Skip to main content

Mesh Editing Based on Discrete Laplace and Poisson Models

  • Conference paper
Advances in Computer Graphics and Computer Vision

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 4))

  • 994 Accesses

Abstract

Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. This intrinsic representation could be derived from differential properties of the mesh, i.e. its Laplacian. The modeling process poses nonzero boundary constraints so that this idea results in a Poisson model. Different ways of representing the intrinsic geometry and the boundary constraints result in alternatives for the properties of the modeling system. In particular, the Laplacian is not invariant to scaling and rotations. Either the intrinsic representation is enhanced to be invariant to (linearized) transformations, or scaling and rotation are computed in a preprocess and are modeled as boundary constraints. Based on this representation, useful editing operations can be developed: Interactive free-form deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric detail between two surfaces, and transplanting of a partial surface mesh into another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of this approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • Alexa, M.: Differential coordinates for local mesh morphing and deformation. The Visual Computer 19(2), 105–114 (2003a)

    MATH  Google Scholar 

  • Alexa, M.: Differential coordinates for local mesh morphing and deformation. The Visual Computer 19(2), 105–114 (2003b)

    MATH  Google Scholar 

  • Bendels, G.H., Klein, R.: Mesh forging: editing of 3d-meshes using implicitly defined occluders. In: Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 207–217. ACM Press, New York (2003)

    Google Scholar 

  • Biermann, H., Martin, I., Bernardini, F., Zorin, D.: Cut-and-paste editing of multiresolution surfaces. In: Proceedings of the 29th annual conference on Computer graphics and interactive techniques, pp. 312–321 (2002)

    Google Scholar 

  • Botsch, M., Kobbelt, L.: An intuitive framework for real-time freeform modeling. ACM Trans. Graph 23(3), 630–634 (2004)

    Article  Google Scholar 

  • Coquillart, S.: Extended free-form deformation: A sculpturing tool for 3D geometric modeling. In: Proceedings of SIGGRAPH 1990, pp. 187–196 (1990)

    Google Scholar 

  • DeCarlo, D., Finkelstein, A., Rusinkiewicz, S., Santella, A.: Suggestive contours for conveying shape. ACM Trans. Graph 22(3), 848–855 (2003)

    Article  Google Scholar 

  • Desbrun, M., Meyer, M., Schröder, P., Barr, A.H.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of ACM SIGGRAPH 1999, pp. 317–324. ACM Press, New York (1999)

    Google Scholar 

  • Fattal, R., Lischinski, D., Werman, M.: Gradient domain high dynamic range compression. In: Proceedings of ACM SIGGRAPH 2002, pp. 249–256. ACM Press, New York (2002)

    Google Scholar 

  • Fleishman, S., Drori, I., Cohen-Or, D.: Bilateral mesh denoising. In: Proceedings of ACM SIGGRAPH 2003, pp. 950–953. ACM Press, New York (2003)

    Chapter  Google Scholar 

  • Floater, M.S.: Mean-value coordinates. Computer Aided Geometric Design 20, 19–27 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • Forsey, D., Bartels, R.: Hierarchical b-spline refinement. In: Proceedings of ACM SIGGRAPH 1988, pp. 205–212. ACM Press, New York (1988)

    Google Scholar 

  • Gooch, B., Gooch, A.: Non-Photorealistic Rendering. A.K. Peters (2001)

    Google Scholar 

  • Guskov, I., Sweldens, W., Schröder, P.: Multiresolution signal processing for meshes. In: Proceedings of ACM SIGGRAPH 1999, pp. 325–334. ACM Press, New York (1999)

    Google Scholar 

  • Hertzmann, A.: Introduction to 3D non-photorealistic rendering: Silhouettes and outlines. In: Green, S. (ed.) Non-Photorealistic Rendering. SIGGRAPH 1999 Course Notes (1999)

    Google Scholar 

  • Hertzmann, A., Zorin, D.: Illustrating smooth surfaces. In: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pp. 517–526 (2000)

    Google Scholar 

  • Hoffman, D.D., Singh, M.: Salience of visual parts. Cognition 63(1), 29–78 (1997)

    Article  Google Scholar 

  • Igarashi, T., Matsuoka, S., Tanaka, H.: Teddy: A sketching interface for 3D freeform design. In: Proceedings of SIGGRAPH 1999, Computer Graphics Proceedings, Annual Conference Series, pp. 409–416 (1999)

    Google Scholar 

  • Kanai, T., Suzuki, H., Mitani, J., Kimura, F.: Interactive mesh fusion based on local 3D metamorphosis. In: Graphics Interface 1999, pp. 148–156 (1999)

    Google Scholar 

  • Kobbelt, L., Campagna, S., Vorsatz, J., Seidel, H.-P.: Interactive multi-resolution modeling on arbitrary meshes. In: Proceedings of ACM SIGGRAPH 1998, pp. 105–114. ACM Press, New York (1998)

    Google Scholar 

  • Kobbelt, L., Vorsatz, J., Seidel, H.-P.: Multiresolution hierarchies on unstructured triangle meshes. Computational Geometry: Theory and Applications 14, 5–24 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Lipman, Y., Sorkine, O., Cohen-Or, D., Levin, D.: Differential coordinates for interactive mesh editing. In: SMI 2004. International Conference on Shape Modeling and Applications 2004, pp. 181–190 (2004)

    Google Scholar 

  • Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Visualization and Mathematics III, pp. 35–57 (2003)

    Google Scholar 

  • Pérez, P., Gangnet, M., Blake, A.: Poisson image editing. In: Proceedings of ACM SIGGRAPH 2003, pp. 313–318. ACM Press, New York (2003)

    Chapter  Google Scholar 

  • Ranta, M., Inui, M., Kimura, F., Mäntylä, M.: Cut and paste based modeling with boundary features. In: SMA 1993: Proceedings of the Second Symposium on Solid Modeling and Applications, pp. 303–312 (1993)

    Google Scholar 

  • Sederberg, T.W., Parry, S.R.: Free-form deformation of solid geometric models. In: Proceedings of SIGGRAPH 1986, pp. 151–160 (1986)

    Google Scholar 

  • Sorkine, O., Lipman, Y., Cohen-Or, D., Alexa, M., Rössl, C., Seidel, H.-P.: Laplacian surface editing. In: Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry processing. Eurographics Association, pp. 179–188. ACM Press, New York (2004)

    Google Scholar 

  • Taubin, G.: A signal processing approach to fair surface design. In: Proceedings of ACM SIGGRAPH 1995, pp. 351–358. ACM Press, New York (1995)

    Google Scholar 

  • Toledo, S.: Taucs: A Library of Sparse Linear Solvers. Tel. Aviv. University (2003)

    Google Scholar 

  • Yu, Y., Zhou, K., Xu, D., Shi, X., Bao, H., Guo, B., Shum, H.-Y.: Mesh editing with poisson-based gradient field manipulation. ACM Trans. Graph 23(3), 644–651 (2004)

    Article  Google Scholar 

  • Zeleznik, R.C., Herndon, K.P., Hughes, J.F.: Sketch: An interface for sketching 3D scenes. In: Proceedings of SIGGRAPH 1996. Computer Graphics Proceedings. Annual Conference Series, pp. 163–170 (1996)

    Google Scholar 

  • Zorin, D., Schröder, P., Sweldens, W.: Interactive multiresolution mesh editing. In: Proceedings of ACM SIGGRAPH 1997, pp. 259–268. ACM Press, New York (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Alexa, M., Nealen, A. (2007). Mesh Editing Based on Discrete Laplace and Poisson Models. In: Braz, J., Ranchordas, A., Araújo, H., Jorge, J. (eds) Advances in Computer Graphics and Computer Vision. Communications in Computer and Information Science, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75274-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-75274-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75272-1

  • Online ISBN: 978-3-540-75274-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics