RIA: Computer Aided Geometric Design and Motion Synthesis

本研究旨在结合运动学和计算机辅助几何设计（GAGD）的概念，从计算几何的角度研究运动插值和逼近问题。目标是开发计算几何结构和算法，适用于有或没有运动学约束的刚体运动的计算机辅助几何综合。基本方法包括将运动综合问题转化为设计曲线、曲面或实体的几何问题。这是通过可定向的运动学映射实现的，该映射将欧几里德空间中的运动（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，曲面或固体。该映射有助于将gad领域的各种方法与计算机算法相结合来解决运动综合问题。该研究将开发图像空间算法来设计一类平滑分段参数运动，该运动通过一系列位移进行插值，并开发几何方法来近似参数运动的代数运动。研究结果，除了在运动计算几何方面的理论兴趣外，在空间机构和操纵器的设计、运动的计算机动画和机械系统仿真方面也有应用。* * * / /

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.*** //