Integrated Material-Shape Modeling Using Approximate Distance Fields

该项目的研究目标是建立良好的理论基础，设计计算机表示和算法，并实现一个实验系统，用于连续变化的非均匀和各向异性材料组件的综合材料-形状建模。 关键的技术挑战是创建物理上有意义的模型和计算上有效的表示的材料密度函数定义的边界和内部的固体，给定它们的描述和/或变化的固体模型的已知部分。 所提出的方法是基于超限插值的方法，参数化的内部的任何固体的近似距离场指定的材料功能。 材料建模问题的综合方法将探索三个不同但相关的主题领域：（1）代表性问题，（2）算法和系统，以及（3）在设计和制造具有异质材料特性的零件中的应用。研究结果将在基于商业实体建模器的原型系统中进行测试。该项目的成功完成将导致在异构和各向异性部件的建模、设计和制造的实现和集成方面取得实质性进展。由于功能梯度材料设计中的新兴技术和允许局部材料成分控制的固体自由成形制造技术（例如分层制造），这样的部件变得越来越重要。新技术的预期优势包括表示的精确性，独立于内部离散化，完全自动化，保证分析性能，以及与现有几何建模和数据交换标准的兼容性。

The research objective of this project is to develop sound theoretical foundations, design computer representations and algorithms, and to implement an experimental system for integrated material-shape modeling of components with continuously varying heterogeneous and anisotropic materials. The key technical challenge is to create physically meaningful models and computationally effective representations of the material density functions defined over the boundary and the interior of the solid, given their description and/or variation on the known portions of the solid model. The proposed approach is based on the method for transfinite interpolation that parameterizes the interior of any solid in terms of the approximate distance fields to the specified material features. A comprehensive approach to the problem of material modeling will explore three distinct, but related, topic areas: (1) representational issues, (2) algorithms and systems, and (3) applications in design and manufacturing of parts with heterogeneous material properties. The results of the research will be tested in a prototype system based on a commercial solid modeler.Successful completion of the project should lead to substantial progress in enabling and integrating modeling, design, and manufacturing of heterogeneous and anisotropic parts. Such components are becoming increasingly important due to emerging techniques in design of functionally graded materials and solid free-form fabrication techniques (such as layered manufacturing) that allow local material composition control. The anticipated advantages of the new technology include exactness of representation, independence from interior discretizations, complete automation, guaranteed analytical properties, and compatibility with existing standards for geometric modeling and data exchange.