基于物理的动态物体建模仿真研究

发布时间：2018-04-22 00:02

本文选题：动态仿真 + 几何建模　；参考：《中国科学技术大学》2017年博士论文

【摘要】：随着数字几何建模技术的发展以及计算机计算能力的提升,人们不断地追求更加精确的模型制作,更加拟真的影视动画体验。在上世纪80年代基于物理的建模仿真技术应运而生,成为计算机图形学重要的研究热门课题之一,并在计算机辅助几何设计、计算机图形与视觉、动画影视、虚拟现实、3D打印、医疗器械等相关领域有着广泛的应用。基于物理的仿真技术使三维模型更加满足物理特性、动画影视更加逼真,并且很大程度上减少了制作的时间与人工成本。随着数值几何处理技术的发展以及微分方程数值解在动画仿真中的不断应用,越来越多的建模仿真问题得到解决。对于花朵的开放仿真建模,传统的方法要么是基于手工关键帧的建模,要么是通过复杂的植物生长参数仿真建模,这些方法往往耗时耗力,不仅要求设计者可以熟练地应用建模软件,也要求设计者有一定专业的植物学知识,大大限制了使用者的范围。本文提出一种基于边缘驱动的开花仿真方法,该方法基于生物观察的基础——花瓣边缘驱动了花朵的开放。本文把花瓣曲面实体视做一个薄板模型,利用包含拉伸能量和弯曲能量的弹簧质点模型来仿真其物理形态,采用边缘引导的机制通过面内生长(in-plane growth)主动地引导花瓣向外弯曲打开。同时本文也采用面外生长(out-of-plane growth)来辅助控制开放过程中花瓣的平坦程度。在一些合理假设的基础上,本文简化主要生长参数为一条生长曲线,简化了生长参数的设定要求,同时也可以使花瓣和花托之间的夹角自动增大,花朵自然打开,产生令人信服的逼真的花朵开放动画。本文方法可以使花瓣边缘产生波纹形状,这些波纹使花瓣更加美丽,仿真结果更加逼真。本文也采用了链接弹簧(连接花骨朵上不同花瓣质点的弹簧)来模拟在花朵开放初始阶段花瓣之间的阻力,产生快速开放的效果。在第四章节中,本文提出一种基本平面液体粒子(hydrodynamic particles)的水膜仿真方法。水膜是一种自然现象,是少量液体通过分子间吸引力,堆积形成的一种有着可见厚度的薄膜。以前方法在建模仿真水膜时,往往要用几天的时间来完成一个场景,或者可以快速仿真,但仿真系统不是无条件稳定的,依赖于水膜的网格质量。本文用平面液体粒子来驱动水膜的运动,考虑水膜的面积、重力等物理因素,并结合水膜的静态方程Yong-Laplace方程,把水膜的建模仿真问题转化为一个几何造型的能量极小化问题。由于最终的能量是一个二次能量模型,在每一次迭代中,只需要求解一个对称正定稀疏的线性系统,可以使用户交互地仿真建模。同时,驱动水膜运动的平面液体粒子采用的是稳定的光滑粒子流体动力学(smoothed particle hydrodynamics)方法,本文方法是无条件稳定的。设定好一个场景后,在时间序列上的正向仿真一般是有解的,而动态仿真建模中的逆问题往往是困难的。在第五章节中,本文给出一种基于微结构的变形物体仿真建模方法。该方法以血管支架表面结构为基础,设计一种弹性微结构的基本单元,利用基本单元来合成可变形物体的曲面形状。本文在尝试解决一个逆问题:给定原始物体曲面形状和目标曲面形状后,问用哪些弹性基本单元结构来合成原始曲面形状,使原始曲面在外界约束下变形为目标曲面形状。本文把此问题转化为一个能量优化问题,通过基因遗传算法优化合成原始物体曲面形状的基本单元,使原始物体在外界约束下尽可能地变形为或者逼近目标形状。此优化迭代过程选择不同的基本单元,相当于选择了不同的弹性结构,并且理论上保证逼近误差是单调递减的。
[Abstract]:With the development of digital geometric modeling technology and the improvement of computer computing power, people continue to pursue more accurate model making and more realistic video animation experience. In the 80s of last century, the modeling and simulation technology based on physics came into being, and became one of the most important research topics in computer graphics, and in computer Auxiliary geometric design, computer graphics and vision, animation, film, video, virtual reality, 3D printing, medical equipment and other related fields are widely used. The physical simulation technology makes the three-dimensional model more satisfied with the physical characteristics, animation and film and television is more realistic, and greatly reduces the time and labor cost of production. With the numerical geometry, with the numerical geometry With the development of processing technology and the continuous application of numerical solutions of differential equations in animation simulation, more and more modeling and simulation problems are solved. For the open simulation modeling of flowers, the traditional methods are either based on the modeling of manual key frames or through the simulation of complex plant growth parameters. These methods often consume time and consumption. Force, not only requires the designer to apply the modeling software skillfully, but also requires the designer to have a certain professional botanical knowledge, which greatly restricts the user's scope. In this paper, a blooming simulation method based on the edge driven is proposed. This method is based on the basis of biological observation - the petal edge drives the flower opening. This paper puts the petals in this paper. The surface entity is regarded as a thin plate model, using the spring particle model containing tensile energy and bending energy to simulate its physical form, using the mechanism of edge guidance to actively guide the petals outwards through the surface growth (in-plane growth). At the same time, this paper also uses out-of-plane growth to assist the control of opening. The flatness of the petals in the process. On the basis of some reasonable assumptions, this paper simplifies the main growth parameters as a growth curve, simplifies the setting requirements of the growth parameters, and can also make the angle between the petals and the floral receptacles automatically increase, and the flowers open naturally to create a convincing and realistic flower opening animation. This method can be used in this paper. In order to create a ripple shape on the edge of the petals, the ripples make the petals more beautiful and the simulation results are more realistic. This paper also uses a link spring (a spring connecting the different petal particles on the flower bone) to simulate the resistance between the petals at the opening stage of the flower and produce a fast and open effect. In the fourth chapter, a basis is proposed. The water film simulation method of the liquid particle (hydrodynamic particles) in this plane is a natural phenomenon. It is a thin film with visible thickness formed by the accumulation of a small amount of liquid through the intermolecular attraction. The former method used a few days to complete a scene, or can be quickly simulated, but can be quickly simulated, but can be quickly simulated when modeling and simulating the water film. The simulation system is not unconditionally stable and depends on the quality of the grid of water film. In this paper, the motion of water film is driven by the plane liquid particles. The physical factors such as the area of water film and gravity are considered, and the Yong-Laplace equation of the static equation of the water film is combined to transform the modeling and Simulation of the water film into a problem of the minimization of the energy of a geometric modeling. The final energy is a two energy model. In each iteration, only a symmetric positive definite sparse linear system is needed to simulate the modeling by user interaction. At the same time, the plane liquid particle driving the motion of water film is a stable smooth particle hydrodynamics (smoothed particle hydrodynamics) method. The method of the text is unconditionally stable. After setting a scene, the forward simulation on the time series is usually solved, and the inverse problem in the dynamic simulation modeling is often difficult. In the fifth chapter, this paper gives a simulation modeling method based on the microstructure of the deformation object. A basic unit of elastic microstructures is used to make use of basic units to synthesize the shape of a deformable object. In this paper, an attempt is made to solve an inverse problem: after a given surface shape of a original object and the shape of a target surface, which elastic basic unit structure is used to synthesize the original surface shape, so that the original surface is transformed into the eye under the external constraint. This problem is transformed into an energy optimization problem. This paper optimizes the basic unit of the surface shape of the original object by genetic algorithm, making the original object deformed as much as possible or approaching the shape of the target under external constraint. This optimization iteration process chooses different basic units, which is equivalent to the selection of different kinds of elements. The elastic structure is theoretically guaranteed that the approximation error is monotonically decreasing.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP391.41

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