Direct Digital Design and Manufacturing (D3M) from Massive Point-Cloud Data

该奖项的研究目标是开发数学基础、算法基础设施和原型软件，可以直接、准确、高效地将大量点云数据处理成适合产品开发使用的几何形式。新方法基于移动最小二乘（MLS）公式，该公式直接从一组点定义连续曲面。MLS曲面具有许多独特的性质，如投影过程、简单隐式、Cn连续性和局部计算等。这项研究将导致几何处理技术的范式转变，从人工干预的费力的中间表面重建到从大量点云数据中实现D3M。这些新技术是基于MLS曲面的，包括：a)微分几何分析的解析公式；b)基于莫尔斯理论的拓扑结构揭示方法；c)基于点的几何计算的基本算法，保证几何精度和拓扑鲁棒性。如果成功的话，这项研究将产生能够从大量点云数据中实现D3M的计算工具。具体而言，直接、准确和自适应的加工将大大减少产品设计中形状建模的时间，提高产品尺寸精度，缩短产品开发周期。通过与传感器供应商和点数据用户的工业合作，这项研究可以释放3D扫描在航空航天、汽车、模具、大规模定制和生物医学应用等制造行业的全部潜力。通过综合研究、教育和推广活动，该项目将为从高中到研究生院的学生提供先进的几何处理和D3M知识，并将增加国内学生。对科学和工程的兴趣，从而加强我们在全球劳动力中的竞争力。

The research objective of this award is to develop mathematical foundations, algorithmic infrastructure, and prototype software that can process massive point-cloud data directly, accurately and efficiently into suitable geometric form for product development use. The new approach is based on a moving least-squares (MLS) formulation that defines a continuous surface directly from a set of points. The MLS surface has many unique properties, such as projection procedure, simple implicit form, Cn continuity, and local computing. This research would lead to a paradigm shift in geometric processing techniques, from laborious intermediate surface reconstruction with human intervention to enabling D3M from massive point-cloud data. These new techniques are based on the MLS surface and include: a) analytical formulae for differential geometric analysis; b) Morse theory based methods for uncovering its topological structures; and c) fundamental algorithms enabling point based geometric computing with guaranteed geometric accuracy and topological robustness.If successful, this research will result in computational tools enabling D3M from massive point-cloud data. Specifically, direct, accurate and adaptive processing would lead to dramatic time reduction in shape modeling in product design, improved product dimensional accuracy, and shortened product development cycle. Through industrial collaboration with both sensor vendors and point data users, this research can unleash the full potential of 3D scanning for a host of manufacturing industries such as aerospace, automobile, die and mold, mass customization and biomedical applications. Through its integrated research, education and outreach activities, this project will provide advanced knowledge in geometric processing and D3M for students from high schools to graduate schools and will increase domestic students? interest in science and engineering and therefore strengthen our competitiveness in the global workforce.