A Dynamic Adaptive Mesh Library Based on Stellar Operators

Abstract In this paper, we present a dynamic adaptive mesh library which maintains a conforming triangulation of time-varying surfaces. The user supplies an initial mesh, a surface sampling procedure, and a set of adaptation criteria. The mesh is automatically modified in order to conform to user-defined characteristics, while the surface changes over time. The mesh representation is based on a half-edge data structure without any extra storage requirements. The mesh has an underlying semiregular multiresolution structure. Furthermore, the specification of desired mesh characteristics can be based on very general adaptation rules. This scheme facilitates the development of graphics applications that manipulate triangulated surfaces. The library source code is available online.

[1]  Hans-Peter Seidel,et al.  Multiresolution Shape Deformations for Meshes with Dynamic Vertex Connectivity , 2000, Comput. Graph. Forum.

[2]  John Dingliana,et al.  Graceful Degradation of Collision Handling in Physically Based Animation , 2000, Comput. Graph. Forum.

[3]  Enrico Puppo,et al.  Variable resolution triangulations , 1998, Comput. Geom..

[4]  Richard Bowden,et al.  Real-time Dynamic Deformable Meshes for Volumetric Segmentation and Visualisation , 1997, BMVC.

[5]  Luiz Velho,et al.  Variable Resolution 4‐k Meshes: Concepts and Applications , 2000, Comput. Graph. Forum.

[6]  Luiz Velho,et al.  Multi-resolution triangulations with adaptation to the domain based on physical compression , 2004, Proceedings. 17th Brazilian Symposium on Computer Graphics and Image Processing.

[7]  Luiz Velho IMPA,et al.  Dynamic Adaptive Meshes and Stellar Theory , 2004 .

[8]  Leif Kobbelt,et al.  OpenMesh: A Generic and Efficient Polygon Mesh Data Structure , 2002 .

[9]  Geert-Jan Giezeman,et al.  On the design of CGAL a computational geometry algorithms library , 2000 .

[10]  W. B. R. Lickorish.  Simplicial moves on complexes and manifolds , 1999 .

[11]  Michael Garland,et al.  Multiresolution Modeling: Survey and Future Opportunities , 1999, Eurographics.

[12]  M. Rivara.  Mesh Refinement Processes Based on the Generalized Bisection of Simplices , 1984 .

[13]  M. Garland,et al.  Multiresolution Modeling: Survey & Future Opportunities , 1999 .

[14]  Jon P. May.  Simplicial objects in algebraic topology , 1993 .

[15]  J. Munkres,et al.  Elementary Differential Topology. , 1967 .

[16]  Alan H. Barr,et al.  Accurate triangulations of deformed, intersecting surfaces , 1987, SIGGRAPH.

[17]  Luiz Velho,et al.  4-8 Subdivision , 2001, Comput. Aided Geom. Des..

[18]  Hugues Hoppe,et al.  Efficient implementation of progressive meshes , 1998, Comput. Graph..

[19]  Enrico Puppo,et al.  Efficient implementation of multi-triangulations , 1998 .