Loop,et al.  Smooth Subdivision Surfaces Based on Triangles , 1987 .