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.*** //

该研究旨在将运动学和计算机辅助几何设计（GAGD）中的概念结合起来，从计算几何学角度研究运动插值和近似问题。目的是开发适用于具有和不具有运动限制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。基本方法涉及将运动合成问题转换为设计曲线，表面或固体的几何问题。使用可定向的运动映射使这是可能的，该运动映射将欧几里得空间中的运动（具有一个或多个自由度）转换为曲线，表面或固体中的运动，在称为图像空间的特殊投影空间中。映射促进了在GAGD和计算机算法领域中的各种方法的集成，以解决运动合成问题。这项研究将开发图像空间算法，用于设计一类平滑的分段参数运动，这些运动通过一系列位移序列插值并开发几何方法，以通过参数运动近似代数运动。结果除了对动作的计算几何学的理论兴趣外，还在空间机制和操纵器的设计中应用了应用，动作的计算机动画和机械系统模拟。*** //