基於混合式模型簡化法的形變模擬

Deformation Simulation Based on Hybrid Model Reduction

黃証揚(Cheng-Yang Huang)

指導教授 ： 林文杰 ； 黃世強

國立交通大學/資訊學院/多媒體工程研究所/碩士(2014年)

https://doi.org/10.6842/NCTU.2014.00752

摘要

In computer graphics, model reduction method that utilizes a low-dimensional subspace to approximate the original, high-dimensional deformation space can simulate deformation well in force-free conditions. However, when external forces are applied to the simulated objects, obvious differences between low-dimensional simulation and full-coordinate
simulation can be observed. Therefore, to improve the simulation accuracy of reduced deformable models when the external forces are applied and to retain its advantage
of fast run-time performance, we present a hybrid framework that utilizes bases constructed from forced and force-free deformations. The forced deformations are precomputed
from data of full-coordinate simulation by applying external forces to different parts of the deformable object. This problem is formulated as a force sampling problem
and solved by space partition and surface sampling. In the run-time stage, if there are external forces, we simulate deformation in the low-dimensional subspace of forced deformations. When the external forces are released, we simulate in another subspace by adopting the modal derivative bases because its computation is automatic and does not need any presimulation. To reduce the artifact in the transition, we linearly blend forced and force-free deformations. Our results show improved accuracy compared to the results of using only the modal derivative bases while the speedup over full-coordinate simulation is still significant.

關鍵字

形變模擬 ； 物理模擬 ； 模型簡化法 ； 有限元素法

並列摘要

In computer graphics, model reduction method that utilizes a low-dimensional subspace to approximate the original, high-dimensional deformation space can simulate deformation well in force-free conditions. However, when external forces are applied to the simulated objects, obvious differences between low-dimensional simulation and full-coordinate
simulation can be observed. Therefore, to improve the simulation accuracy of reduced deformable models when the external forces are applied and to retain its advantage
of fast run-time performance, we present a hybrid framework that utilizes bases constructed from forced and force-free deformations. The forced deformations are precomputed
from data of full-coordinate simulation by applying external forces to different parts of the deformable object. This problem is formulated as a force sampling problem
and solved by space partition and surface sampling. In the run-time stage, if there are external forces, we simulate deformation in the low-dimensional subspace of forced deformations. When the external forces are released, we simulate in another subspace by adopting the modal derivative bases because its computation is automatic and does not need any presimulation. To reduce the artifact in the transition, we linearly blend forced and force-free deformations. Our results show improved accuracy compared to the results of using only the modal derivative bases while the speedup over full-coordinate simulation is still significant.

並列關鍵字

Deformation Simulation ； Physical Simulation ； Model Reduction ； Finite Element Method

參考文獻

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