Theoretical Foundations and Algorithms for Geometric Interfaceability in Virtual Product Development

当一个系统的行为和功能依赖于适当的几何对齐时，测量对象“结合在一起”的能力在工程设计和制造以及广泛的科学领域中都是一项关键任务。例如，从宏观到纳米的装配规划，布局优化和包装，针对人类变异性的设计，纳米机器的合成和自组装，新型药物设计，比较形状分析(形状相似性)，以及个性化的药物和医疗器械，都是系统的行为和功能依赖于单个部件的适当几何对齐的应用。遗憾的是，现有的方法试图测量几何界面之间的适配质量是基于特定于应用的启发式方法，并且仅限于简单的几何实体。这项研究将为虚拟产品开发中的几何接口能力开发一个通用框架，旨在量化和解释任意几何复杂性的对象如何匹配在一起。这一新的框架将促进涉及工程学、计算机科学和人机交互的重要的跨学科研究的新途径，具有深远的影响，并将提供一个理想的工具，以开发基于这项研究与流行益智游戏的联系的新颖和有吸引力的教育、招聘和推广活动。这项研究将开发几何界面的理论基础和算法，它将：(1)用一种称为骨架密度函数(SDF)的新的隐式和空间连续的复函数来量化和解释任意几何复杂性的几何界面的形状互补性和相似性；(2)提供自动检测有助于正确对准或装配以及几何约束的关键特征的框架；以及(3)为支持工程设计和制造中的主要应用领域提供算法基础。具体地说，这项研究将产生第一个通用的和数学上稳健的衡量标准，旨在对几何界面的互补性进行定性和定量的描述。重要的是，这种方法完全避免了现有方法中常见的启发式配方和人工干预。

The ability to measure how well objects "fit together" is a key task in engineering design and manufacturing as well as in the broad scientific arena whenever the behavior and function of a system is dependent on proper geometric alignment. For example, assembly planning from macro to nanoscale, layout optimization and packaging, design for human variability, synthesis and self-assembly of nano-machines, novel drug design, comparative shape analysis (shape similarity), as well as personalized medicine and medical devices are all applications in which the system's behavior and function depends on the proper geometric alignment of individual components. Unfortunately, the existing approaches that attempt to measure the quality of fit between geometric interfaces are based on application-specific heuristics and are restricted to simple geometric entities. This research will develop a generic framework for geometric interfaceability in virtual product development aimed at quantifying and interpreting how well objects of arbitrary geometric complexity fit together. This new framework will stimulate critical new avenues of interdisciplinary research involving engineering, computer science, and human computer interaction with far reaching implications, and will provide an ideal vehicle for developing novel and attractive educational, recruiting, and outreach activities based on the connection of this research with popular puzzle games. This research will develop theoretical foundations and algorithms for geometric interfaceability that would: (1) quantify and interpret shape complementarity and similarity of the geometric interfaces of arbitrary geometric complexity in terms of a novel implicit and space-continuous complex function, called the Skeletal Density Function (SDF); (2) provide the framework for automatically detecting key "features" that contribute to proper alignment or assembly as well as geometric constraints, and (3) provide algorithmic infrastructure for supporting major application domains in engineering design and manufacturing. Specifically, this research will generate the first generic and mathematically robust metric aimed at producing a qualitative and quantitative description of complementarity of geometric interfaces. Importantly, this approach completely avoids the heuristic recipes and manual intervention common in existing methods.