项目名称: 基于极小曲面的几何造型理论及应用
项目编号: No.11526098
项目类型: 专项基金项目
立项/批准年度: 2016
项目学科: 数理科学和化学
项目作者: 郝永霞
作者单位: 江苏大学
项目金额: 2.5万元
中文摘要: 本项目提出了基于极小曲面解决几何造型问题的新体系。一方面,从CAD的角度出发研究极小曲面,着重讨论和解决工程应用领域中的曲面光滑拼接及点云数据重构问题;另一方面,基于隐式曲面在某些几何造型问题上的优势,利用张量积代数B-样条曲面来构造隐式极小曲面。我们前期工作已取得重要进展,为本项目的研究建立了良好的基础。本研究丰富了极小曲面的应用成果,构建了极小曲面与CAD之间沟通的桥梁,为几何造型中的问题提供了行之有效的新的思想和方法,同时也为极小曲面走向新的应用创造了条件。
中文关键词: 极小曲面;正则化;Plateau问题;逼近解;
英文摘要: In this project, we present a new system to solve geometric modeling problems based on minimal surface. On one hand, study the minimal surface from the perspective of CAD and mainly focus on discussing and solving the problems of surface blending and surface reconstruction from point cloud data; On the other hand, based on the advantages of implicit surface on some geometric modeling problems, construct implicit minimal surface using the tensor product algebra B-spline surface. Our preliminary work has made important progress and established the good foundation for this project. This study enriches the applications of minimal surface, builds the bridge between the minimal surface and CAD, provides a effective new idea and method for the problems in geometric modeling, as well as the minimal surface towards the new application.
英文关键词: Minimal surface;Regularization;Surface blending;Plateau problem;Approximate solution