程序式動畫是一種根據使用者所提供的高階運動參數，自動產生動畫的方法。藉著高階的運動參數，程序式動畫比運動擷取資料有著更高的彈性。使用者可透過調整參數，輕易地讓動畫滿足情境上所需的限制。但如何調整適當的運動參數以產生擬真的動畫仍屬不易，因此程序式動畫常有在視覺上觀感不自然的問題。本研究的目標是，將運動擷取資料擬真的要素，帶到程序式動畫之中，以改進程序式動畫的品質。我們將問題定義成一個最佳化問題：給定一段運動擷取資料，系統該如何調整程序式動畫之參數，使得程序式動畫與運動擷取資料的差距盡可能地縮小？我們的系統可以參考一段運動擷取資料，以最佳化演算法，自動調整程序式動畫的參數，搜尋能產生出與運動擷取資料最為相似的運動參數。為了進一步讓產生之動畫符合環境的限制需求，多組最佳化過後的運動參數可以再透過內插，重新產生出一組符合限制需求的運動參數。實驗結果顯示，我們的方法不但使程序式動畫得以保留原來彈性的優點，也改善了程序式動畫常有的視覺觀感不自然的缺點。 / Procedural animation provides a way for a user to generate animation according to the high-level motion parameters that the user supplies. With the high-level motion parameters, procedural animation has the flexibility of generating animation accommodating the requested constraints in a scenario. However, tuning parameters to generate realistic animations usually is a difficult task. Therefore, animations produced with this approach often have the drawback of unrealistic-looking. Our goal is to improve the quality of procedural animation by bringing the naturalness of motion capture data into procedural animation. We model our problem as an optimization problem: given a motion captured clip, how does the system tune the motion parameters in an animation procedure to minimize the difference between animations produced by a procedure and captured in a motion clip? Our proposed system takes a motion captured clip as a reference and tunes the motion parameters of the animation procedure with an optimization algorithm. In order to generate animation satisfying environmental constraints, multiple optimized motion parameters can be interpolated to create a new set of motion parameters which can also satisfy the constraints. Our experimental results show that our method not only retains the flexibility of procedural animation, but also enhances the quality of procedural animation.

量子擾動及挫折性兩者均可破壞絕對零溫的磁序，為近代凝態物 理關注的有趣現象。在外加橫場下的三角晶格易辛反鐵磁兼具量子臨 界現象(quantum criticality)及幾何挫折性，可謂量子磁性物質之一典 範理論模型。本論文利用平衡態及非平衡態量子蒙地卡羅(quantum Monte Carlo)方法探測三角晶格易辛反鐵磁之量子相變，其界定零溫 時無磁性的順磁態及具 Z6 對稱破缺的有序態(所謂時鐘態)。這裡的 量子蒙地卡羅方法為運用算符的零溫投射(zero-temperature projector) 及隨機序列展開(stochastic series expansion)演算法。在非平衡模擬 中，我們分別沿降溫過程及量子絕熱過程逼近量子相變點，藉此我們 得到動力學指數，及其它相關臨界指數。 / The destruction of magnetic long-range order at absolute zero temperature arising from quantum fluctuations and frustration is an interesting theme in modern condensed-matter physics. The triangular lattice Ising antiferromag- net in a transverse field provides a playground for the study of the combined effects of quantum criticality and geometrical frustration. In this thesis we use quantum Monte Carlo methods both in equilibrium and non-equilibrium setups to study the properties of the quantum critical point in the triangular lattice antiferromagnet, which separates a disordered paramagnetic state and an ordered clock state exhibiting Z6 symmetry breaking; The methods are based on a zero-temperature projector algorithm and the stochastic series ex- pansion algorithm. For the non-equilibrium setups, we obtain the dynamical exponent and other critical exponents at the quantum critical point approached by slowly decreasing temperature and through quantum annealing.