RIA: Computer Aided Geometric Design and Motion Synthesis

这项研究试图结合运动学和计算机辅助几何设计(GAGD)的概念，从计算几何的角度来研究运动插补和逼近问题。其目标是开发适用于具有和不具有运动约束的刚体运动的计算机辅助几何综合的计算几何结构和算法。基本方法包括将运动合成问题转换为设计曲线、曲面或实体的几何问题。这是通过使用可定向运动学映射实现的，该映射将欧几里得空间中的运动(具有一个或多个自由度)转换为称为图像空间的特殊投影空间中的曲线、曲面或实体。该映射便于将GAGD领域的各种方法与计算机算法相结合来解决运动合成问题。这项研究将开发图像空间算法来设计一类通过位移序列进行插补的光滑分段参数运动，并开发用参数运动来逼近代数运动的几何方法。除了在运动的计算几何方面的理论兴趣之外，这些结果还在空间机构和机械手的设计、运动的计算机动画和机械系统模拟中得到应用。

The research seeks to combine concepts in Kinematics and Computer Aided Geometric Design (GAGD) to study motion interpolation and approximation problems from a computational geometric perspective. The goal is to develop computational geometric structure and algorithms that are suitable for computer aided geometric synthesis of rigid body motions both with and without kinematic constraints. The basic approach involves converting the motion synthesis problem into a geometric problem of designing curves, surfaces, or solids. This is made possible using an orientable kinematic mapping which transforms motions (with one or more degrees of freedom) in the Euclidean space into curves, surfaces, or solids in a special projective space called the image space. The mapping facilitates integration of various methods in the fields of GAGD and computer algorithms to solve the motion synthesis problem. The research will develop image- space algorithms for designing a class of smooth piecewise parametric motions that interpolates through a sequence of displacements and develop geometric methods for approximating algebraic motions with the parametric motions. The results, in addition to their theoretical interest in computational geometry of motions, have applications in the design of spatial mechanisms and manipulators, computer animation of motions, and mechanical system simulation.*** //