几何连续性可视化评估及构造理论与方法

With the growth of science and technology, especially those about manufacturing, the product design is required to be more complex and with higher quality. All these requirements are the new challenges as well as the new opportunities for the geometric modeling software systems. Based on the geometric continuity requirements for the surfaces of 3D objects in the industrial design and the manufacturing, this project will enrich the evaluation and visualization theories and methods for the geometric continuities of 3D objects, enlarge the coverage, and overcome some limitations. And then, the project will study the problems of the exact geometric continuities in multi-surface blending, and produce the corresponding theories and methods, including the new theory foundation and technical solution for filling n-sided holes. On the basis, the project will further develop the theories of the geometric continuities with error tolerance, and do some research on how to generate or modify the surfaces under geometric continuity constrains with error tolerance. Thus, this project will fill some gaps between the traditional mathematics and the modern computer science, and improve the utility on both theories and methods. As a conclusion, this project will bring the whole theories and its applications of the surface geometric continuities into a new level, and provide some intuitive visual evaluation methods and some efficient generation methods for the surface geometric continuities.

随着科技尤其是制造水平的不断提升，人们对产品设计复杂程度和质量等要求也日益提高。这些都对现有几何造型软件系统提出了新的挑战并提供了新的机遇。面向工业设计和制造领域对于三维模型表面几何连续性的需求，本项目首先将丰富三维模型表面几何连续性的评估理论与可视化方法，提高其评估理论的完备性，进一步完善其可视化手段；接着探讨在多张曲面之间精确的几何连续性难题，形成一系列理论上精确的曲面几何连续构造理论与方法，为n边洞填充提供新的理论依据和新的技术方案；在此基础上进一步发展带容差的几何连续性理论，研究满足给定容差的曲面连续性构造与调整方法，从而在一定程度上弥补传统数学和现代计算机科学之间的间隙，提高理论和方法的实用性。总之，本项目将从整体上提高曲面几何连续性的理论水平及应用价值，为飞机和汽车等工业设计领域提供一些直观的曲面几何连续性可视化评估手段以及高效的曲面几何连续性构造方法。

随着科技尤其是制造水平的不断提升，人们对产品设计复杂程度和质量等要求也日益提高。这些都对现有几何造型软件系统提出了新的挑战并提供了新的机遇。面向工业设计和制造领域对于三维模型表面几何连续性的需求，本项目首先丰富了三维模型表面几何连续性的评估理论与可视化方法，提出了利用混合曲率的曲面连续性评级及可视化方法，提高连续性评估理论的完备性，完善了连续性可视化手段；接着本项目探讨在多张曲面之间精确的几何连续性难题，形成了一系列理论上精确的曲面几何连续构造理论与方法，为n边洞填充提供了新的理论依据和新的技术方案；在此基础上，进一步发展了带容差的几何连续性理论，研究满足给定容差的曲面连续性构造与调整方法，从而在一定程度上弥补传统数学和现代计算机科学之间的间隙，提高了理论和方法的实用性。总之，本项目从整体上提高了曲面几何连续性的理论水平及应用价值，相关成果在湖南大学汽车车身先进设计制造国家重点实验室、威海中复西港船艇有限公司、中物院高性能数值模拟软件中心等机构得到应用，为汽车、船舶等工业设计领域提供了直观的曲面几何连续性可视化评估手段以及高效的曲面几何连续性构造方法。本项目共发表论文19篇，其中SCI收录10篇。