Advertisement

On the Spine of a PDE Surface

  • Hassan Ugail
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2768)

Abstract

The spine of an object is an entity that can characterise the object’s topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations.

The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the chosen PDE is utilised. It is shown that the spine of the PDE surface is then computed as a by-product of this analytic solution.

This paper also discusses how the of a PDE surface can be used to manipulate the shape. The solution technique adopted here caters for periodic surfaces with general boundary conditions allowing the possibility of the spine based shape manipulation for a wide variety of free-form PDE surface shapes.

Keywords

Surface Patch General Boundary Condition Freeform Surface Remainder Function Intuitive Appeal 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arcelli, C., Sanniti di Baja, G.: Ridge Points in Euclidean Distance Maps. Pattern Recognision Letters 13(4), 237–243 (1992)CrossRefGoogle Scholar
  2. 2.
    Bloor, M.I.G., Wilson, M.J.: Generating Blend Surfaces Using Partial Differential Equations. Computer-Aided Design 21, 165–171 (1989)zbMATHCrossRefGoogle Scholar
  3. 3.
    Bloor, M.I.G., Wilson, M.J.: Using Partial Differential Equations to Generate Freeform Surfaces. Computer Aided Design 22, 202–212 (1990)zbMATHCrossRefGoogle Scholar
  4. 4.
    Bloor, M.I.G., Wilson, M.J.: Spectral Approximations to PDE Surfaces. Computer-Aided Design 28, 145–152 (1996)CrossRefGoogle Scholar
  5. 5.
    Bloor, M.I.G., Wilson, M.J.: Method for Efficient Shape Parametrization of Fluid Membranes and Vesicles. Physical Review E 61(4), 4218–4229 (2000)CrossRefGoogle Scholar
  6. 6.
    Blum, H.: A transformation for Extracting New Descriptors of Shape. In: Wathen-Dunn, W. (ed.) Models for Perception of Speech and Visual Form, pp. 362–381. MIT Press, Cambridge (1976)Google Scholar
  7. 7.
    Boissonnat, J.D.: Geometric Surfaces for 3-Dimensional Shape Representation. ACM Transactions on Graphics 3(4), 244–265 (1984)CrossRefGoogle Scholar
  8. 8.
    Du, H., Qin, H.: Direct Manipulation and Interactive Sculpting of PDE Surfaces. In: Computer Graphics Forum (Proceedings of Eurographics 2000), vol. 19(3), pp. 261–270 (2000)Google Scholar
  9. 9.
    Dutta, D., Hoffmann, C.M.: On the Skeleton of Simple CSG Objecs. ASME Journal of Mechanical Design 115(1), 87–94 (1992)CrossRefGoogle Scholar
  10. 10.
    Leymarie, F., Levine, M.D.: Skeleton from Snakes, Progress in Image Analysis and Processing. World Scientific, Singapore (1990)Google Scholar
  11. 11.
    Nackman, L.R., Pizer, S.M.: Three-Dimensional Shape Description using Symmetric Axis Transform. IEEE Transactions on Pattern Analysis and Machine Intelligence 7(2), 187–202 (1985)CrossRefGoogle Scholar
  12. 12.
    Patrikalakis, N.M., Gursoy, H.N.: Shape Interrogation by Medial Axis Transform. In: Ravani, B. (ed.) Advances in Design Automation: Computer-Aided Computational Design, ASME, vol. 1, pp. 77–88 (1990)Google Scholar
  13. 13.
    Tsao, Y.F., Fu, K.S.: A Parallel Thinning Algorithm for 3-D Pictures. Computer Graphics Image Process 17, 315–331 (1981)CrossRefGoogle Scholar
  14. 14.
    Ugail, H., Bloor, M.I.G., Wilson, M.J.: Techniques for Interactive Design Using the PDE Method. ACM Transactions on Graphics 18(2), 195–212 (1999)CrossRefGoogle Scholar
  15. 15.
    Ugail, H., Bloor, M.I.G., Wilson, M.J.: Manipulations of PDE Surfaces Using an Interactively Defined Parameterisation. Computers and Graphics 24(3), 525–534 (1999)Google Scholar
  16. 16.
    Vida, J., Martin, R.R., Varady, T.: A Survey of Blending Methods that use Parametric Surfaces. Computer-Aided Design 26(5), 341–365 (1994)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Hassan Ugail
    • 1
  1. 1.Department of Electronic Imaging and Media Communications, School of InformaticsUniversity of BradfordBradfordUK

Personalised recommendations