布料仿真中增强真实感技术研究

发布时间：2018-06-15 07:00

本文选题：布料仿真 + 应变限制　；参考：《中国科学技术大学》2017年硕士论文

【摘要】：布料仿真技术,旨在通过计算机生成虚拟的布料模型,同时模拟其真实的动态效果。伴随着硬件性能的进步,各种大型虚拟现实应用成为可能,布料仿真技术也随之日益火热。布料仿真技术覆盖的学科广,其研究领域涵盖计算机图形学、动力学、有限元分析、材料力学、计算几何等等。由于布料复杂的物理特性,如何增强仿真布料真实感可谓是一个颇有挑战性的研究课题。本文讨论的仿真布料真实感主要体现在两个方面——布料的运动与形变。针对上述两个方面,本文对布料仿真系统中能够进一步地增强真实感的关键技术展开研究,主要工作如下:1)分析了布料在拉格朗日动力学视角下的拉格朗日方程,总结了布料的动能公式;借鉴分段线性模型对布料的本构关系进行近似,得到了布料的面内拉伸力与弯曲力分别和其面内应变与曲率的关系。从而得到了完整的拉格朗日方程组,最终通过隐式时间积分的方法将微分方程组转化为线性方程组,并通过LU分解进行求解。2)实现了基于尺度场的自适应各向异性布料网格重划算法,然后分析了网格重划后可能带来的碰撞问题,通过采用基于AABB的层次包围盒算法进行碰撞检测,再通过简单回溯的方式,结合碰撞响应邻域,简单而高效地对碰撞进行响应处理。实验表明,自适应网格重划一方面可以在面片数相当的情况下更好地展现布料的仿真情况,另一方面能够在一定程度上避免因网格面片数过多而产生的不真实"震荡"现象,从而更好地起到了提高仿真布料的真实感的作用。3)在每一帧都对仿真布料进行网格重划的基础上,为布料添加了自适应的各向异性应变限制约束,通过定义内积倒数映射,将规定的布料全局应变限制转化为各个三角形形变主轴的局部应变限制,保证了在每次网格重划之后局部应变限制仍然能够和全局应变限制保持一致。同时提出了改进乘子法来求解应变限制带来的约束非线性规划问题。实验表明,本文所提出的方法有效地提高了应变限制的准确性,从而增强了布料仿真的真实感。
[Abstract]:The technology of cloth simulation aims at creating virtual cloth model by computer and simulating its real dynamic effect. With the progress of hardware performance, a variety of large-scale virtual reality applications become possible, cloth simulation technology has become increasingly hot. Cloth simulation technology covers a wide range of disciplines, its research fields include computer graphics, dynamics, finite element analysis, mechanics of materials, computational geometry and so on. Because of the complex physical properties of cloth, how to enhance the realistic sense of cloth simulation is a challenging research topic. The realistic sense of simulation cloth discussed in this paper is mainly reflected in two aspects-the movement and deformation of cloth. In view of the above two aspects, this paper studies the key technologies in the cloth simulation system which can further enhance the reality. The main work is as follows: 1) the Lagrange equation of cloth under Lagrange dynamics is analyzed. The kinetic energy formula of cloth is summarized and the relationship between in-plane tensile force and bending force and in-plane strain and curvature are obtained by using piecewise linear model to approximate the constitutive relation of cloth. The complete Lagrangian equations are obtained, and the differential equations are transformed into linear equations by implicit time integral method. An adaptive anisotropic cloth mesh redenomination method based on scale field is implemented by LU decomposition. Then the collision problem caused by mesh redrawing is analyzed. In this paper, the hierarchical bounding box algorithm based on AABB is used for collision detection, and then the collision response is processed simply and efficiently by a simple backtracking method combined with the collision response neighborhood. Experimental results show that, on the one hand, the adaptive mesh redrawing can better show the simulation of the cloth under the condition of equal number of surfaces, and on the other hand, it can avoid the unreal "oscillation" phenomenon caused by the excessive number of mesh surfaces to a certain extent. Thus, the function of improving the realistic sense of simulation cloth is better. 3) on the basis of mesh redrawing of each frame, adaptive anisotropic strain constraint is added to the cloth, and the reciprocal mapping of inner product is defined. The global strain limit of the cloth is transformed into the local strain limit of each triangular deformation spindle, which ensures that the local strain limit can still be consistent with the global strain limit after each grid redrawing. At the same time, an improved multiplier method is proposed to solve the constrained nonlinear programming problems caused by strain constraints. Experimental results show that the proposed method improves the accuracy of strain limitation and enhances the reality of cloth simulation.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TS941;TP391.9

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