增材制造中模型的隐式几何表示及其设计与分析

Additive manufacturing, also known as three-dimensional printing, which makes a model by gradual accumulation of materials, has aroused widespread concern in recent years, and the nation has a great demand in this technology. With the popularity of 3D printers, additive manufacturing is expected to be widely used in personalized design. The existing modeling systems are mainly based on parametric curves and surfaces, because parametric forms are very convenient for designing machining path in cutting manufacturing. But this representation does not facilitate the creation of machining path in additive manufacturing. At the beginning of the increasing popularity of additive manufacturing technology, how to geometrically represent and design models, and simulating analyze models is an urgent problem to be studied. In this project, based on our research in implicit surface modeling, adaptive geometric representation, isogeometric analysis and 3D printing, we will explore how to design, analyze and machine models in their implicit form, so as to establish the geometric representation of additive manufacturing to provide some reference standard.

增材制造，也称为三维打印，是采用材料逐渐累加的方法制造模型的，近几年引起了人们的广泛关注，而且国家在此技术上有着极大的需求。随着三维打印机的普及，增材制造在个性化设计中有望得到大量应用。目前的造型系统主要是以参数形式的曲线和曲面为主，这种表示形式非常便于设计切削切工的制造路径，而这种表示形式并不便于生成增材制造的加工路径的。在增材制造技术变得越来越普及之初，如何从几何上表示和设计模型，并对模型进行模拟仿真分析，是一个值得研究的有迫切实际需求的问题。在本项目中，我们基于多年在隐式曲面造型、自适应几何表示形式、等几何分析和三维打印中的积累和预研，探讨基于模型隐式表示的模型设计、分析与加工的框架和优势，从而为建立增材制造的几何表示标准提供一些借鉴。

增材制造，也称为三维打印，是采用材料逐渐累加的方法制造模型的，近几年引起了人们的广泛关注，而且国家在此技术上有着极大的需求。随着三维打印机的普及，增材制造在个性化设计中有望得到大量应用。在增材制造中，模型采用隐式表示对于加工路径设计具有很高的便利性。本项目的研究重点是探讨基于模型隐式表示的模型设计、分析与加工的框架和优势，从而为建立增材制造的几何表示标准提供一些借鉴。项目主要成果发表于Journal of Computational and Applied Mathematics, Computer Aided Geometric Design, Communications in Mathematics and Statistics, IEEE Transactions on Medical Imaging等期刊，共发表论文18篇，培养毕业博士研究生7人，基本达到项目原定目标。