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Delaunay deformable mesh for the weathering and erosion of 3D terrain

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Abstract

Computer-generated erosion and weathering are important to convey setting and mood in computer generated images. Heightmap based landforms are good for distant scenes, but inadequate for scenes containing concave rock formations. Voxel based terrain editing algorithms do admit concave surfaces but do not scale. We introduce weathering on triangulated surface meshes, using a memory efficient modification of the Delaunay deformable model. This structure allows the freedom of an unorganized point cloud, the geometric information and visualization of a surface mesh, and the topological freedom of volumetric approaches—all while scaling linearly with surface complexity. We implement both spheroidal weathering and hydraulic erosion algorithms on this structure and demonstrate that the resulting terrain is visually plausible at modest computational cost.

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References

  1. Alliez, P., Cohen-Steiner, D., Yvinec, M., Desbrun, M.: Variational tetrahedral meshing. In: International Conference of Computer Graphics and Interactive Techniques (SIGGRAPH), pp. 617–625. ACM, New York (2005)

    Google Scholar 

  2. Autodesk: Maya 2008 (2008)

  3. Bargteil, A.W., Wojtan, C., Hodgins, J.K., Turk, G.: A finite element method for animating large viscoplastic flow. ACM Trans. Graph. 26(3) (2007)

  4. Beneš, B., Těšínský, V., Hornyš, J., Bhatia, S.: Hydraulic erosion. Comput. Animat. Virtual Worlds 17(2), 99–108 (2006)

    Article  Google Scholar 

  5. Blum, H.: A transformation for extracting new descriptors of shape. In: Wathen-Dunn, W. (ed.) Models for the Perception of Speech and Visual Form, pp. 362–380. MIT Press, Cambridge (1967)

    Google Scholar 

  6. Cgal, Computational Geometry Algorithms Library. http://www.cgal.org

  7. Chen, Y., Xia, L., Wong, T.T., Tong, X., Bao, H., Guo, B., Shum, H.Y.: Visual simulation of weathering by γ-ton tracing. In: SIGGRAPH ’05: Proceedings of the 32nd Annual Conference on Computer Graphics and Interactive Techniques, pp. 1127–1133. ACM Press, New York (2005)

    Google Scholar 

  8. Choi, S., Amenta, N.: Delaunay triangulation programs on surface data. In: SODA ’02: Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 135–136. Society for Industrial and Applied Mathematics, Philadelphia (2002)

    Google Scholar 

  9. Cutler, B., Dorsey, J., McMillan, L., Müller, M., Jagnow, R.: A procedural approach to authoring solid models. In: SIGGRAPH ’02: Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques, pp. 302–311. ACM, New York (2002)

    Chapter  Google Scholar 

  10. Devillers, O.: The Delaunay hierarchy. Int. J. Found. Comput. Sci. 13(2), 163–180 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Dorsey, J., Edelman, A., Jensen, H., Legakis, J., Pedersen, H.: Modeling and rendering of weathered stone. In: SIGGRAPH ’99: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, pp. 225–234. ACM Press, New York (1999). doi:10.1145/311535.311560

    Chapter  Google Scholar 

  12. Ito, T., Fujimoto, T., Moraoka, K., Chiba, N.: Modeling rocky scenery taking into account joints. In: Proceedings of Computer Graphics International 2003, pp. 244–247. IEEE Computer Society, Los Alamitos (2003)

    Chapter  Google Scholar 

  13. Joe, B.: Three-dimensional triangulations from local transformations. SIAM J. Sci. Stat. Comput. 10(4), 718–741 (1989). doi:10.1137/0910044

    Article  MATH  MathSciNet  Google Scholar 

  14. Jones, M.D., Farley, M., Butler, J., Beardall, M.: Directable weathering of concave rock using curvature estimation. IEEE Trans. Vis. Comput. Graph. 16(1) (2010)

  15. Kelley, A., Malin, M., Nielson, G.: Terrain simulation using a model of stream erosion. In: SIGGRAPH ’88: Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, pp. 263–268. ACM, New York (1988)

    Chapter  Google Scholar 

  16. Lachaud, J.O., Montanvert, A.: Deformable meshes with automated topology changes for coarse-to-fine three-dimensional surface extraction. Med. Image Anal. 3(2), 187–207 (1999). doi:10.1016/S1361-8415(99)80006-1

    Article  Google Scholar 

  17. McInerney, T., Terzopoulos, D.: Medical image segmentation using topologically adaptable surfaces. In: CVRMed-MRCAS ’97: Proceedings of the First Joint Conference on Computer Vision, Virtual Reality and Robotics in Medicine and Medial Robotics and Computer-Assisted Surgery, pp. 23–32. Springer, London (1997)

    Google Scholar 

  18. Milligan, M.: Geology of Goblin Valley State Park, Utah. In: Geology of Utah’s Parks and Monuments, pp. 421–432. Utah Geological Association and Bryce Canyon Natural History Association (2003)

  19. Mullen, P., McKenzie, A., Tong, Y., Desbrun, M.: A variational approach to Eulerian geometry processing. In: SIGGRAPH ’07: ACM SIGGRAPH 2007 Papers, p. 66. ACM, New York (2007). doi:10.1145/1275808.1276459

    Google Scholar 

  20. Musgrave, F.K., Kolb, C.E., Mace, R.S.: The synthesis and rendering of eroded fractal terrains. In: SIGGRAPH ’89: Proceedings of the 16th Annual Conference on Computer Graphics and Interactive Techniques, pp. 41–50. ACM Press, New York (1989). doi:10.1145/74333.74337

    Chapter  Google Scholar 

  21. Nagashima, K.: Computer generation of eroded valley and mountain terrains. Vis. Comput. 13, 456–464 (1997)

    Article  Google Scholar 

  22. Pons, J.P., Boissonnat, J.D.: Delaunay deformable models: Topology-adaptive meshes based on the restricted Delaunay triangulation. In: IEEE Conference on Computer Vision and Pattern Recognition. IEEE Computer Society, Minneapolis (2007)

    Google Scholar 

  23. Sibson, R.: Locally equiangular triangulations. Comput. J. 21(3), 243–245 (1978)

    Article  MathSciNet  Google Scholar 

  24. Stichting Blender Foundation: Blender 2.49 (2009)

  25. Turk, G.: Re-tiling polygonal meshes. Comput. Graph. 26(2), 55–64 (1992) (Proceedings of SIGGRAPH’92)

    Article  Google Scholar 

  26. Štáva, O., Beneš, B., Brisbin, M., Křivánek, J.: Interactive terrain modeling using hydraulic erosion. In: Eurographics/ACM Symposium on Computer Animation. The Eurographics Association (2008)

  27. Zhou, H., Sun, J., Turk, G., Rehg, J.M.: Terrain synthesis from digital elevation models. IEEE Trans. Vis. Comput. Graph. 13(4), 834–848 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Virginia, Charlottesville, USA

    L. A. Tychonievich

  2. Brigham Young University, Provo, USA

    M. D. Jones

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  1. L. A. Tychonievich
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  2. M. D. Jones
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Correspondence to M. D. Jones.

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Tychonievich, L.A., Jones, M.D. Delaunay deformable mesh for the weathering and erosion of 3D terrain. Vis Comput 26, 1485–1495 (2010). https://doi.org/10.1007/s00371-010-0506-2

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