Empirical Analysis of Surface Interpolation by Spatial Environment Graphs

  • Robert Mencl
  • Heinrich Müller
Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)


An empirical analysis of a new algorithm for reconstruction of surfaces from three-dimensional point clouds is presented. The particular features of the algorithm are the reconstruction of open surfaces with boundaries from data sets of variable density, and the treatment of sharp edges, that is, locations of infinite curvature. The empirical data in particular confirm a formal analysis which has been performed for compact surfaces of limited curvature without boundary.


Line Segment Empirical Analysis Dihedral Angle Sharp Edge Triangular Mesh 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    U. Adamy, J. Giesen and M. John, New Techniques for Topologically Correct Surface Reconstruction, Proceedings of IEEE Visualization 2000, IEEE Computer Society Press, 2000.Google Scholar
  2. 2.
    N. Amenta, M. Bern and M. Kamvysselis, A new Voronoi-based surface reconstruction algorithm, Proceedings of SIGGRAPH’98, 1998, 415–421.Google Scholar
  3. 3.
    N. Amenta, S. Choi, T.K. Dey and N. Leekha, A simple algorithm for homeomorphic surface reconstruction, In Proc. 16th ACM Sympos. Comput. Geom., 2000.Google Scholar
  4. 4.
    N. Amenta, S. Choi and R. K. Kolluri, The Power Crust, Unions of Balls, and the Medial Axis Transform, Computational Geometry: Theory and Applications, 2001, 19 (2–3), 127–153.MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    D.G. Kirkpatrick, J.D. Radke, A framework for computational morphology, in: G.T. Toussaint (ed.), Computational Geometry, Elsevier Science Publisher B.V., North-Holland, 1985, 217–248.Google Scholar
  6. 6.
    W.E. Lorensen, H.E. Cline, Marching Cubes: A high resolution 3D-surface construction algorithm, Computer Graphics, 1987, 21 (4), 163–169.CrossRefGoogle Scholar
  7. 7.
    R. Mencl, A Graph-Based Approach to Surface Reconstruction, Computer Graphics Forum, 1995, 14 (3), 445–456.CrossRefGoogle Scholar
  8. 8.
    R. Mend, Reconstruction of Surfaces from Unorganized Three-Dimensional Point Clouds, PhD thesis, Informatik VII, University of Dortmund, Germany, 2001.Google Scholar
  9. 9.
    R. Mend and H. Müller, Graph-Based Surface Reconstruction Using Structures in Scattered Point Sets, Proceedings of CGI ‘88 (Computer Graphics International), Hannover, Germany, 1998, 298–311.Google Scholar
  10. 10.
    R. Mencl, H. Müller, Interpolation and Approximation of Surfaces from Three-Dimensional Scattered Data Points, Proceedings of Scientific Visualization - Dagstuhl ‘87, IEEE Computer Society Press, 2000.Google Scholar
  11. 11.
    R. Mend, H. Müller, Surface interpolation by spatial environment graphs, In: Data Visualization: The State of the Art, Kluwer Academic Publishers, 2002.Google Scholar
  12. 12.
    F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction, Springer Verlag, 1985.Google Scholar
  13. 13.
    J.D. Radke, On the shape of a set of points, in: Computational Morphology, G.T. Toussaint (ed.), Elsevier Science Publisher B.V., North Holland, 1988, 105–136.Google Scholar
  14. 14.
    S.V. Rao, Some studies on beta-skeletons, PhD thesis, Dept. of Computer Science Engineering, Indian Institute of Technology, India, 1998.Google Scholar
  15. 15.
    R.C. Veltkamp, Closed Object Boundaries from Scattered Points, Lecture Notes in Computer Science 885, Springer Verlag, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Robert Mencl
    • 1
  • Heinrich Müller
    • 1
  1. 1.Informatik VIIUniversity of DortmundDortmundGermany

Personalised recommendations