自由曲面的最优参数化及重新参数化关键算法研究

项目名称： 自由曲面的最优参数化及重新参数化关键算法研究

项目编号： No.61202146

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 计算机科学学科

项目作者： 杨义军

作者单位： 山东大学

项目金额： 23万元

中文摘要： 自由曲面（NURBS曲面）在现代制造业和建筑业中扮演了越来越重要的角色。机械零件、建筑、汽车、轮船以及飞机的制造商们主要关心最后生成的产品形状，而面向大多数应用的几何算法很大程度上依赖于产品模型中曲面当前的参数化。现有的曲面修改及生成算法往往只考虑最后生成曲面的形状，而忽略其参数特性，直接影响了后续操作的可行性及结果质量。针对上述问题，本项目拟研究自由曲面的最优参数化及重新参数化，并将之应用到包括渲染、离散、求交、曲面拟合以及曲线生成等算法中，重点解决：1）自由曲面的分段二次重新参数化及其在曲面参数优化中的应用；2）具有均匀、正交、保角、保面积以及它们组合特性的自由曲面显式表示及其构造算法；3）最优参数化及重新参数化在曲面拟合、曲面上曲线生成等算法中的应用。本项目对于提升曲面处理相关算法的结果质量，改进其效率和鲁棒性，帮助我们更好的理解自由曲面的内在本质具有非常重要的意义。

中文关键词： 共形参数化；自由曲面；保面积参数化；双线性变换；数值优化

英文摘要： Freeform surfaces play an increasingly important role in contemporary Computer Aided Design and architecture design. While the manufactures of mechanical parts, architecture buildings, cars and planes are mainly concerned with the final geometric shapes, geometric algorithms for most CAD applications are highly dependent on the surface parameterization. The existing surface modification and generation algorithms pay more attention to the shape of the final surface while the parameterization of the final surface is neglected, which influences the results and possibility of the following algorithms. To solve the above problems, we plan to study the reparameterization and optimal parameterization of free form surfaces and apply the results to applications such as rendering, tessellation, intersection, surface fitting and curve generation in this research project. We focus on the following three subjects: 1) the composite quadratic reparameterization of NURBS surfaces and its application in the optimization of the surface parameterization; 2) the NURBS surfaces with parameterization characters such as uniformity, orthogonality, conformality, area-preserve and their combinations; 3) the applications of the surface reparameterization and optimal parameterization in surface fitting and curves on surfaces. This research

英文关键词： Conformal parameterization；Freeform surfaces；Equiareal parameterization；Bilinear transformations；Numerical optimization