本文選題：動態(tài)仿真 + 幾何建模　； 參考：《中國科學技術大學》2017年博士論文

【摘要】：隨著數字幾何建模技術的發(fā)展以及計算機計算能力的提升,人們不斷地追求更加精確的模型制作,更加擬真的影視動畫體驗。在上世紀80年代基于物理的建模仿真技術應運而生,成為計算機圖形學重要的研究熱門課題之一,并在計算機輔助幾何設計、計算機圖形與視覺、動畫影視、虛擬現實、3D打印、醫(yī)療器械等相關領域有著廣泛的應用。基于物理的仿真技術使三維模型更加滿足物理特性、動畫影視更加逼真,并且很大程度上減少了制作的時間與人工成本。隨著數值幾何處理技術的發(fā)展以及微分方程數值解在動畫仿真中的不斷應用,越來越多的建模仿真問題得到解決。對于花朵的開放仿真建模,傳統(tǒng)的方法要么是基于手工關鍵幀的建模,要么是通過復雜的植物生長參數仿真建模,這些方法往往耗時耗力,不僅要求設計者可以熟練地應用建模軟件,也要求設計者有一定專業(yè)的植物學知識,大大限制了使用者的范圍。本文提出一種基于邊緣驅動的開花仿真方法,該方法基于生物觀察的基礎——花瓣邊緣驅動了花朵的開放。本文把花瓣曲面實體視做一個薄板模型,利用包含拉伸能量和彎曲能量的彈簧質點模型來仿真其物理形態(tài),采用邊緣引導的機制通過面內生長(in-plane growth)主動地引導花瓣向外彎曲打開。同時本文也采用面外生長(out-of-plane growth)來輔助控制開放過程中花瓣的平坦程度。在一些合理假設的基礎上,本文簡化主要生長參數為一條生長曲線,簡化了生長參數的設定要求,同時也可以使花瓣和花托之間的夾角自動增大,花朵自然打開,產生令人信服的逼真的花朵開放動畫。本文方法可以使花瓣邊緣產生波紋形狀,這些波紋使花瓣更加美麗,仿真結果更加逼真。本文也采用了鏈接彈簧(連接花骨朵上不同花瓣質點的彈簧)來模擬在花朵開放初始階段花瓣之間的阻力,產生快速開放的效果。在第四章節(jié)中,本文提出一種基本平面液體粒子(hydrodynamic particles)的水膜仿真方法。水膜是一種自然現象,是少量液體通過分子間吸引力,堆積形成的一種有著可見厚度的薄膜。以前方法在建模仿真水膜時,往往要用幾天的時間來完成一個場景,或者可以快速仿真,但仿真系統(tǒng)不是無條件穩(wěn)定的,依賴于水膜的網格質量。本文用平面液體粒子來驅動水膜的運動,考慮水膜的面積、重力等物理因素,并結合水膜的靜態(tài)方程Yong-Laplace方程,把水膜的建模仿真問題轉化為一個幾何造型的能量極小化問題。由于最終的能量是一個二次能量模型,在每一次迭代中,只需要求解一個對稱正定稀疏的線性系統(tǒng),可以使用戶交互地仿真建模。同時,驅動水膜運動的平面液體粒子采用的是穩(wěn)定的光滑粒子流體動力學(smoothed particle hydrodynamics)方法,本文方法是無條件穩(wěn)定的。設定好一個場景后,在時間序列上的正向仿真一般是有解的,而動態(tài)仿真建模中的逆問題往往是困難的。在第五章節(jié)中,本文給出一種基于微結構的變形物體仿真建模方法。該方法以血管支架表面結構為基礎,設計一種彈性微結構的基本單元,利用基本單元來合成可變形物體的曲面形狀。本文在嘗試解決一個逆問題:給定原始物體曲面形狀和目標曲面形狀后,問用哪些彈性基本單元結構來合成原始曲面形狀,使原始曲面在外界約束下變形為目標曲面形狀。本文把此問題轉化為一個能量優(yōu)化問題,通過基因遺傳算法優(yōu)化合成原始物體曲面形狀的基本單元,使原始物體在外界約束下盡可能地變形為或者逼近目標形狀。此優(yōu)化迭代過程選擇不同的基本單元,相當于選擇了不同的彈性結構,并且理論上保證逼近誤差是單調遞減的。
[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.

【學位授予單位】：中國科學技術大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：TP391.41

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