Theoretical Foundations and Algorithms for Geometric Interfaceability in Virtual Product Development

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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.