Integrated Material-Shape Modeling Using Approximate Distance Fields

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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.