近年來人物角色的動作合成越來越重要，例如現在許多電影以及電腦遊戲等都用到虛擬的人物，因此如何做出虛擬人物們的動作之研究在近年來變的很重要。本篇論文提出一種新的動作合成法，它主要是利用已有的動作再加上一些使用者可以給定的幾何限制條件、以及動作模擬器參數來合成出符合限制條件與希望的動作品質的新動作。
本文將利用反向運動學(Inverse Kinematics ,簡稱為IK) 來計算關節角度，並用單格合成(Per-Frame) 的方法來合成模擬，將原有的動作加上個位移差量(Displacement)來修正出想要的新動作，系統會依據使用者給定的幾何限制條件來合成出符合要求的位移量。並且引用了動作模擬器Proportional Derivative Controller (簡稱 PD - Controller) 來將新動作模擬出一些動作品質的變化，因此使用者可以依需求調整參數做出不同品質的動作。本文結合了運動學與動力學的方法，將運動學的結果交給動力學方法處理，而後動力學的結果又回饋給運動學方法，如此反覆的運算出結果。我們主要專注於走路的例子，讓使用者設定一些手、腳的新目標，系統將自動合成產生出可達到限制條件的新動作。

In recent years, the study of motion synthesis of articulated figures has played an important role. For example, there are many movies and computer games using synthesized virtual characters. Therefore, how to create realistic motions for virtual characters becomes an important research topic. This thesis presents a new method to synthesize desired motions based on given motions plus some geometric constraints.
Our method uses Inverse Kinematics (IK) to compute the angles of articulated figure’s joints. We synthesize the motion by per-frame method. The basic idea of our method is to compute the displacement base on the given motion and the constraints. We introduce Proportional Derivative Controller (or known as PD-Controller) to simulates motion qualities for the new motion. Our method combines both kinematics and dynamics methods, and allows users to set their constraints on end-effectors such as hands and feet. Empirical examples are given to demonstrate that the proposed system can automatically synthesizes the desired motion with given geometric constraints.

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