本文選題：布料仿真 + 應(yīng)變限制�。� 參考：《中國(guó)科學(xué)技術(shù)大學(xué)》2017年碩士論文

【摘要】：布料仿真技術(shù),旨在通過(guò)計(jì)算機(jī)生成虛擬的布料模型,同時(shí)模擬其真實(shí)的動(dòng)態(tài)效果。伴隨著硬件性能的進(jìn)步,各種大型虛擬現(xiàn)實(shí)應(yīng)用成為可能,布料仿真技術(shù)也隨之日益火熱。布料仿真技術(shù)覆蓋的學(xué)科廣,其研究領(lǐng)域涵蓋計(jì)算機(jī)圖形學(xué)、動(dòng)力學(xué)、有限元分析、材料力學(xué)、計(jì)算幾何等等。由于布料復(fù)雜的物理特性,如何增強(qiáng)仿真布料真實(shí)感可謂是一個(gè)頗有挑戰(zhàn)性的研究課題。本文討論的仿真布料真實(shí)感主要體現(xiàn)在兩個(gè)方面——布料的運(yùn)動(dòng)與形變。針對(duì)上述兩個(gè)方面,本文對(duì)布料仿真系統(tǒng)中能夠進(jìn)一步地增強(qiáng)真實(shí)感的關(guān)鍵技術(shù)展開(kāi)研究,主要工作如下:1)分析了布料在拉格朗日動(dòng)力學(xué)視角下的拉格朗日方程,總結(jié)了布料的動(dòng)能公式;借鑒分段線性模型對(duì)布料的本構(gòu)關(guān)系進(jìn)行近似,得到了布料的面內(nèi)拉伸力與彎曲力分別和其面內(nèi)應(yīng)變與曲率的關(guān)系。從而得到了完整的拉格朗日方程組,最終通過(guò)隱式時(shí)間積分的方法將微分方程組轉(zhuǎn)化為線性方程組,并通過(guò)LU分解進(jìn)行求解。2)實(shí)現(xiàn)了基于尺度場(chǎng)的自適應(yīng)各向異性布料網(wǎng)格重劃算法,然后分析了網(wǎng)格重劃后可能帶來(lái)的碰撞問(wèn)題,通過(guò)采用基于AABB的層次包圍盒算法進(jìn)行碰撞檢測(cè),再通過(guò)簡(jiǎn)單回溯的方式,結(jié)合碰撞響應(yīng)鄰域,簡(jiǎn)單而高效地對(duì)碰撞進(jìn)行響應(yīng)處理。實(shí)驗(yàn)表明,自適應(yīng)網(wǎng)格重劃一方面可以在面片數(shù)相當(dāng)?shù)那闆r下更好地展現(xiàn)布料的仿真情況,另一方面能夠在一定程度上避免因網(wǎng)格面片數(shù)過(guò)多而產(chǎn)生的不真實(shí)"震蕩"現(xiàn)象,從而更好地起到了提高仿真布料的真實(shí)感的作用。3)在每一幀都對(duì)仿真布料進(jìn)行網(wǎng)格重劃的基礎(chǔ)上,為布料添加了自適應(yīng)的各向異性應(yīng)變限制約束,通過(guò)定義內(nèi)積倒數(shù)映射,將規(guī)定的布料全局應(yīng)變限制轉(zhuǎn)化為各個(gè)三角形形變主軸的局部應(yīng)變限制,保證了在每次網(wǎng)格重劃之后局部應(yīng)變限制仍然能夠和全局應(yīng)變限制保持一致。同時(shí)提出了改進(jìn)乘子法來(lái)求解應(yīng)變限制帶來(lái)的約束非線性規(guī)劃問(wèn)題。實(shí)驗(yàn)表明,本文所提出的方法有效地提高了應(yīng)變限制的準(zhǔn)確性,從而增強(qiáng)了布料仿真的真實(shí)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.
【學(xué)位授予單位】：中國(guó)科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TS941;TP391.9

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相關(guān)期刊論文 前1條

1 石敏;毛天露;夏時(shí)洪;王兆其;;布料動(dòng)畫(huà)方法研究進(jìn)展及問(wèn)題[J];計(jì)算機(jī)學(xué)報(bào);2012年12期

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本文編號(hào)：2021128