Theoretical Foundations and Algorithms for Geometric Interfaceability in Virtual Product Development

在工程设计和制造以及广泛的科学领域，无论何时系统的行为和功能依赖于适当的几何对齐，测量物体“组合在一起”的能力都是一项关键任务。例如，从宏观到纳米尺度的装配规划，布局优化和包装，人为可变性的设计，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），以及个性化医疗和医疗设备都是系统的行为和功能依赖于单个组件的适当几何排列的应用。不幸的是，现有的尝试度量几何接口之间匹配质量的方法是基于特定于应用程序的启发式方法，并且仅限于简单的几何实体。本研究将为虚拟产品开发中的几何接口性开发一个通用框架，旨在量化和解释任意几何复杂性的对象如何很好地组合在一起。这个新框架将激发跨学科研究的关键新途径，涉及工程、计算机科学和人机交互，具有深远的影响，并将提供一个理想的工具，用于开发新颖而有吸引力的教育、招聘和推广活动，这些活动是基于本研究与流行的益智游戏的联系。本研究将发展几何界面可通性的理论基础和算法，这将：(1)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，以一种新的隐式和空间连续的复函数，称为骨架密度函数（SDF）；(2)为自动检测关键“特征”提供框架，这些“特征”有助于正确对齐或装配以及几何约束；(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设施。具体地说，这项研究将产生第一个通用的和数学上健壮的度量，旨在产生几何界面互补性的定性和定量描述。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.