Abstract
Most of the phenomena that are relevant to computer animation are inherently non-linear. These include the equations governing the flow of smoke and water, the dynamics of skin and flesh, and functions that form intricate Julia sets. Which of these non-linearities are visually important, and which just introduce unnecessary trouble? I examine a few case studies.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Braverman M, Yampolsky M (2006) Non-computable Julia sets. J Am Math Soc 19(3):551–578
Bridson R, Houriham J, Nordenstam M (2007) Curl-noise for procedural fluid flow. ACM Trans Graph 26(3)
Douady A, Hubbard JH, Lavaurs P (1984) Etude dynamique des polynômes complexes
Hart JC, Sandin DJ, Kauffman LH (1989) Ray tracing deterministic 3-d fractals. In: ACM SIGGRAPH computer graphics, vol 23. ACM, pp 289–296
Irving G, Teran J, Fedkiw R (2004) Invertible finite elements for robust simulation of large deformation. In: Proceedings of the 2004 ACM SIGGRAPH/eurographics symposium on computer animation, SCA ’04. Eurographics Association, Aire-la-Ville, Switzerland, pp 131–140. https://doi.org/10.1145/1028523.1028541
Kim B, Liu Y, Llamas I, Rossignac J (2005) Flowfixer: using BFECC for fluid simulation. In: Eurographics conference on natural phenomena, pp 51–56
Kim T (2015) Quaternion Julia set shape optimization. Comput Graph Forum 34(5):167–176
Kim T, Tessendorf J, Thürey N (2013) Closest point turbulence for liquid surfaces. ACM Trans Graph 32(2):15:1–15:13
Kim T, Thürey N, James D, Gross M (2008) Wavelet turbulence for fluid simulation. ACM Trans Graph 27(3):50:1–50:6
Lindsey KA, Younsi M (2016) Fekete polynomials and shapes of Julia sets. arXiv:1607.05055
Losasso F, Gibou F, Fedkiw R (2004) Simulating water and smoke with an octree data structure. ACM Trans Graph 23(3):457–462
Mandelbrot BB, Pignoni R (1983) The fractal geometry of nature, vol 173. WH Freeman, New York
Mercier O, Beauchemin C, Thuerey N, Kim T, Nowrouzezahrai D (2015) Surface turbulence for particle-based liquid simulations. ACM Trans Graph 34(6):202:1–202:10
Mullen P, Crane K, Pavlov D, Tong Y, Desbrun M (2009) Energy-preserving integrators for fluid animation. ACM Trans Graph 28(3):38:1–38:8
Müller M, Dorsey J, McMillan L, Jagnow R, Cutler B (2002) Stable real-time deformations. In: Proceedings of the ACM SIGGRAPH/eurographics symposium on computer animation, pp 49–54
Narain R, Sewall J, Carlson M, Lin MC (2008) Fast animation of turbulence using energy transport and procedural synthesis. ACM Trans Graph 27(5):166:1–166:8
Norton A (1982) Generation and display of geometric fractals in 3-d. In: ACM SIGGRAPH computer graphics, vol 16. ACM, pp 61–67
Sanders J, Kandrot E (2010) CUDA by example: an introduction to general-purpose GPU programming, portable documents. Addison-Wesley Professional, Boston
Savelsberg R, van de Water W (2008) Turbulence of a free surface. Phys. Rev. Lett. 100:034,501. https://doi.org/10.1103/PhysRevLett.100.034501
Selle A, Fedkiw R, Kim B, Liu Y, Rossignac J (2008) An unconditionally stable maccormack method. J Sci Comput 35(2):350–371
Stam J (1999) Stable fluids. In: Proceedings of SIGGRAPH, pp 121–128
Stam J, Fiume E (1993) Turbulent wind fields for gaseous phenomena. In: Proceedings of the 20th annual conference on computer graphics and interactive techniques, pp 369–376
Zhang X, Bridson R, Greif C (2015) Restoring the missing vorticity in advection-projection fluid solvers. ACM Trans Graph 34(4):52:1–52:8
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Kim, T. (2019). Just Enough Non-linearity. In: Dobashi, Y., Kaji, S., Iwasaki, K. (eds) Mathematical Insights into Advanced Computer Graphics Techniques. MEIS MEIS 2016 2017. Mathematics for Industry, vol 32. Springer, Singapore. https://doi.org/10.1007/978-981-13-2850-3_7
Download citation
DOI: https://doi.org/10.1007/978-981-13-2850-3_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-2849-7
Online ISBN: 978-981-13-2850-3
eBook Packages: EngineeringEngineering (R0)