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Flexible terrain erosion

Published: 05 June 2024 Publication History

Abstract

In this paper, we present a novel particle-based method for simulating erosion on various terrain representations, including height fields, voxel grids, material layers, and implicit terrains. Our approach breaks down erosion into two key processes—terrain alteration and material transport—allowing for flexibility in simulation. We utilize independent particles governed by basic particle physics principles, enabling efficient parallel computation. For increased precision, a vector field can adjust particle speed, adaptable for realistic fluid simulations or user-defined control. We address material alteration in 3D terrains with a set of equations applicable across diverse models, requiring only per-particle specifications for size, density, coefficient of restitution, and sediment capacity. Our modular algorithm is versatile for real-time and offline use, suitable for both 2.5D and 3D terrains.

References

[1]
Argudo O, Galin E, Peytavie A, Paris A, and Guérin E Simulation, modeling and authoring of glaciers ACM Trans. Gr. 2020 39 1-14
[2]
Baraff, D., Witkin, A.: Large steps in cloth simulation. In: Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1998, pp. 43–54 (1998).
[3]
Beardall M, Butler J, Farley M, and Jones MD Directable weathering of concave rock using curvature estimation IEEE Trans. Vis. Comput. Gr. 2010 16 1 81-94
[4]
Becher, M., Krone, M., Reina, G., Ertl, T.: Feature-based volumetric terrain generation. In: Proceedings - I3D 2017: 21st ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games (2017).
[5]
Beneš B, Těšínský V, Hornyš J, and Bhatia SK Hydraulic erosion Comput. Anim. Virtual Worlds 2006 17 2 99-108
[6]
Beneš, B., Forsbach, R.: Layered data representation for visual simulation of terrain erosion. In: Proceedings - Spring Conference on Computer Graphics, SCCG 2001, pp. 80–86 (2001).
[7]
Caretto, L.S., Gosman, A.D., Patankar, S.V., Spalding, D.B.: Two calculation procedures for steady, three-dimensional flows with recirculation. In: Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, vol. 19, pp. 60–68 (1973)
[8]
Cordonnier G, Braun J, Cani MP, Beneš B, Peytavie A, and Guérin É Large scale terrain generation from tectonic uplift and fluvial erosion IEEE Trans. Vis. Comput. Graph. 2017
[9]
Cordonnier G, Cani MP, Beneš B, Braun J, and Galin É Sculpting mountains: interactive terrain modeling based on subsurface geology IEEE Trans. Vis. Comput. Graph. 2018
[10]
Cordonnier G, Ecormier-nocca P, Galin É, Gain J, Beneš B, and Cani MP Interactive generation of time-evolving, snow-covered landscapes with avalanches Comput. Graph. Forum 2018 37 2 497-509
[11]
Cordonnier G, Galin É, Gain J, Beneš B, Guérin É, Peytavie A, and Cani MP Authoring landscapes by combining ecosystem and terrain erosion simulation ACM Trans. Graph. 2017
[12]
Cordonnier G, Jouvet G, Peytavie A, Braun J, Cani MP, Benes B, Galin E, Guérin E, and Gain J Forming terrains by glacial erosion ACM Trans. Graph. 2023 42 14
[13]
Dey R, Doig JG, and Gatzidis C Procedural feature generation for volumetric terrains using voxel grammars Entertain. Comput. 2018 27 128-136
[14]
Eisemann, E., Decoret, X.: Single-pass gpu solid voxelization for real-time applications, pp. 73–80 (2008)
[15]
Emilien A, Poulin P, Cani MP, and Vimont U Interactive procedural modelling of coherent waterfall scenes Comput. Graph. Forum 2015 34 22-35
[16]
Gain, J., Marais, P., Straßer, W.: Terrain sketching. In: Proceedings of I3D 2009: the 2009 ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, vol. 1(212), pp. 31–38 (2009).
[17]
Galin E, Guérin E, Peytavie A, Cordonnier G, Cani MP, Benes B, and Gain J A review of digital terrain modeling Comput. Graph. Forum 2019 38 553-577
[18]
Guérin É, Digne J, Galin É, and Peytavie A Sparse representation of terrains for procedural modeling Comput. Graph. Forum 2016 35 2 177-187
[19]
Guérin E, Peytavie A, Masnou S, Digne J, Sauvage B, Gain J, and Galin E Gradient terrain authoring Comput. Graph. Forum 2022 41 85-95
[20]
Hong, Q.: A skeleton-based technique for modelling implicit surfaces. In: Proceedings of the 2013 6th International Congress on Image and Signal Processing, CISP 2013, vol. 2(Cisp), pp. 686–691 (2013).
[21]
Ito, T., Fujimoto, T., Muraoka, K., Chiba, N.: Modeling rocky scenery taking into account joints. In: Proceedings of Computer Graphics International Conference, CGI 2003-Janua(July 2014), pp. 244–247 (2003).
[22]
Jones BD and Williams JR Fast computation of accurate sphere-cube intersection volume Eng. Comput. 2017 34 1204-1216
[23]
Kaufman, A., Cohen, D Yagel, R,: Volume graphics. Computer 26(7), 51–64 (1993).
[24]
Koschier D, Bender J, Solenthaler B, and Teschner M A survey on SPH methods in computer graphics Comput. Graph. Forum 2022 41 2 737-760
[25]
Krištof P, Beneš B, Křivánek J, and Št’ava O Hydraulic erosion using smoothed particle hydrodynamics Comput. Graph. Forum 2009 28 2 219-228
[26]
Lengyel, E.: Voxel-based terrain for real-time virtual simulations, p. 148 (2010)
[27]
Mei, X., Decaudin, P., Hu, B.G.: Fast hydraulic erosion simulation and visualization on GPU. In: Proceedings - Pacific Conference on Computer Graphics and Applications, pp. 47–56 (2007).
[28]
Musgrave, F.K., Kolb, C.E., Mace, R.S.: The synthesis and rendering of eroded fractal terrains. In: Proceedings of the 16th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1989, pp. 41–50 (1989).
[29]
Neidhold, B., Wacker, M., Deussen, O.: Interactive physically based fluid and erosion simulation. Natural Phenomena, pp. 25–32 (2005)
[30]
O’Brien, J.F., Hodgins, J.K.: Dynamic simulation of splashing fluids. In: Proceedings Computer Animation, CA, pp. 198–205 (1995).
[31]
Olsen, J.: Realtime procedural terrain generation. Department of Mathematics And Computer Science ( ...) p. 20 (2004)
[32]
Onoue, K., Nishita, T.: A method for modeling and rendering dunes with wind-ripples. In: Proceedings - Pacific Conference on Computer Graphics and Applications 2000-January, pp. 427–428 (2000).
[33]
Paris A, Galin E, Peytavie A, Guérin E, and Gain J Terrain amplification with implicit 3d features ACM Trans. Graph. 2019 38 1-15
[34]
Paris A, Guérin E, Peytavie A, Collon P, and Galin E Synthesizing geologically coherent cave networks Comput. Graph. Forum 2021 40 277-287
[35]
Paris A, Peytavie A, Guérin E, Argudo O, and Galin E Desertscape simulation Comput. Graph. Forum 2019 38 47-55
[36]
Peytavie A, Galin E, Grosjean J, and Merillou S Arches: a framework for modeling complex terrains Comput. Graph. Forum 2009 28 457-467
[37]
Ranz WE, Talandis GR, and Gutterman B Mechanics of particle bounce I.Ch.E. J 1960 6 124-127
[38]
Richardson, J.F., Zaki, W.N.: The sedimentation of a suspension of uniform spheres under conditions of viscous flow. Chem. Eng. Sci. 3 (1954)
[39]
Rigaudière, D., Gesquière, G., Faudot, D.: Shape Modelling with Skeleton based Implicit Primitives. Methods (2000)
[40]
Roa, T., Benes, B.: Simulating desert scenery. Winter School of Computer Graphics SHORT communication Papers. In: Proceedings, pp. 17–22 (2004)
[41]
Roose, D., Leuven, K.U., López, Y.R.: Dynamic refinement for fluid flow simulations with sph particle refinement for fluid flow simulations with sph (2011)
[42]
Roudier P, Peroche B, and Perrin M Landscapes Synthesis Achieved through Erosion and Deposition Process Simulation Computer Graphics Forum 1993 12 3 375-383
[43]
Schott, H., Paris, A., Fournier, L., Guérin, E., Galin, E.: Large-scale terrain authoring through interactive erosion simulation (2023)
[44]
Smelik, R.M., Kraker, K.J.D., Groenewegen, S.A., Tutenel, T., Bidarra, R.: A survey of procedural methods for terrain modelling. Proceedings of the CASA workshop on 3D advanced media in gaming and simulation (3AMIGAS) (2009)
[45]
Stachniak, S., Stuerzlinger, W.: An algorithm for automated fractal terrain deformation. In Proceedings of Computer Graphics and Artificial Intelligence pp. 64–76 (2005)
[46]
Stam, J.: Stable fluids. Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1999 pp. 121–128 (1999).
[47]
Stam, J.: Flows on surfaces of arbitrary topology. ACM Transactions on Graphics 22(3), 724–731 (2003).
[48]
Stokes, G.G.: On the Effect of the Internal Friction of Fluids on the Motion of Pendulums, pp. 1–10. Cambridge University Press (2009).
[49]
Swope WC, Andersen HC, Berens PH, and Wilson KR A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters J. Chem. Phys. 1982 76 1 637-649
[50]
Tychonievich, L.A., Jones, M.D.: Delaunay deformable mesh for the weathering and erosion of 3D terrain. Visual Computer 26(12), 1485–1495 (2010).
[51]
Verlet, L.: Computer "experiments" on classical fluids. i. thermodynamical properties of lennard-jones molecules. Phys. Rev. 159, 98–103 (1967).
[52]
Wojtan, C., Carlson, M., Mucha, P.J., Turk, G.: Animating corrosion and erosion. Natural Phenomena pp. 15–22 (2007)
[53]
Yan, P., Zhang, J., Kong, X., Fang, Q.: Numerical simulation of rockfall trajectory with consideration of arbitrary shapes of falling rocks and terrain. Computers and Geotechnics 122 (2020).

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Published In

cover image The Visual Computer: International Journal of Computer Graphics
The Visual Computer: International Journal of Computer Graphics  Volume 40, Issue 7
Jul 2024
502 pages

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 05 June 2024
Accepted: 30 April 2024

Author Tags

  1. Procedural modeling
  2. Terrain morphing
  3. Natural phenomena
  4. Erosion processes

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