Engineered Model Simplification for Simulation Based Structural Design

AbstractSimulation based structural design usually involves frequent conversions between implicit and explicit models. In this paper, a fast and robust mesh simplification method is proposed to improve the efficiency of implicit evaluation of large size engineered models. The mesh is simplified via edge collapse with a metric consisting of edge length and curvature information. A progressive multi-pass strategy makes the simplification reasonable and effective. Topology consistency is maintained by a validity check before each primitive edge removed. Most importantly, this method guarantees the practical utility of simplified model in downstream simulation based structural design. Satisfactory results of mesh simplification and its application are provided to demonstrate the capability.

[1]  Arie E. Kaufman,et al.  Voxel based object simplification , 1995, Proceedings Visualization '95.

[2]  Peter Lindstrom,et al.  Out-of-core simplification of large polygonal models , 2000, SIGGRAPH.

[3]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[4]  Roni Yagel,et al.  Octree-based decimation of marching cubes surfaces , 1996, Proceedings of Seventh Annual IEEE Visualization '96.

[5]  Christian Rössl,et al.  Geometric modeling based on polygonal meshes Video files associated with this course are available from the citation page , 2007, SIGGRAPH Courses.

[6]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[7]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

[8]  J. Strain.  Semi-Lagrangian Methods for Level Set Equations , 1999 .

[9]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.

[10]  Michael Garland,et al.  Surface simplification using quadric error metrics , 1997, SIGGRAPH.

[11]  Michael Garland,et al.  Simplifying surfaces with color and texture using quadric error metrics , 1998, Proceedings Visualization '98 (Cat. No.98CB36276).

[12]  Pierre Alliez,et al.  Geometric Modeling Based on Polygonal Meshes , 2008, Eurographics.

[13]  Hans-Peter Seidel,et al.  BSP Shapes , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[14]  Adam W. Bargteil.  A semi-Lagrangian contouring method for fluid simulation , 2005, SIGGRAPH '05.

[15]  Jarek Rossignac,et al.  Multi-resolution 3D approximations for rendering complex scenes , 1993, Modeling in Computer Graphics.

[16]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[17]  Greg Turk,et al.  Re-tiling polygonal surfaces , 1992, SIGGRAPH.

[18]  Jules Bloomenthal,et al.  An Implicit Surface Polygonizer , 1994, Graphics Gems.

[19]  Ichiro Hagiwara,et al.  A Topology Preserved Mesh Simplification Algorithm , 2009, 2009 WRI World Congress on Computer Science and Information Engineering.

[20]  Tony DeRose,et al.  Mesh optimization , 1993, SIGGRAPH.

[21]  G. Allaire,et al.  Structural optimization using topological and shape sensitivity via a level set method , 2005 .

[22]  Charlie C. L. Wang,et al.  Volume and complexity bounded simplification of solid model represented by binary space partition , 2010, SPM '10.

[23]  Mark Meyer,et al.  Discrete Differential-Geometry Operators for Triangulated 2-Manifolds , 2002, VisMath.