This Article 
 Bibliographic References 
 Add to: 
Directable Weathering of Concave Rock Using Curvature Estimation
January/February 2010 (vol. 16 no. 1)
pp. 81-94
Michael D. Jones, Brigham Young University, Provo
McKay Farley, Brigham Young University, Provo
Joseph Butler, Brigham Young University, Provo
Matthew Beardall, Caselle Inc., Spanish Fork
We address the problem of directable weathering of exposed concave rock for use in computer-generated animation or games. Previous weathering models that admit concave surfaces are computationally inefficient and difficult to control. In nature, the spheroidal and cavernous weathering rates depend on the surface curvature. Spheroidal weathering is fastest in areas with large positive mean curvature and cavernous weathering is fastest in areas with large negative mean curvature. We simulate both processes using an approximation of mean curvature on a voxel grid. Both weathering rates are also influenced by rock durability. The user controls rock durability by editing a durability graph before and during weathering simulation. Simulations of rockfall and colluvium deposition further improve realism. The profile of the final weathered rock matches the shape of the durability graph up to the effects of weathering and colluvium deposition. We demonstrate the top-down directability and visual plausibility of the resulting model through a series of screenshots and rendered images. The results include the weathering of a cube into a sphere and of a sheltered inside corner into a cavern as predicted by the underlying geomorphological models.

[1] Indiana Jones and the Temple of Doom, Lucasfilm, Ltd., 1984.
[2] The Mormons Part 2: Church and State, Public Broadcasting Service, Inc., 2007.
[3] Wile E. Coyote and Roadrunner: Zoom and Bored. Warner Brothers, 1957.
[4] Boundin. Pixar, 2003.
[5] Galaxy Quest. Dreamworks SKG, 1999.
[6] M. Gamito and F.K. Musgrave, “Procedural Landscapes with Overhangs,” Proc. 10th Portuguese Computer Graphics Meeting, pp.33-42, 2001.
[7] T. Ito, T. Fujimoto, K. Moraoka, and N. Chiba, “Modeling Rocky Scenery Taking into Account Joints,” Proc. Computer Graphics Int'l Conf., pp. 244-247, 2003.
[8] B. Beneš, V. Tšínský, J. Hornyš, and S. Bhatia, “Hydraulic Erosion,” Computer Animation and Virtual Worlds, vol. 17, no. 2, pp.99-108, 2006.
[9] F.K. Musgrave, C.E. Kolb, and R.S. Mace, “The Synthesis and Rendering of Eroded Fractal Terrains,” Proc. ACM SIGGRAPH, pp. 41-50, 1989.
[10] J. Dorsey, A. Edelman, H. Jensen, J. Legakis, and H. Pedersen, “Modeling and Rendering of Weathered Stone,” Proc. ACM SIGGRAPH, pp. 225-234, 1999.
[11] Bryce 6.0. DAZ Productions, 2006.
[12] Vue-6 infinite. e-on Software, 2006.
[13] Maya 2008. Autodesk, 2008.
[14] Blender 2.48a. Stichting Blender Foundation, 2008.
[15] S.W. Wang and A.E. Kaufman, “Volume Sculpting,” Proc. Symp. Interactive 3D Graphics (SI3D '95), pp. 151-156, 1995.
[16] M. Beardall, M. Farley, D. Ouderkirk, J. Smith, C. Rheimschussel, M. Jones, and P. Egbert, “Goblins by Spheroidal Weathering,” Proc. Eurographics Workshop Natural Phenomena, pp. 1-8, 2007.
[17] H. Huinink, L. Pel, and K. Kopinga, “Simulating the Growth of Tafoni,” Earth Surface Processes and Landforms, vol. 29, pp. 1225-1233, 2004.
[18] A.V. Turkington, “Cavernous Weathering in Sandtone: Lessons to be Learned from Natural Exposure,” Quarterly J. Eng. Geology, vol. 31, pp. 375-383, 1998.
[19] M. Milligan, “Geology of Goblin Valley State Park, Utah,” Geology of Utah's Parks and Monuments, Utah Geological Assoc. and Bryce Canyon Natural History Assoc., pp. 421-432, 2003.
[20] P. Prusinkiewicz, L. Mundermann, R. Karwowski, and B. Lane, “The Use of Positional Information in the Modeling of Plants,” Proc. ACM SIGGRAPH, pp. 289-300, 2001.
[21] Y. Dobashi, K. Kusumoto, T. Nishita, and T. Yamamoto, “Feedback Control of Cumuliform Cloud Formation Based on Computational Fluid Dynamics,” Proc. ACM SIGGRAPH, vol. 27, no. 3, 2008.
[22] T. Vicsek, “Pattern Formation in Diffusion-Limited Aggregation,” Physical Rev. Letters, vol. 53, no. 24, pp. 2281-2284, Dec. 1984.
[23] P. Pimienta, W. Carter, and E. Garboczi, “Cellular Automaton Algorithm for Surface Mass Transport Due to Curvature Gradients: Simulation of Sintering,” Computational Materials Science, vol. 1, pp. 63-77, 1992.
[24] B. Mandelbrot, The Fractal Geometry of Nature. W.H. Freeman and Co., 1982.
[25] A. Fournier, D. Fussell, and L. Carpenter, “Computer Rendering of Stochastic Models,” Comm. ACM, vol. 25, no. 6, pp. 371-384, June 1982.
[26] A. Kelley, M. Malin, and G. Nielson, “Terrain Simulation Using a Model of Stream Erosion,” Proc. ACM SIGGRAPH, pp. 263-268, 1988.
[27] N. Chiba, K. Muraoka, and K. Fujita, “An Erosion Model Based on Velocity Fields for the Visual Simulation of Mountain Scenery,” J.Visualization and Computer Animation, vol. 9, no. 4, pp. 185-194, 1998.
[28] F. Belhadj and P. Audibert, “Modeling Landscapes with Ridges and Rivers: Bottom up Approach,” Proc. Third Int'l Conf. Computer Graphics and Interactive Techniques in Australasia and South East Asia (GRAPHITE '05), pp. 447-450, 2005.
[29] Fractals in Nature: From Characterization to Simulation, H.-O. Peitgen and D. Saupe, eds., ch. 1, pp. 21-70. Springer-Verlag, 1988.
[30] P. Prusinkiewicz and M. Hammel, “A Fractal Model of Mountains with Rivers,” Proc. Graphics Interface Conf., pp. 174-180, 1993.
[31] K. Nagashima, “Computer Generation of Eroded Valley and Mountain Terrains,” The Visual Computer, vol. 13, pp. 456-464, 1997.
[32] O. Št'ava, B. Beneš, M. Brisbin, and J. Křivánek, “Interactive Terrain Modeling Using Hydraulic Erosion,” Proc. ACM Eurographics/Symp. Computer Animation, 2008.
[33] Y. Chen, L. Xia, T.-T. Wong, X. Tong, H. Bao, B. Guo, and H.-Y. Shum, “Visual Simulation of Weathering by $\gamma$ -Ton Tracing,” Proc. ACM SIGGRAPH, pp. 1127-1133, 2005.
[34] S. Hsu and T. Wong, “Simulating Dust Accumulation,” IEEE Computer Graphics and Applications, vol. 15, no. 1, pp. 18-22, Jan. 1995.
[35] R. Sarracino, G. Prasad, and M. Hoohlo, “A Mathematical Model of Spheroidal Weathering,” Math. Geology, vol. 19, pp. 269-289, 1987.
[36] G. Miller, “Efficient Algorithms for Local and Global Accessibility Shading,” Proc. ACM SIGGRAPH, pp. 319-326, 1994.
[37] K. Perlin, “An Image Synthesizer,” Computer Graphics, vol. 19, no. 3, pp. 287-296, 1985.
[38] W. Lorensen and H. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Proc. ACM SIGGRAPH, pp.163-169, 1987.
[39] C.R. Twidale and J.R.V. Romani, Landforms and Geology of Granite Terrains. CRC Press, 2005.
[40] Y. Matsukura and Y. Tanaka, “Effect of Rock Hardness and Moisture Content on Tafoni Weathering in the Granite of Mount Doeg-Sung, Korea,” Geografiska Annaler, vol. 82, pp. 59-67, 2000.

Index Terms:
Physically based modeling, modeling packages.
Michael D. Jones, McKay Farley, Joseph Butler, Matthew Beardall, "Directable Weathering of Concave Rock Using Curvature Estimation," IEEE Transactions on Visualization and Computer Graphics, vol. 16, no. 1, pp. 81-94, Jan.-Feb. 2010, doi:10.1109/TVCG.2009.39
Usage of this product signifies your acceptance of the Terms of Use.