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DOI: 10.14489/vkit.2022.12.pp.012-020
Вяткин С. И., Долговесов Б. С.
РЕНДЕРИНГ НЕОДНОРОДНЫХ ОБЪЕМОВ С ПРИМЕНЕНИЕМ ФУНКЦИЙ ВОЗМУЩЕНИЯ
(с. 12-20)
Аннотация. Представлен метод рендеринга неоднородных объемов с применением функций возмущения. Предлагается подход для выборки путей передачи света в неоднородных средах. Для ускорения вычислений неоднородная среда разбивается на однородную и остаточную части. Остаточная часть представляет собой разность между неоднородной и однородной средой. Для однородной части строятся пути передачи света в аналитическом виде. Далее используется алгоритм отслеживания путей. Выборки в пути передачи света в однородной и остаточной частях делаются отдельно. Это позволяет свести к минимуму дорогостоящие вычисления коэффициентов прямого рассеяния, которые изменяются при обходе пространства.
Ключевые слова: функции возмущения; неоднородный объем; рендеринг; выборка; коэффициент пропускания; отслеживание пути.
Vyatkin S. I., Dolgovesov B. S.
RENDERING OF INHOMOGENEOUS VOLUMES USING PERTURBATION FUNCTIONS
(pp. 12-20)
Abstract. Modeling of light transmission in heterogeneous volumes is of great importance in many fields, such as medical imaging, scientific visualization and synthesis of realistic images. Visual effects use complex three-dimensional structures such as smoke and clouds. However, modeling light transmission requires many calculations. For example, Monte-Carlo methods, which are based on path tracing, require the construction of a huge number of light paths. At the same time, each light path consists of thousands of scattering parts. A method for rendering inhomogeneous volumes using perturbation functions is presented. An approach is proposed for sampling light transmission paths in inhomogeneous media. The approach is based on the radiation transfer equation, using the integral formulation of the direct scattering algorithm. Bounding shells based on perturbation functions are used. To speed up calculations an inhomogeneous medium is divided into homogeneous and residual parts. The residual part is the difference between an inhomogeneous and homogeneous medium. For a homogeneous part light transmission paths are constructed in an analytical form. Next, the path-tracing algorithm is used. Samples in the light transmission path in the homogeneous and residual parts are made separately. This minimizes the costly calculations of direct scattering coefficients that change when traversing space. The method has advantages in comparison with approaches using an octal tree, with a large volume resolution the efficiency of calculations increases. The results of the work are integrated into the path tracer. Objects based on perturbation functions as an acceleration structure are used. The empty space is determined and approximate local extremes of the base volumes are stored. Objects based on perturbation functions adapt to volume uniformity. Voluminous data sets based on voxels are stored. Performance is compared using the number of queries, visualization time, root mean square error and metrics, that is, the search in units of variance.
Keywords: Perturbation functions; Inhomogeneous volume; Rendering; Sampling; Transmission coefficient; Path-tracing.
С. И. Вяткин, Б. С. Долговесов (Институт автоматики и электрометрии Сибирского отделения Российской академии наук, Новосибирск, Россия) E-mail:
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S. I. Vyatkin, B. S. Dolgovesov (Institute of Automation and Electrometry of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia) E-mail:
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1. Mayer B. (2009). Radiative Transfer in the Cloudy Atmosphere. The European Physical Journal Conferences, Vol. 1, pp. 75 – 99. DOI: 10.1140/epjconf/e2009-00912-1
2. Reiter D. (2008). The Monte Carlo Method, an Introduction. Lecture Notes in Physics, Vol. 739, pp. 63 – 78. DOI: 10.1007/978-3-540-74686-7_3
3. Ueki T. (2017). Monte Carlo Criticality Analysis under Material Distribution Uncertainty. Journal of Nuclear Science and Technology, Vol. 54(3), pp. 267 – 279. DOI: 10.1080/00223131.2016.1260066
4. Salvat F., Fernandez-Varea J. M. (2009). Overview of Physical Interaction Models for Photon and Electron Transport Used in Monte Carlo Codes. Metrologia, Vol. 46(2). DOI: 10.1088/0026-1394/46/2/S08
5. Liu M., Ma Y., Guo X., Liu S. (2017). An Improved Tracking Method for Particle Transport Monte Carlo Simulations. Journal of Computational Physics, Vol. 437(5), 110330. DOI: 10.1016/j.jcp.2021.110330
6. Li W., Hahn J. K. (2021). Efficient Ray Casting Polygonized Isosurface of Binary Volumes. The Visual Computer, Vol. 37, pp. 3139 – 3149. DOI: 10.1007/s00371-021-02302-3
7. Yao R., Intes X., Fang Q. (2015). Generalized Mesh-Based Monte Carlo for Wide-Field Illumination and Detection Via Mesh Retessellation. Biomedical Optics Express, Vol. 7(1), pp. 171–184. DOI: 10.1364/BOE.7.000171
8. Tregan J.-M., Blanco S., Dauchet J., Mouna E. H. (2020). Convergence Issues in Derivatives of Monte Carlo Null-Collision Integral Formulations: A Solution. Journal of Computational Physics, Vol. 413(11):109463. DOI: 10.1016/j.jcp.2020.109463
9. Kettunen M., d'Eon E., Pantaleoni J., Novak J. (2021). An Unbiased Ray-Marching Transmittance Estimator. ACM Transactions on Graphics, Vol. 40(4), pp. 1 – 20. DOI: 10.1145/3476576.3476711
10. Yue Y. (2018). Bringing Computer and Physics Closer. Journal of Physics Conference Series, Vol. 1036(1):012013. DOI: 10.1088/1742-6596/1036/1/012013
11. Howell J. R., Daun K. (2021). The Past and Future of the Monte Carlo Method in Thermal Radiation Transfer. Journal of Heat Transfer, Vol. 143(10):100801. DOI: 10.1115/1.4050719
12. Vyatkin S. I. (2007). Complex Surface Modeling Using Perturbation Functions. Optoelectronics, Instrumentation and Data Processing, Vol. 43, (3), pp. 40 – 47.
13. Galtier M., Blanco S., Caliot C. et al. (2013). Integral Formulation of Null Collision Monte Carlo Algorithms. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 125, pp. 57 – 68. DOI: 10.1016/j.jqsrt.2013.04.001
14. Galtier M., Blanco S., Dauchet J. et al. (2016). Radiative Transfer and Spectroscopic Databases: A Line-Sampling Monte Carlo Approach. Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 172, pp. 83 – 97. DOI: 10.1016/j.jqsrt.2015.10.016
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