Physically-based dynamic cell representation with consistent cell neighbor relationships

ABSTRACT

In this paper, we study a novel way to dynamically represent cellular materials' characteristics using Voronoi diagram and. Mass-Spring System (MSS). MSS is the key component which is applied on Delaunay edges. Once some selected site points are moved, MSS will drive the other connected site points and keep redistributing them until the internal forces between the Voronoi cells are balanced. The restriction imposed on cell neighbor relationships preserves the consistency of the deformable cellar material's topology.

REFERENCES

• 1: Mark de Berg , Marc van Kreveld , Mark Overmars , Otfried Schwarzkopf, Computational geometry: algorithms and applications, Springer-Verlag New York, Inc., Secaucus, NJ, 1997
• 2: Roberts, A. P. and Garboczi, E. J. Elastic moduli of model random three-dimensional closed-cell cellular solid. Acta Mater, 2001, 49:189~197.
• 3: Vejen, N. and Pyrz, R. Modelling of Microcellular Materials Using Voronoi Cell Finite Element Method (VCFEM) -- the Homogeneous Case, September 99.
• 4: Atsuyuki Okabe , Barry Boots , Kokichi Sugihara, Spatial tessellations: concepts and applications of Voronoi diagrams, John Wiley & Sons, Inc., New York, NY, 1992
• 5: Gibson, S. F. F. and Mirtich, B. A Survey of Deformable Modeling in Computer Graphics, MERL Technical Report, TR97-19, 1997.
• 6: Luciani, A., Jimenez, S., Florens, J. L., Cadoz, C., and Raoult, O. Computational physics: a modeler simulator for animated physical objects. In Eurographics'91, Vienna, Austria, September 1991.
• 7: Matthias Teschner , Bruno Heidelberger , Matthias Muller , Markus Gross, A Versatile and Robust Model for Geometrically Complex Deformable Solids, Proceedings of the Computer Graphics International, p.312-319, June 16-19, 2004 [doi>10.1109/CGI.2004.6]
• 8: Gilles Debunne , Mathieu Desbrun , Marie-Paule Cani , Alan H. Barr, Dynamic real-time deformations using space & time adaptive sampling, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.31-36, August 2001 [doi>10.1145/383259.383262]
• 9: Cristian Lorenz , Nils Krahnstöver, Generation of point-based 3D statistical shape models for anatomical objects, Computer Vision and Image Understanding, v.77 n.9, p.175-191, Feb. 2000
• 10: Chew, P. Voronoi Diagram / Delaunay Triangulation JAVA Applet: http://www.cs.cornell.edu/Info/People/chew/Delaunay.html
• 11: Bourguignon, D. and Cani, M. P. Controlling Anisotropy in Mass-Spring Systems. Eurographics, pp. 113--123. Eurographics Assoc., 2000
• 12: Cooper, L. and Maddock, S. Preventing Collapse Within Mass-Spring-Damper Models of Deformable Objects. The 5th Int. Conf. in Central Europe on Comput. Graphics and Vis. 1997

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Physically based modeling

General Terms:
Algorithms, Theory

Keywords:
Delaunay, Voronoi, cellular material, deformation, mass-spring system