RIA: Computer Aided Geometric Design and Motion Synthesis

RIA：计算机辅助几何设计和运动合成

• 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

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.*** //

该研究旨在结合运动学和计算机辅助几何设计（GAGD）中的概念，从计算几何角度研究运动插值和近似问题。目标是开发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合成的计算几何结构和算法。基本方法是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来实现的，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射影空间中的曲线、曲面或实体。该映射有助于集成 GAGD 和计算机算法领域的各种方法来解决运动合成问题。该研究将开发图像空间算法来设计一类通过一系列位移进行插值的平滑分段参数运动，并开发用参数运动来近似代数运动的几何方法。这些结果除了对运动计算几何的理论兴趣外，还应用于空间机构和操纵器的设计、计算机运动动画和机械系统仿真。*** //