破碎的图形建模与绘制技术研究
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摘要
物体破碎现象的模拟不仅在游戏开发中备受关注，在其他一些领域，如电影特效制作、材料分析、军事仿真及虚拟战场环境等都有着重要的理论和实际意义。由于人们对于仿真、电影以及游戏中破碎现象模拟的真实感提出越来越高的要求，破碎模拟逐渐成为计算机图形学领域的一大热点问题。本文对破碎特效的图形建模方法及绘制技术进行了广泛而深入的研究，所做的主要工作和取得的成果有：
（1）针对传统的基于有限元分析的破碎模拟方法需要进行复杂的物理计算，难以满足游戏、仿真中实时性的要求问题，提出了一种基于Voronoi图的刚体破碎模拟方法，通过采用预先破碎计算处理技术，实现了具有较强物理真实感的刚体破碎实时模拟。首先对脆性刚体材料破碎过程进行分析，得到拟合性较好的正态分布种子点，在此基础上采用脱机增量算法和格雷厄姆凸壳生成算法生成刚体破碎的Voronoi多边形。然后，根据能量守恒方程和材料力学分析，得到破碎区和裂纹区的半径，并根据碰撞过程中的能量转换约束条件对破碎后的碎片速度进行推导，最后对碎片间的碰撞检测以及碰撞后的速度、姿态等进行计算。实验结果表明：该方法不仅能在交互性上满足游戏、仿真的实时性需求，同时碎片的产生以及运动符合真实的物理规律，具有较强的真实感。
（2）提出一种基于粒子和逆向破碎机制的物体受外力冲击破碎实时模拟方法。首先将对象物体离散成空间中的一系列粒子，然后采用扩展离散单元法（EDEM）来计算每个粒子的受力、加速度、速度及位置等属性；采用从微观到宏观的逆向破碎机制，通过聚类分析，将某些粒子重新组合，宏观上形成碎片；采用统一网格的数据结构，将物理计算映射到GPU通过CUDA进行计算。实验结果验证了所提出方法的有效性和鲁棒性。
（3）提出一种基于移动元胞自动机的非均质物体破碎建模与绘制方法。将对象物体离散成空间中的元胞集合，采用移动元胞自动机方法(Movable CellularAutomata, MCA)模拟物体的材料和物理属性，并决定破碎发生的条件。采用统一网格数据结构在CUDA上实现了基于MCA的破碎模拟计算，模拟计算结果存储在顶点缓冲对象中并直接运用GPU进行绘制。实验结果表明，本文方法能更为真实地模拟非均质材质的破碎现象，同时采用GPU技术大大提高了计算与绘制的效率，与同类方法相比，性能提升了1-2个数量级，绘制帧速率基本满足实时交互需求。
（4）针对传统无网格法在处理裂纹尖端应力场具有奇异性的问题，提出一种基于局部径向基点插值（LRPIM）的物体变形与破裂无网格模拟算法。在构造无网格法形函数时，对基函数进行径向扩充，添加一个奇异项，有效避免裂纹尖端模拟的奇异性；在此基础上，结合局部径向基点插值无网格法和基于损伤力学的破裂准则，实现了物体变形及破裂的模拟仿真过程。模拟结果由基于点的Splatting绘制技术进行显示。实验结果表明，相比以往的无网格的破碎模拟方法，本文方法解决了模拟裂纹尖端的奇异性问题，同时采用基于点的Splatting绘制技术提高了绘制的效率。
The simulation of the phenomenon of fracture has attracted widespread attention inrecent years. It has important theoretical and practical significance not only in gamedevelopment, but also in other areas, such as the production of movie special effects,materials analysis, military simulation and virtual battlefield environment, etc. As acommon physical phenomenon in everyday life, fracturing effects greatly affect theuser’s experience in virtual reality, computer game and film industry. Thus, thefracturing simulation has become a new hotspot in computer graphics in recent years.This dissertation has done deep research on graphical modeling and renderingtechnology of fracture.
The main research achievements are detailed as follows:
(1) Fracturing rigid body has been one of the hotspots and the difficulties in thefield of computer graphics in recent years. The common used finite element analysisalways needs complex physical calculations, which cannot meet the real-timerequirements of game and simulation. In this dissertation, a novel Voronoi diagrambased fracturing rigid body simulation approach is proposed, which gets a result withstrong physical reality in real time, by using the pre-fracture technology. Firstly, withthe analysis of fracturing progress of brittle rigid body, the seed points which fit well ofthe normal distribution are obtained, and the Voronoi polygons are generated throughthe off-line incremental algorithm and Graham Convex Hull algorithm. Secondly,according to the energy conservation equation and mechanical analysis, the radius of thefracture area and the crack area are ascertained, and in accordance with the restriction ofcollision energy conversion, the velocities of fragments are derived. Lastly, the collisiondetection has been realized and the velocity, attitude, etc. of the fragments are calculated.Experimental results show that this method can meet the real-time requirements ofgames and the interactive simulation, while the generation and movement of fragmentsconsistent with the true physical laws, and have a strong sense of reality.
(2) In this dissertation, a particle-based framework is presented to simulate thefracture phenomenon in computer graphics field. First, the object is represented asdiscrete particles, and then we introduce the Extend Discrete Element Method (EDEM)simulation to describe the interactions between neighbouring particles based on thematerial mechanics analysis. To process the fracture, a reverse idea to traditionalmethod is used to cooperate with auxiliary cone algorithm, which called anti-fracturemechanism. The physical computation is executed on the GPU with CUDA and auniform grid data structure is used in order to search the neighbouring elementseffectively. Experiment results demonstrate the feasibility and effectiveness of ourmethod.
(3) We introduce a novel method to simulate the fracture of heterogeneousmaterials and implement it efficiently on GPU with CUDA. First, the object isrepresented as discrete particles, named movable cellular automata, and then theMovable Cellular Automata method (MCA) is used to simulate the material andphysical properties as well as to determine when the fracture occurs. The simulation andrendering all run on GPU and the vertex buffer object (VBO) is used to avoid the costlycommunication between CPU and GPU. We demonstrate the feasibility andeffectiveness of the proposed method by the experimental results.
(4) The traditonal meshless method is difficult to address the singularity problemof the stress field of the crack tips. This dissertation presents an efficient approach tosimulate the deformation and fracture based on the local radial point interpolationmethod (LRPIM). When the shape function is constructed, a singular term is added forthe expansion of the radial basis function. Combining the LRPIM and the fracturecriterion based on the damage mechnism, the simulation process of deformation andfracture has been implemented. And the simulation results are rendered by the splattingtechnology based on point. The experimental results show that, compared to theconventional meshless method, our method can solve the singularity problem of thecrack tips, and the efficiency of rendering has been improved profiting from thesplatting technology.
（1）针对传统的基于有限元分析的破碎模拟方法需要进行复杂的物理计算，难以满足游戏、仿真中实时性的要求问题，提出了一种基于Voronoi图的刚体破碎模拟方法，通过采用预先破碎计算处理技术，实现了具有较强物理真实感的刚体破碎实时模拟。首先对脆性刚体材料破碎过程进行分析，得到拟合性较好的正态分布种子点，在此基础上采用脱机增量算法和格雷厄姆凸壳生成算法生成刚体破碎的Voronoi多边形。然后，根据能量守恒方程和材料力学分析，得到破碎区和裂纹区的半径，并根据碰撞过程中的能量转换约束条件对破碎后的碎片速度进行推导，最后对碎片间的碰撞检测以及碰撞后的速度、姿态等进行计算。实验结果表明：该方法不仅能在交互性上满足游戏、仿真的实时性需求，同时碎片的产生以及运动符合真实的物理规律，具有较强的真实感。
（2）提出一种基于粒子和逆向破碎机制的物体受外力冲击破碎实时模拟方法。首先将对象物体离散成空间中的一系列粒子，然后采用扩展离散单元法（EDEM）来计算每个粒子的受力、加速度、速度及位置等属性；采用从微观到宏观的逆向破碎机制，通过聚类分析，将某些粒子重新组合，宏观上形成碎片；采用统一网格的数据结构，将物理计算映射到GPU通过CUDA进行计算。实验结果验证了所提出方法的有效性和鲁棒性。
（3）提出一种基于移动元胞自动机的非均质物体破碎建模与绘制方法。将对象物体离散成空间中的元胞集合，采用移动元胞自动机方法(Movable CellularAutomata, MCA)模拟物体的材料和物理属性，并决定破碎发生的条件。采用统一网格数据结构在CUDA上实现了基于MCA的破碎模拟计算，模拟计算结果存储在顶点缓冲对象中并直接运用GPU进行绘制。实验结果表明，本文方法能更为真实地模拟非均质材质的破碎现象，同时采用GPU技术大大提高了计算与绘制的效率，与同类方法相比，性能提升了1-2个数量级，绘制帧速率基本满足实时交互需求。
（4）针对传统无网格法在处理裂纹尖端应力场具有奇异性的问题，提出一种基于局部径向基点插值（LRPIM）的物体变形与破裂无网格模拟算法。在构造无网格法形函数时，对基函数进行径向扩充，添加一个奇异项，有效避免裂纹尖端模拟的奇异性；在此基础上，结合局部径向基点插值无网格法和基于损伤力学的破裂准则，实现了物体变形及破裂的模拟仿真过程。模拟结果由基于点的Splatting绘制技术进行显示。实验结果表明，相比以往的无网格的破碎模拟方法，本文方法解决了模拟裂纹尖端的奇异性问题，同时采用基于点的Splatting绘制技术提高了绘制的效率。
The simulation of the phenomenon of fracture has attracted widespread attention inrecent years. It has important theoretical and practical significance not only in gamedevelopment, but also in other areas, such as the production of movie special effects,materials analysis, military simulation and virtual battlefield environment, etc. As acommon physical phenomenon in everyday life, fracturing effects greatly affect theuser’s experience in virtual reality, computer game and film industry. Thus, thefracturing simulation has become a new hotspot in computer graphics in recent years.This dissertation has done deep research on graphical modeling and renderingtechnology of fracture.
The main research achievements are detailed as follows:
(1) Fracturing rigid body has been one of the hotspots and the difficulties in thefield of computer graphics in recent years. The common used finite element analysisalways needs complex physical calculations, which cannot meet the real-timerequirements of game and simulation. In this dissertation, a novel Voronoi diagrambased fracturing rigid body simulation approach is proposed, which gets a result withstrong physical reality in real time, by using the pre-fracture technology. Firstly, withthe analysis of fracturing progress of brittle rigid body, the seed points which fit well ofthe normal distribution are obtained, and the Voronoi polygons are generated throughthe off-line incremental algorithm and Graham Convex Hull algorithm. Secondly,according to the energy conservation equation and mechanical analysis, the radius of thefracture area and the crack area are ascertained, and in accordance with the restriction ofcollision energy conversion, the velocities of fragments are derived. Lastly, the collisiondetection has been realized and the velocity, attitude, etc. of the fragments are calculated.Experimental results show that this method can meet the real-time requirements ofgames and the interactive simulation, while the generation and movement of fragmentsconsistent with the true physical laws, and have a strong sense of reality.
(2) In this dissertation, a particle-based framework is presented to simulate thefracture phenomenon in computer graphics field. First, the object is represented asdiscrete particles, and then we introduce the Extend Discrete Element Method (EDEM)simulation to describe the interactions between neighbouring particles based on thematerial mechanics analysis. To process the fracture, a reverse idea to traditionalmethod is used to cooperate with auxiliary cone algorithm, which called anti-fracturemechanism. The physical computation is executed on the GPU with CUDA and auniform grid data structure is used in order to search the neighbouring elementseffectively. Experiment results demonstrate the feasibility and effectiveness of ourmethod.
(3) We introduce a novel method to simulate the fracture of heterogeneousmaterials and implement it efficiently on GPU with CUDA. First, the object isrepresented as discrete particles, named movable cellular automata, and then theMovable Cellular Automata method (MCA) is used to simulate the material andphysical properties as well as to determine when the fracture occurs. The simulation andrendering all run on GPU and the vertex buffer object (VBO) is used to avoid the costlycommunication between CPU and GPU. We demonstrate the feasibility andeffectiveness of the proposed method by the experimental results.
(4) The traditonal meshless method is difficult to address the singularity problemof the stress field of the crack tips. This dissertation presents an efficient approach tosimulate the deformation and fracture based on the local radial point interpolationmethod (LRPIM). When the shape function is constructed, a singular term is added forthe expansion of the radial basis function. Combining the LRPIM and the fracturecriterion based on the damage mechnism, the simulation process of deformation andfracture has been implemented. And the simulation results are rendered by the splattingtechnology based on point. The experimental results show that, compared to theconventional meshless method, our method can solve the singularity problem of thecrack tips, and the efficiency of rendering has been improved profiting from thesplatting technology.
引文
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