應用粒子系統於可形物體模擬之研究

Abstract

三維物體模擬是計算機圖學領域中的一個相當令人感興趣的一個研究題材，對一個三維物體而言，我們依據材質的不同而使用不同的模擬機制，使得模擬結果能更具真實性。然而物體依材質分類可分為：剛體(solid object)、可形變物體(deformable object)與模糊物質(fuzzy object)三類。 目前在三維物體模擬方面的研究，多集中於可形變物體的模擬，原因在於，相較於其他兩種物質的模擬，在可形變物體模擬的研究中，粒子之間存在著某一關係而互相影響，於是乎，如何描述粒子之間的互動關係便成為一項相當引人感到興趣的研究題材了。近年來有許多學者專家皆致力於發展出一套系統，使得可形變物體模擬的結果能兼具即時性以及真實性這兩大需求。然而這其中存在著許多的困難點需要被克服，如：數值積分(numerical integration)、彈性限制(elastic constraints)等。 在本論文中將會探討三種物質的模擬機制，並且分別對於布料與皮球方面的研究提出新的模擬機制。在布料模擬方面，我們提出使用具有自我結構化之模糊控制器(self-organizing fuzzy logic controller; SOFC)為布料模擬的機制，使得系統可針對各種不同特性的布料自動做調整，免除了傳統布料模擬中參數調整的手續。由實驗結果得知，相較於使用彈簧模型為布料模擬機制，使用具有自我結構化之模糊控制器為布料模擬機制時，可得到較為真實的模擬結果，並且可改善在布料模擬中所產生的超彈性效應(super-elastic effect)。這是由於，使用具有自我結構化之模糊控制器為布料模擬機制時，系統是動態地調整布料參數而非整體性地作調整。對於皮球模擬方面，我們加入了球體質心與表面質點間的彈簧，用以模擬由球體內部壓力所產生的作用力。由實驗結果發現，在加入由球體內部壓力所產生的作用力之後，所得到的模擬結果較為真實。

Three dimension object simulation is an interesting topic in computer graphics. For a 3-D object, we choose a proper simulation mechanism according its material in order to get more realistic result. However, 3-D objects are classified according to their material into rigid body, deformable object or fuzzy object. In the 3-D object simulation research area, researchers focused on cloth simulation research. As a result of the particles in deformable objects effects on each other because there exists some relationship between the particles. Thus, the most interesting topic is how to describe the interaction between the particles. For this reason, many researchers make more efforts in developing a simulation mechanism such that the cloth simulation result can be more realistic. However, there are many difficulties need to be overcome, for example: numerical integration and elastic constraints problem. In this thesis, we will discuss the simulation mechanism of three materials and develop new simulation mechanism in cloth and ball simulation separately. For cloth simulation research, we apply self-organizing fuzzy logic controller (SOFC) as simulation mechanism. According to the different property of cloths, the system will adjust cloth parameter automatically. According to the experimental results, when we apply self-organizing fuzzy logic controller as cloth simulation mechanism, the simulation result is more realistic than using spring-model and the super-elastic effect is improved efficiently. This is owing to the system will dynamically adjust cloth parameter rather than globally adjust cloth parameter. For the ball simulation, we add the spring between mass-center and surface mass in order to simulate the force produced by internal pressure. According to the experiment results, the simulation results are more realistic after apply the force produced by internal pressure.