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Fusion of disconnected mesh components with branching shapes

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Abstract

Branching structure is a common feature of many natural objects. Given some mesh components with a branching shape missing, this paper presents a novel approach to fuse the mesh components: connectivity graph of the branching shape is constructed to seamlessly connect the boundaries of given components; then, natural geometry is imposed on the connectivity graph exploiting the information of given boundaries. We present a method to construct a branching connectivity graph to connect arbitrary number of given boundaries. Also, a method to generate natural geometry of the connectivity graph that smoothly fuses the boundaries of mesh components is exploited. Some examples are given to demonstrate that our new scheme can be used in a couple of applications, such as fast tree trunk modeling, mesh composition and shell generation.

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References

  1. Bloomenthal, J.: Modeling the mighty maple. Comput. Graph. 19(3), 305–311 (1985)

    Article  Google Scholar 

  2. Boskamp, T., Hahn, H., Hindennach, M., Zidowitz, S., Oeltze, S., Preim, B., Peitgen, H.-O.: Geometrical and structural analysis of vessel systems in 3d medical image data sets. In: Medical Imaging Systems Technology, vol. 5, pp. 1–60 (2005)

  3. Bloomenthal, J., Shoemake, K.: Convolution surfaces. In: Proceedings of SIGGRAPH, 91, pp. 251–256 (1991)

  4. MacMurchy, P.: The use of subdivision surfaces in the modeling of plants. Ph.D. thesis, University of Calgary (2004)

  5. Bloomenthal, J.: Skeletal design of natural forms. PhD thesis, University of Calgary (1995)

  6. Oeltze, S., Preim, B.: Visualization of anatomic tree structures with convolution surfaces. In: IEEE/Eurographics Symposium on Visualization, pp. 311–320 (2004)

  7. Felkel, P., Kanitsar, A., Fuhrmann, A.-L., Wegenkittl, R.: Surface models of tube trees. In: Proceedings of Computer Graphics International, vol. 4, pp. 70–77 (2004)

  8. Galbraith, C., Mundermann, L., Wyvill, B.: Implicit visualization and inverse modeling of growing trees. Comput. Graph. Forum 23(3), 351–360 (2004)

    Article  Google Scholar 

  9. Taubin, G.: A signal processing approach to fair surface design. In: ACM SIGGRAPH’95, pp. 351–358 (1995)

  10. Kobbelt, L., Campagna, S., Vorsatz, J., Seidel, H.P.: Interactive multi-resolution modeling on arbitrary meshes. In: Proc of ACM SIGGRAPH’98, pp. 105–114 (1998)

  11. Bloor, M.I.G., Wilson, M.J.: Using partial differential equations to generate free-form surfaces. Comput.-Aided Des. 22(4), 202–212 (1990)

    Article  MATH  Google Scholar 

  12. Welch, W., Witkin, A.: Free-form shape design using triangulated surfaces. In: Proc of ACM SIGGRAPH’94, pp. 247–256 (1994)

  13. Desbrun, M., Meyer, M., Schroder, P., Barr, A.H.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: ACM SIGGRAPH’99, pp. 317–324 (1999)

  14. Sorkine, O., Cohen-Or, D.: Least-squares meshes. In: Proceedings of Shape Modeling International, pp. 191–199 (2004)

  15. Isenburg, M., Gumhold, S., Gotsman, C.: Connectivity shapes. In: Proceedings of IEEE Visualization 2001, pp. 135–142 (2001)

  16. Nealen, A., Igarashi, T., Sorkine, O., Alexa, M.: Fibermesh: Designing freeform surfaces with 3d curves. ACM Trans. Graph. 26(3), 41 (2007)

    Article  Google Scholar 

  17. Wang, C.-C.-L., Tang, K.: Optimal boundary triangulations of an interpolating ruled surface. J. Comput. Inf. Sci. Eng., ASME Trans. 5(4), 291–301 (2005)

    Article  Google Scholar 

  18. Meyer, M., Desbrun, M., Schroder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. Vis. Math. 3, 35–57 (2002)

    Google Scholar 

  19. Wardetzky, M., Bergou, M., Harmon, D., Zorin, D., Grinspun, E.: Discrete quadratic curvature energies. Comput. Aided Geom. Des. 24(8–9), 499–518 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. Prusinkiewicz, P., James, M., Mech, R.: Synthetic topiary. In: Computer Graphics, pp. 351–358 (1994)

  21. Tan, P., Zeng, G., Wang, J., Kang, S.-B., Quan, L.: Image-based tree modeling. ACM Trans. Graph. 26(3) (2007)

  22. Okabe, M., Owada, S., Igarashi, T.: Interactive design of botanical trees using freehand sketches and example based editing. Comput. Graph. Forum 24(3), 487–496 (2005)

    Article  Google Scholar 

  23. Chen, X., Neubert, B., Xu, Y.-Q., Deussen, O., Kang, S.-B.: Sketch-based tree modeling using Markov random field. ACM Trans. Graph. 27(5) (2008)

  24. Lluch, J., Vivo, R., Monserrat, C.: Modeling tree structures using a single polygonal mesh. Graph. Models 66(2), 89–101 (2004)

    Article  MATH  Google Scholar 

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

  26. Sharf, A., Blumenkrants, M., Shamir, A., Cohen-Or, D.: Snappaste: An interactive technique for easy mesh composition. Vis. Comput. 22(9), 835–844 (2006)

    Article  Google Scholar 

  27. Jin, X., Lin, J., Wang, C.-C.-L., Feng, J., Sun, H.: Mesh fusion using functional blending on topologically incompatible sections. Vis. Comput. 22(4), 266–275 (2006)

    Article  Google Scholar 

  28. Lin, J., Jin, X., Wang, C.-C.-L., Hui, K.-C.: Mesh composition on models with arbitrary boundary topology. IEEE Trans. Vis. Comput. Graph. 14(3), 653–665 (2008)

    Article  Google Scholar 

  29. Porumbescu, S.-D., Budge, B., Feng, L., Joy, K.-I.: Shell maps. ACM Trans. Graph. 24(3), 626–633 (2005)

    Article  Google Scholar 

  30. Kraevoy, V., Sheffer, A.: Template-based mesh completion. In: Proc of Eurographics Symposium on Geometry Processing (2005)

  31. Podolak, J., Rusinkiewicz, S.: Atomic volumes for mesh completion. In: Proc of Eurographics Symposium on Geometry Processing (2005)

  32. Davis, J., Marschner, S.-R., Garr, M., Levoy, M.: Filling holes in complex surfaces using volumetric diffusion. In: Proc of First International Symposium on 3D Data Processing, Visualization, and Transmission, pp. 428–438 (2001)

  33. Xu, G., Pan, Q., Bajaj, C.: Discrete surface modeling using partial differential equations. Comput. Aided Geom. Des. 23(2), 125–145 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  34. Liepa, P.: Filling holes in meshes. In: Proc of Eurographics/ACM SIGGRAPH Symposium on Geometry Processing 2003, pp. 200–205 (2003)

  35. Bhat, P., Ingram, S., Turk, G.: Geometric texture synthesis by example. In: Proc of Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 41–44 (2004)

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Authors and Affiliations

  1. State Key Lab of CAD & CG, Zhejiang University, Hangzhou, 310027, PR China

    Juncong Lin & Xiaogang Jin

  2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong

    Charlie C. L. Wang

Authors
  1. Juncong Lin
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  2. Xiaogang Jin
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  3. Charlie C. L. Wang
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Correspondence to Xiaogang Jin.

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Lin, J., Jin, X. & Wang, C.C.L. Fusion of disconnected mesh components with branching shapes. Vis Comput 26, 1017–1025 (2010). https://doi.org/10.1007/s00371-010-0460-z

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