Atlas of Connectivity Maps for Semiregular Models

Semiregular models are an important subset of models in computer graphics. They are typically obtained by applying repetitive regular refinements on an initial arbitrary model. As a result, their connectivity strongly resembles regularity due to these refinement operations. Although data structures exist for regular or irregular models, a data structure designed to take advantage of this semiregularity is desirable. In this paper, we introduce such a data structure called atlas of connectivity maps for semiregular models resulting from arbitrary refinements. This atlas maps the connectivity information of vertices and faces on separate 2D domains called connectivity maps. The connectivity information between adjacent connectivity maps is determined by a linear transformation between their 2D domains. We also demonstrate the effectiveness of our data structure on subdivision and multiresolution applications.

[1]  Hujun Bao,et al.  √2 Subdivision for quadrilateral meshes , 2004, The Visual Computer.

[2]  Peter Schröder,et al.  Interactive multiresolution mesh editing , 1997, SIGGRAPH.

[3]  Dominique Bechmann,et al.  Extension of half-edges for the representation of multiresolution subdivision surfaces , 2009, The Visual Computer.

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

[5]  Marc Alexa,et al.  Refinement operators for triangle meshes , 2002, Comput. Aided Geom. Des..

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

[7]  Jörg Peters,et al.  A realtime GPU subdivision kernel , 2005, SIGGRAPH 2005.

[8]  Neil A. Dodgson,et al.  A generative classification of mesh refinement rules with lattice transformations , 2004, Comput. Aided Geom. Des..

[9]  Kevin Weiler,et al.  Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments , 1985, IEEE Computer Graphics and Applications.

[10]  Leif Kobbelt,et al.  √3-subdivision , 2000, SIGGRAPH.

[11]  Luke Olsen.  Constraining Wavelets for Multiresolution , 2006 .

[12]  Faramarz F. Samavati,et al.  A Discrete Approach to Multiresolution Curves and Surfaces , 2008, 2008 International Conference on Computational Sciences and Its Applications.

[13]  Richard H. Bartels,et al.  Multiresolution for curves and surfaces based on constraining wavelets , 2007, Comput. Graph..

[14]  Jörg Peters,et al.  Ternary subdivision for quadrilateral meshes , 2007, Comput. Aided Geom. Des..

[15]  Ali Mahdavi-Amiri,et al.  Connectivity Maps for Subdivision Surfaces , 2016, GRAPP/IVAPP.

[16]  Martin Bertram,et al.  Biorthogonal Loop-Subdivision Wavelets , 2004, Computing.

[17]  Prosenjit Bose,et al.  Efficient algorithms for Petersen's matching theorem , 1999, SODA '99.

[18]  Cláudio T. Silva,et al.  State of the Art in Quad Meshing , 2012 .

[19]  Jörg Peters,et al.  A pattern-based data structure for manipulating meshes with regular regions , 2005, Graphics Interface.

[20]  Hanan Samet,et al.  Foundations of multidimensional and metric data structures , 2006, Morgan Kaufmann series in data management systems.

[21]  Jörg Peters,et al.  The simplest subdivision scheme for smoothing polyhedra , 1997, TOGS.

[22]  Daniele Panozzo,et al.  Practical quad mesh simplification , 2010, Comput. Graph. Forum.

[23]  David Salesin,et al.  Wavelets for computer graphics: theory and applications , 1996 .