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DOI: 10.14489/vkit.2024.06.pp.014-022
Вяткин С. И., Долговесов Б. С.
МОДЕЛИРОВАНИЕ ДИНАМИКИ ДЕФОРМИРУЕМЫХ ОБЪЕКТОВ НА ОСНОВЕ ОБЪЕМНЫХ ПАТЧЕЙ СВОБОДНЫХ ФОРМ
(c.14-22)
Аннотация. Предложен метод решения нелинейных задач неявного численного интегрирования на основе объемных патчей свободных форм для моделирования деформируемых объектов с высокоскоростной динамикой. Данный метод повышает точность, согласованность и управляемость моделирования деформации и анимации. Он отличается быстродействием, точностью, стабильностью и хорошо подходит для моделирования деформируемых тел с большим временным шагом в широком диапазоне динамики деформации.
Ключевые слова: анимация; деформация; оптимизация; объемные патчи свободных форм.
Vyatkin S. I., Dolgovesov B. S.
MODELING THE DYNAMICS OF DEFORMABLE OBJECTS BASED ON VOLUMETRIC PATCHES OF FREE FORMS
(pp.14-22)
Abstract. A method for solving nonlinear implicit numerical integration problems based on volumetric patches of free forms for modeling deformable objects with high-speed dynamics is proposed. This method improves the accuracy, consistency and controllability of deformation modeling and animation. The method is characterized by speed, accuracy, stability and uses optimization with region decomposition. The method is well suited for modeling deformable bodies with a large time step, in a wide range of deformation dynamics. We propose decomposed optimization, an optimization method based on free-form patches with region decomposition to minimize incremental potentials at each time step. The method uses quadratic matrix decomposition to combine non-overlapping subregions. The Hessian is evaluated once at the beginning of the time step. The advantages of the method are as follows. Geometric primitives and their mathematical models are proposed, which allow the reasonable application of these primitives to solve problems of volume-oriented modeling. Such requirements are met by volumetric patches of free forms based on analytical perturbation functions relative to the base triangles. The decomposed Hessian is constructed for each subregion and calculated using a set of vertices taken from a complete non-decomposed grid. The weights add the missing second-order Hessian data to the vertices of the subregions from the neighbors along the decomposition boundaries. Thanks to this, the descent is performed along the grid coordinates. There is no need to add gradients. During the descent, the gradient is determined. The Hessians under the region are calculated and factorized in parallel once per time step. They are used as an initializer at each iteration. Then the results are mixed together. This ensures stable and continuous high-quality modeling. An automated and reliable optimization method adapted for modeling nonlinear materials, high-speed dynamics and large deformations is proposed.
Keywords: Animation; Deformation; Optimization; Volumetric patches of free forms.
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. Tangherloni A., Nobile M. S., Cazzaniga P., Capitoli G. (2021). FiCoS: A fine-grained and coarse-grained GPU-powered deterministic simulator for bio-chemical networks. PLoS Computational Biology, 17(9), 1 – 16. DOI: 10.1371/journal.pcbi.1009410
2. Guihal J. M., Auger F., Bernard N., Schaeffer E. (2022). Efficient Implementation of Continuous-Discrete Extended Kalman Filters for State and Parameter Estimation of Nonlinear Dynamic Systems. IEEE Transactions on Industrial Informatics, 18(5), 3077 – 3085. DOI: 10.1109/TII.2021.3109095
3. Vabishchevich P. (2017). Two-level schemes for the advection equation. Journal of Computational Physics, 363(3), 1 – 28. DOI: 10.1016/j.jcp.2018.02.044
4. Vabishchevich P. (2019). Three-Level Schemes for the Advection Equation. Differential Equations, 55(7), 905 – 914. DOI: 10.1134/S0012266119070048
5. Wang X., Li M., Fang Y., Zhang X. (2020). Hierarchical Optimization Time Integration for CFL-Rate MPM Stepping. ACM Transactions on Graphics, 39(3), 1 – 16. DOI: 10.1145/3386760
6. Zhang M., Wang T., Ceylan D., Mitra N. J. (2021). Deep Detail Enhancement for Any Garment. Computer Graphics Forum, 40(2), 399 – 411. DOI: 10.1111/cgf.142642
7. Lyu W., Wang X. (2021). Stokes–Darcy system, small-Darcy-number behaviour and related interfacial conditions. Journal of Fluid Mechanics, 922, 1 – 26. Moscow. DOI: 10.1017/jfm.2021.509
8. Bornia G., Chierici A., Chirco L., Giovacchini V. (2021). A multigrid local smoother approach for a domain decomposition solver over nonmatching grids. Numerical Methods for Partial Differential Equations, 38(2), 1794 – 1822. DOI: 10.1002/num.22835
9. Aanjaneya M., Gao M., Liu H., Batty C. (2017). Power diagrams and sparse paged grids for high resolution adaptive liquids. ACM Transactions on Graphics, 36(4), 1 – 12. DOI: 10.1145/3072959.3073625
10. Qu Z., Zhang X., Gao M., Jiang C. (2019). Effi-cient and conservative fluids using bidirectional mapping. ACM Transactions on Graphics, 38(4), 1 – 12. DOI: 10.1145/3306346.3322945
11. Zhang J., Zhong Y., Gu C. (2018). Ellipsoid bounding region-based ChainMail algorithm for soft tissue deformation in surgical simulation. International Journal on Interactive Design and Manufacturing (IJIDeM), 12, 903 – 918, Project: Real-Time Simulation of Soft Tissue Deformation for Surgical Simulation, DOI: 10.1007/s12008-017-0437-5
12. Yin H., Varava A., Kragic D. (2021). Modeling, learning, perception, and control methods for deformable object manipulation. Science Robotics, 54(6), eabd8803. DOI: 10.1126/scirobotics.abd8803
13. Abdulali A., Jeon S. (2021). Data-driven Haptic Modeling of Plastic Flow via Inverse Reinforcement Learning. IEEE World Haptics Conference, 115 – 120. Montreal. DOI: 10.1109/WHC49131.2021.9517181
14. Bergou E. H., Diouane Y., Kungurtsev V., Diouane Y. (2021). Complexity iteration analysis for strongly convex multi-objective optimization using a Newton path-following procedure. Optimization Letters, 15(4), 1215 – 1227. DOI: 10.1007/s11590-020-01623-x
15. Naitsat A., Naitzat G., Zeevi Y. Y. (2021). On Inversion-Free Mapping and Distortion Minimization. Journal of Mathematical Imaging and Vision, 63(6), 974 – 1009. DOI: 10.1007/s10851-021-01038-y
16. Vyatkin S. I., Dolgovesov B. S. (2023). Method of anisotropic deformation of elastic materials based on free-form patches. BOHR International Journal of Biocomputing and Nano Technology, 2(1), 8 – 13. DOI: 10.54646/bijbnt.2023.12
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