This book aim to address the open problem of articulated and undulatory motion analysis for action/activity recognition and 3-D animation synthesis. Concisely, the main goal is to propose general models and methods of middle level analysis (e.g. detection-tracking algorithms), aiming at high level analysis for humans (e.g. action and activity recognition) and 3-D animation synthesis for animals. Moreover, we study the curve equipartition problem (EP), which consists a fundamental geometrical problem that has risen from undulatory motion analysis and has applications in computer science.