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RIA: Computer Aided Geometric Design and Motion Synthesis

RIA：计算机辅助几何设计和运动合成

基本信息

批准号：
9211490
负责人：
Qiaode Jeffrey Ge
金额：
$ 3.3万
依托单位：
University of New Orleans
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
1992
资助国家：
美国
起止时间：
1992-08-15 至 1994-01-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9211490&HistoricalAwards=false
关键词：
RIA Computer Aided Geometric Design

项目摘要

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.*** //

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 * //