Abstract
Simulation of stellar atmospheres, such as that of our own sun, is a common task in CGI for scientific visualization, movies and games. A fibrous volumetric texture is a visually dominant feature of the solar corona---the plasma that extends from the solar surface into space. These coronal fibers can be modeled as magnetic filaments whose shape is governed by the magnetohydrostatic equation. The magnetic filaments provide a Lagrangian curve representation and their initial configuration can be prescribed by an artist or generated from magnetic flux given as a scalar texture on the sun's surface. Subsequently, the shape of the filaments is determined based on a variational formulation. The output is a visual rendering of the whole sun. We demonstrate the fidelity of our method by comparing the resulting renderings with actual images of our sun's corona.
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- M. D. Altschuler and G. Newkirk. 1969. Magnetic Fields and the Structure of the Solar Corona. Sol. Phys. 9, 1 (1969), 131--149.Google Scholar
Cross Ref
- A. Angelidis and F. Neyret. 2005. Simulation of Smoke based on Vortex Filament Primitives. In Proc. Symp. Comp. Anim. ACM, New York, NY, USA, 87--96.Google Scholar
- B. Angles, D. Rebain, M. Macklin, B. Wyvill, L. Barthe, J. P. Lewis, J. von der Pahlen, S. Izadi, J. Valentin, S. Bouaziz, and A. Tagliasacchi. 2019. VIPER: Volume Invariant Position-Based Elastic Rods. Proc. ACM Comput. Graph. Interact. Tech. 2, 2 (2019), 19:1--19:26.Google Scholar
- M. J. Aschwanden, K. Reardon, and D. B. Jess. 2016. Tracing the Chromospheric and Coronal Magnetic Field with AIA, IRIS, IBIS, and ROSA Data. Astrophys. J. 826, 1 (2016), 61.Google Scholar
Cross Ref
- P. Boerner, C. Edwards, J. Lemen, A. Rausch, C. Schrijver, R. Shine, L. Shing, R. Stern, T. Tarbell, C. J. Wolfson, et al. 2012. Initial Calibration of the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO). Sol. Phys. 275, 1--2 (2012), 41--66.Google Scholar
Cross Ref
- K. Borkiewicz, A. J. Christensen, D. Berry, C. Fluke, G. Shirah, and K. Elkins. 2019. Cinematic Scientific Visualization: The Art of Communicating Science. In SIGGRAPH Asia 2019 Courses. ACM, New York, NY, USA, Article 107, 313 pages.Google Scholar
- CADENS. 2015. Solar Superstorms. Centrality of Advanced Digitally ENabled Science.Google Scholar
- R. Chodura and A. Schlüter. 1981. A 3D code for MHD Equilibrium and Stability. J. Comput. Phys. 41, 1 (1981), 68--88.Google Scholar
Cross Ref
- C. E. DeForest and C. C. Kankelborg. 2007. Fluxon Modeling of Low-Beta Plasmas. J. Atmos. Sol.-Terr. Phys. 69, 1 (2007), 116--128.Google Scholar
Cross Ref
- V. Garcia, E. Debreuve, and M. Barlaud. 2008. Fast k Nearest Neighbor Search using GPU. In 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops. IEEE, Anchorage, AK, USA, 1--6.Google Scholar
- F. A. Gent, V. Fedun, S. J. Mumford, and R. Erdélyi. 2013. Magnetohydrostatic Equilibrium - I. Three-Dimensional Open Magnetic Flux Tube in the Stratified Solar Atmosphere. Mon. Notices Royal Astron. Soc. 435, 1 (2013), 689--697.Google Scholar
Cross Ref
- J. Gómez, J. Blinn, D. Em, and S. Rueff. 2017. History of the JPL Computer Graphics Lab. ACM SIGGRAPH 2017 Panel.Google Scholar
- H. Grad and H. Rubin. 1958. Hydromagnetic Equilibria and Force-Free Fields. J. nucl. Energy 7, 3--4 (1958), 284--285.Google Scholar
- J. Gross, M. Köster, and A. Krüger. 2019. Fast and Efficient Nearest Neighbor Search for Particle Simulations. In Computer Graphics and Visual Computing (CGVC). The Eurographics Association, 55--63.Google Scholar
- S. Hadap and N. Magnenat-Thalmann. 2001. Modeling Dynamic Hair as a Continuum. Comp. Graph. Forum 20, 3 (2001), 329--338.Google Scholar
Cross Ref
- D. Hahn and C. Wojtan. 2015. High-Resolution Brittle Fracture Simulation with Boundary Elements. ACM Trans. Graph. 34, 4 (2015), 1--12.Google Scholar
Digital Library
- B. Inhester and T. Wiegelmann. 2006. Nonlinear Force-Free Magnetic Field Extrapolations: Comparison of the Grad Rubin and Wheatland Sturrock Roumeliotis Algorithm. Sol. Phys. 235, 1 (2006), 201--221.Google Scholar
Cross Ref
- Å. M. Janse, B. C. Low, and E. N. Parker. 2010. Topological Complexity and Tangential Discontinuity in Magnetic Fields. Phys. Plasmas. 17, 9 (2010), 092901.Google Scholar
Cross Ref
- R. Jonker and A. Volgenant. 1987. A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems. Comp. 38, 4 (1987), 325--340.Google Scholar
Digital Library
- R. Kippenhahn and A. Schlüter. 1957. Eine Theorie der Solaren Filamente. Mit 7 Textabbildungen. Z. Astrophys. 43 (1957), 36--62.Google Scholar
- R. Lionello, J. A. Linker, and Z. Mikić. 2008. Multispectral Emission of the Sun During the First Whole Sun Month: Magnetohydrodynamic Simulations. Astrophys. J. 690, 1 (2008), 902.Google Scholar
Cross Ref
- B. C. Low. 1982. Magnetostatic atmospheres with variations in three dimensions. Astrophys. J. 263 (1982), 952--969.Google Scholar
Cross Ref
- G. M. Machado, F. Sadlo, T. Müller, D. Müller, and T. Ertl. 2012. Visualizing Solar Dynamics Data. In Vision, Modeling and Visualization. The Eurographics Association, 95--102.Google Scholar
- H. Moradi, C. Baldner, A. C. Birch, D. C. Braun, R. H. Cameron, T. L. Duvall, L. Gizon, D. Haber, S. M. Hanasoge, B. W. Hindman, J. Jackiewicz, E. Khomenko, R. Komm, P. Rajaguru, M. Rempel, M. Roth, R. Schlichenmaier, H. Schunker, H. C. Spruit, K. G. Strassmeier, M. J. Thompson, and S. Zharkov. 2010. Modeling the Subsurface Structure of Sunspots. Sol. Phys. 267, 1 (2010), 1--62.Google Scholar
Cross Ref
- M. S. Nabizadeh, A. Chern, and R. Ramamoorthi. 2021. Kelvin Transformations for Simulations on Infinite Domains. ACM Trans. Graph. 40, 4 (2021), 97:1--97:15.Google Scholar
Digital Library
- J. P. Naiman, K. Borkiewicz, and A. J. Christensen. 2017. Houdini for Astrophysical Visualization. Publ. Astron. Soc. Pac. 129, 975 (2017), 058008.Google Scholar
Cross Ref
- NASA Scientific Visualization Studio. 2018. The Dynamic Solar Magnetic Field with Introduction.Google Scholar
- NASA Solar Dynamics Observatory. 2022. NASA AIA/HMI Data.Google Scholar
- M. Negri. 2021. A Quasi-Static Model for Craquelure Patterns. In Mathematical Modeling in Cultural Heritage. Springer, Cham, 147--164.Google Scholar
- M. Padilla, A. Chern, F. Knöppel, U. Pinkall, and P. Schröder. 2019. On Bubble Rings and Ink Chandeliers. ACM Trans. Graph. 38, 4 (2019), 129:1--129:14.Google Scholar
Digital Library
- E. N. Parker. 1994. Spontaneous Current Sheets in Magnetic Fields: With Applications to Stellar X-Rays. Vol. 1. Ox. U. P., New York, NY.Google Scholar
- Y. Peng, B. Deng, J. Zhang, F. Geng, W. Qin, and L. Liu. 2018. Anderson Acceleration for Geometry Optimization and Physics Simulation. ACM Trans. Graph. 37, 4 (2018), 42:1--42:14.Google Scholar
Digital Library
- H. Peter, S. Bingert, and S. Kamio. 2012. Catastrophic Cooling and Cessation of Heating in the Solar Corona. Astron. Astrophys. 537 (2012), A152.Google Scholar
Cross Ref
- E. R. Priest. 2014. Magnetohydrodynamics of the Sun. Cam. U. P.Google Scholar
- E. R. Priest. 2019. Magnetohydrodynamics and Solar Dynamo Action. In The Sun as a Guide to Stellar Physics. Elsevier, 239--266.Google Scholar
- C. Prior and A. R. Yeates. 2016a. Twisted Versus Braided Magnetic Flux Ropes in Coronal Geometry - I. Construction and Relaxation. Astron. Astrophys. 587 (2016), 15.Google Scholar
- C. Prior and A. R. Yeates. 2016b. Twisted Versus Braided Magnetic Flux Ropes in Coronal Geometry - II. Comparative Behaviour. Astron. Astrophys. 591 (2016), 20.Google Scholar
- L. A. Rachmeler, C. E. DeForest, and C. C. Kankelborg. 2009. Reconnectionless CME Eruption: Putting the Aly-Sturrock Conjecture to Rest. Astrophys. J. 693, 2 (2009), 1431--1436.Google Scholar
Cross Ref
- F. Reale. 2014. Coronal Loops: Observations and Modeling of Confined Plasma. Living Rev. Sol. Phys. 11, 1 (2014), 1--94.Google Scholar
Cross Ref
- F. Reale and G. Peres. 1999. TRACE-Derived Temperature and Emission Measure Profiles along Long-Lived Coronal Loops: The Role of Filamentation. Astrophys. J. Lett. 528, 1 (1999), L45.Google Scholar
Cross Ref
- M. Reddiger and B. Poirier. 2020. On the Differentiation Lemma and the Reynolds Transport Theorem for Manifolds with Corners. arXiv:1906.03330 [math-ph]Google Scholar
- R. Rosner, W. H. Tucker, and G. S. Vaiana. 1978. Dynamics of the Quiescent Solar Corona. Astrophys. J. 220 (1978), 643--645.Google Scholar
Cross Ref
- T. Sakurai. 1982. Green's Function Methods for Potential Magnetic Fields. Sol. Phys. 76, 2 (1982), 301--321.Google Scholar
Cross Ref
- C. J. Schrijver and M. L. DeRosa. 2003. Photospheric and Heliospheric Magnetic Fields. Solar Physics 212, 1 (2003), 165--200.Google Scholar
Cross Ref
- C. J. Schrijver, A. W. Sandman, M. J. Aschwanden, and M. L. De Rosa. 2005. Coronal Heating and the Appearance of Solar and Stellar Coronae. In 13th Cambridge Workshop on Cool Stars, Stellar Systems and the Sun, Vol. 560. European Space Agency, 65.Google Scholar
- N. R. Sheeley, C. R. DeVore, and J. P. Boris. 1985. Simulations of the Mean Solar Magnetic Field During Sunspot Cycle 21. Sol. Phys. 98, 2 (1985), 219--239.Google Scholar
Cross Ref
- D. Stansby, A. R. Yeates, and S. T. Badman. 2020. pfsspy: A Python Package for Potential Field Source Surface Modelling. J. Open Source Softw. 5, 54 (2020), 2732.Google Scholar
Cross Ref
- V. S. Titov, C. Downs, Z. Mikić, T. Török, J. A. Linker, and R. M. Caplan. 2018. Regularized Biot-Savart Laws for Modeling Magnetic Flux Ropes. Astrophys. J. Lett. 852, 2 (2018), L21.Google Scholar
Cross Ref
- R. Toader and C. Zanini. 2009. An Artificial Viscosity Approach to Quasistatic Crack Growth. Bolletino dell Unione Mat. Ital. 2, 1 (2009), 1--35.Google Scholar
- H. P. Warren, N. A. Crump, I. Ugarte-Urra, X. Sun, M. J. Aschwanden, and T. Wiegelmann. 2018. Toward a Quantitative Comparison of Magnetic Field Extrapolations and Observed Coronal Loops. Astrophys. J. 860, 1 (2018), 46.Google Scholar
Cross Ref
- S. Weißmann and U. Pinkall. 2010. Filament-based Smoke with Vortex Shedding and Variational Reconnection. ACM Trans. Graph. 29, 4 (2010), 115:1--12.Google Scholar
Digital Library
- T. Wiegelmann and S. K. Solanki. 2004a. Similarities and Differences between Coronal Holes and the Quiet Sun: Are Loop Statistics the Key? Sol. Phys. 225, 2 (2004), 227--247.Google Scholar
Cross Ref
- T. Wiegelmann and S. K. Solanki. 2004b. Why Are Coronal Holes Indistinguishable from the Quiet Sun in Transition Region Radiation?. In SOHO 15 Coronal Heating, Vol. 575. European Space Agency, 35.Google Scholar
- T. Williams, R. W. Walsh, A. R. Winebarger, D. H. Brooks, J. W. Cirtain, B. De Pontieu, L. Golub, K. Kobayashi, D. E. McKenzie, R. J. Morton, H. Peter, L. A. Rachmeler, S. L. Savage, P. Testa, S. K. Tiwari, H. P. Warren, and B. J. Watkinson. 2020. Is the High-Resolution Coronal Imager Resolving Coronal Strands? Results from AR 12712. Astrophys. J. 892, 2 (2020), 134.Google Scholar
Cross Ref
- A. R. Winebarger, H. P. Warren, and D. A. Falconer. 2008. Modeling X-Ray Loops and EUV "Moss" in an Active Region Core. Astrophys. J. 676, 1 (2008), 672.Google Scholar
Cross Ref
- A. R. Yeates. 2020. How Good is the Bipolar Approximation of Active Regions for Surface Flux Transport? Sol. Phys. 295, 9 (2020), 119.Google Scholar
Cross Ref
- A. R. Yeates, T. Amari, I. Contopoulos, X. Feng, D. H. Mackay, Z. Mikić, T. Wiegelmann, J. Hutton, C. A. Lowder, H. Morgan, et al. 2018. Global Non-Potential Magnetic Models of the Solar Corona During the March 2015 Eclipse. Space Sci. Rev. 214, 5 (2018), 99.Google Scholar
- C. Yu, H. Schumacher, and K. Crane. 2021. Repulsive Curves. ACM Trans. Graph. 40, 2 (2021), 268:1--268:19.Google Scholar
Digital Library
- J. Zhuleku, J. Warnecke, and H. Peter. 2020. Stellar Coronal X-ray Emission and Surface Magnetic Flux. Astron. Astrophys. 640 (2020), A119.Google Scholar
Cross Ref
Index Terms
Filament based plasma
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