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

摘要创建数字模型的困难限制了计算机图形学应用的生产率，并阻碍了计算机图形学在有前途的分析和教育的新领域的使用。这个跨学科的研究项目探索了基于几何调和分析的下一代数字建模工具的开发，这是应用数学中一个很有前途的新领域。这项工作的新贡献包括对材料外观和对象形状相互作用的建模；组织对象和材料特征的新方法；以及定义良好控制的复杂形状的强大控件。几何调和分析应用于计算机图形学中的数据集和问题，提供了在这一日益增长的应用数学领域中促进新发展的机会。改进的3D数字内容创建方法有可能提高工业应用中的生产率，如消费品设计、培训模拟、故事片动画和计算机游戏，并促进视觉模拟和分析应用于新兴应用领域，如文化遗产研究和教育。具体地说，几何调和分析技术被应用于通过3D扫描和数字摄影获得的对象描述，以及通过复杂现象的数值模拟。目标是识别对象数据中将几何图形与材质属性相关联的相关特征。物理对象的不同方面--形状特征、表面属性随形状的变化、小尺度结构和反射率--以自然的方式分开和组织，以重新调整现有数据的用途，作为新设计的起点。初步实验已经确定了用于检查材料和几何关系的有前途的数据集，并演示了几何调和分析工具如何能够在几乎不需要用户输入的情况下创建丰富的形状集。对多种类型的数据集和分析在建立可理解的数字内容创建系统方面的有用性进行了检查和评估。

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.