在本篇論文中，我們提出了一個以繪製人體末端關節在空間中運動的二維軌跡來產生三維人體動作的方法。在傳統的動畫製作上，美術人員欲繪製較複雜的人體動作時，常會先繪出幾個重要的關節運動的軌跡，再根據這些軌跡去完成整段動作。我們基於此種做法，並將其推展至三維空間的人體動作，藉由繪製腹部、頭部、左右手腕、左右腳跟等六個關節點在空間中運動的軌跡投影至側面的二維曲線，經過反式運動學（Inverse Kinematics）的計算，便可產生三維空間的人體動作。為使關節運動形成的軌跡更為平順，我們採用了B-Spline做為軌跡曲線的表現工具。我們並提出了一個將經過初步反式運動學計算出的動作資料做最佳化的方法，讓最後的成品動作有更佳的品質。

In this thesis, we present a novel three-dimensional human motion synthesis method by sketching two-dimensional trajectories of end joints. According to conventional 2D animation work, before an artist draws a complicated human motion, he usually first sketches trajectories of some important joints and then completes the desired motion based on these trajectories. In this study we extended this approach to three-dimensional human motion synthesis. By sketching the projected trajectories of root, head, left wrist, right wrist, left ankle and right ankle to a side plan, we propose an inverse- kinematics-based algorithm for synthesizing three-dimensional human motions. Moreover, in order to smooth the trajectories of joints, we use b-spline to represent trajectory curves. We also present an optimization method to improve the quality of synthesizes motion. Finally, several examples are given to demonstrate the effectiveness of the proposed method.

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