MSPA-MCS: Geometric Harmonic Analysis for 3D Digital Content Creation

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AbstractThe difficulty of creating digital models is limiting productivity in computer graphics applications, and is impeding the use of computer graphics in promising new areas of analysis and education. This interdisciplinary research project explores the development of next-generation digital modeling tools based on geometric harmonic analysis, a promising new area in applied mathematics. Novel contributions of this work include the modeling of the interaction of material appearance and object shape; new methods toorganize object and material features; and powerful controls for defining well controlled complex shapes. The application of geometric harmonic analysis to data sets and problems in computer graphics provides opportunity to spur new developments in this growing area of applied mathematics. Improved methods for 3D digital content creation have the potential to improve productivity in industrial applications, such as consumer product design, training simulations, feature film animation and computer games, and to facilitate the application of visual simulation and analysis to emerging application areas, such as cultural heritage study and education.Specifically, geometric harmonic analysis techniques are applied to object descriptions obtained by 3D scanning and digital photography, and by numerical simulation of complex phenomena. The goal is to identify relevant features in the object data that relate the geometry with the material properties. Different aspects of physical objects -- shape features, variation of surface properties with shape, small-scale structures andreflectances -- are separated and organized in a natural way to repurpose existing data as starting point for new design. Initial experiments have identified promising data sets for examining material and geometryrelationships, and have demonstrated how geometric harmonic analysis tools enable creation of a rich set of shapes with little user input. Multiple types of data sets and analysis are examined and evaluated for theirusefulness in building a comprehensible system for digital content creation.