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DOI: 10.14489/vkit.2025.05.pp.003-009
Вяткин С. И., Долговесов Б. С.
МЕТОД АНИМАЦИИ ЭНЕРГЕТИЧЕСКОГО РАЗРУШЕНИЯ ФУНКЦИОНАЛЬНО ЗАДАННЫХ ОБЪЕКТОВ
(с. 3-9)
Аннотация. Анимация разрушения трехмерных объектов – одна из важных задач компьютерной графики. Существуют методы анимации, основанные на механике сплошных сред. Они физически точны, но требуют затратных вычислений упругой деформации. Альтернативные методы моделирования основаны на динамике твердого тела с ограничениями при его разрушении. Простое удаление ограничений при достижении пороговых значений силы или смещения игнорирует упругую энергию. Здесь предложен метод разрушения функционально заданных объектов. При этом вычисляется внутренняя энергия, которая накапливается непосредственно перед разрушением объектов и в последующем преобразуется в кинетическую энергию. Это позволяет избежать дорогостоящих вычислений механики сплошных сред. В результате вычисления являются физически точными, а по времени сопоставимы с вычислительной эффективностью моделирования твердого тела.
Ключевые слова: функционально заданный объект; разрушение; динамика; физическое моделирование.
Vyatkin S. I., Dolgovesov B. S.
A METHOD FOR ANIMATING THE ENERGY DESTRUCTION OF FUNCTIONALLY DEFINED OBJECTS
(pp. 3-9)
Abstract. The animation of the destruction of three-dimensional objects is an important task of computer graphics. For this, there are methods based on continuum mechanics that are physically accurate, but require expensive calculations of elastic deformation. Alternative modeling methods are based on the dynamics of a rigid body with constraints on its fracture. Simply removing constraints when force or displacement thresholds are reached ignores elastic energy. The main advantages of the rigid body approach are simplicity and speed, however, this method is not physically accurate. For realistic animation of destruction, it is necessary to take into account the internal elastic energy, which is converted into kinetic energy of individual parts during destruction. The internal elastic energy, partially converted into kinetic energy of individual parts during destruction, is an important element of realistic destruction animation. This aspect is missing from existing solid-state approaches. We remove this limitation by measuring energy and converting it into kinetic energy, which leads to a more realistic simulation of destruction. The purpose of this work is to eliminate the limitations of the rigid body method by measuring the energy accumulated in the constraints during the dynamics of functionally specified objects, and explicitly converting it into kinetic energy by applying pulses when the constraints are removed. In this paper, we propose a method for destroying functionally specified objects. The momentum is calculated in one time step based on the mass of the objects involved, the direction of the forces and torques applied by the constraint. The direction determined by the momentum of the resolution restriction in the previous time step is calculated. The direction orthogonal to the torque and linear forces applied by the constraint before breaking is selected. This leads to movement in directions corresponding to the moment created by bending or stretching deformations. Since only one object is considered when calculating the pulse, coupling can be ignored due to any remaining constraints in the system and damping. This simplifies calculations and improves the manageability of the method. The approach calculates the energy that accumulates immediately before the destruction of objects. It is then reused as kinetic energy. This avoids expensive calculations of continuum mechanics. As a result, the calculations are physically accurate, and the time is comparable to the computational efficiency of modeling a solid body.
Keywords: Functionally defined object; Destruction; Dynamics; Physical modeling.
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. Mandal A., Chaudhuri P., Chaudhuri S. (2022). Remeshing-free Graph-based Finite Element Method for Fracture Simulation. Computer Graphics Forum, 42(4), 117 – 134. DOI: 10.1111/cgf.14725
2. Wolper J. (2021). Material Point Methods for Simulating Material Fracture. Thesis for: PhDAdvisor: Chenfanfu Jiang. DOI: 10.13140/RG.2.2.16345.60001
3. Fan L., Chitalu F. M., Komura T. (2022). Simulating Brittle Fracture with Material Points. ACM Transactions on Graphics, 41(5), 1 – 20. DOI: 10.1145/3522573
4. Yan M., Wu D. (2023). A New Fracture Simulation Algorithm Based On Peridynamics for Brittle Objects. IEEE Access, 11, 88609 – 88617. DOI: 10.1109/ACCESS.2023.3305631
5. Chen W., Zhu F., Zhao J. et al. (2017). Peridynamics-Based Fracture Animation for Elastoplastic Solids. Computer Graphics Forum, 37(2), 112 – 124. DOI: 10.1111/cgf.13236
6. Fichera S., Mariggio G., Corrado M., Ventura G. (2023). Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis. Algorithms, 16(6), 290 – 311. DOI: 10.3390/a16060290
7. Hahn D., Wojtan C. (2016). Fast approximations for boundary element based brittle fracture simulation. ACM Transactions on Graphics, 35(4), 1 – 11. DOI: 10.1145/2897824.2925902
8. Lu J. M., Li C., Cao G. C., Hu S. M. (2022). Simulating Fractures with Bonded Discrete Element Method. IEEE Transactions on Visualization and Computer Graphics, 28(12), 4810 – 4824. DOI: 10.1109/TVCG.2021.3106738
9. Wolper J., Fang Y., Li M. et al. (2019). CD-MPM: continuum damage material point methods for dynamic fracture animation. ACM Transactions on Graphics, 38(4), 1 – 15. DOI: 10.1145/3306346.3322949
10. Wolper J., Chen Y., Li M. et al. (2020). AnisoMPM: Animating Anisotropic Damage Mechanics. ACM Transactions on Graphics, 39(4), 1 – 16. DOI: 10.1145/3386569.3392428
11. Chitalu F. M., Miao Q., Subr K., Komura T. (2020). Displacement-Correlated XFEM for Simulating Brittle Fracture. Computer Graphics Forum, 39(2), 569 – 583. DOI: 10.1111/cgf.13953
12. Thomas R., Zhang W. (2022). Real-time fracturing in video games. Multimedia Tools and Applications, 82(3), 1 - 26. DOI: 10.1007/s11042-022-13049-x
13. Wei X., Liu M., Ling Z., Su H. (2022). Approximate Convex Decomposition for 3D Meshes with Collision-Aware Concavity and Tree Search. ACM Transactions on Graphics, 41(4), 1 – 18. DOI: 10.1145/3528223.3530103
14. Vyatkin S. I., Dolgovesov B. S. (2018). Compression of Geometric Data with the Use of Perturbation Functions. Optoelectronics, Instrumentation and Data Processing, 54(4), 334 – 339. DOI: 10.3103/S8756699018040039
15. Yildirim S., Arslan E. (2018). ODE (Open Dynamics Engine) Based Walking Control Algorithm for Six Legged Robot. Journal of New Results in Science, 7(2, 35 – 46. DOI: 10.1016/J.MEASUREMENT.2018.03.057
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