RIA: Computer Aided Geometric Design and Motion Synthesis

本研究试图将运动学和计算机中的概念联合收割机结合起来 辅助几何设计（GAGD），研究运动插补和 计算几何近似问题 perspective.我们的目标是发展计算几何 结构和算法，适用于计算机辅助 刚体运动的几何综合 运动学约束基本方法是将 运动综合问题转化为几何设计问题 曲线、曲面或实体。这是通过使用 可定向的运动学映射，其将运动（其中一个 或更多自由度）在欧几里得空间中转换成曲线， 曲面或固体在一个特殊的射影空间称为 图像空间该映射促进了各种 GAGD和计算机算法领域的方法来解决 运动合成问题。该研究将开发图像- 设计一类分段光滑空间算法 参数化运动，通过一系列 位移和发展几何方法近似 代数运动和参数运动。中的结果 除了他们对计算的理论兴趣之外， 运动的几何学，在空间设计中有应用 机构和机械手，运动的计算机动画，以及 机械系统仿真 * //

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.*** //