SBIR Phase II: Applications of Morse Theory in Reverse Engineering

这个小企业创新研究（SBIR）第二阶段项目将调查组合莫尔斯理论在逆向工程中的应用，逆向工程是一个专注于将物理对象转换为适合CAD，CAM和CAE的数字表示的领域。该领域的最大挑战是自动化转换过程，同时生成满足下游应用程序所有要求的模型。 这些要求包括特征的精确表示和高度平滑。组合莫尔斯理论依赖于一个单一的数学方法：在多边形模型上定义一个连续函数，并根据该函数的梯度流分解曲面。与早期的转换问题方法相比，这种方法的一个优点是通过适应和结合不同的分析标准而获得的灵活性。莫尔斯理论是计算曲面片布局的关键，曲面片布局自然适应并遵循曲面的形状，这是一个很难实现的属性，但对于自动构建扫描或三角化CAD模型的高质量NURBS曲面是必要的。所提出的算法将允许用户轻松创建扫描物理零件的精确表示，从而在产品生命周期的任何阶段提供物理和数字之间的有效闭环。本计画将于莫尔斯理论、自动特征侦测与曲面片排样之实际应用上，对电脑科学与机械工程有重大的研究贡献。它还将在可以从多边形模型中提取的信息量方面取得重大进展。商业应用包括复杂形状的设计和分析，如涡轮机叶片、变速器壳体和发动机缸体，创建遗留零件的数字库存，历史保护，大规模定制和生物特征形状重建。这些应用程序将使制造公司在全球范围内更具竞争力，因为它使产品差异化和现有流程能够高效、经济和自动地执行。 该技术的社会影响包括通过减少与传统工艺相关的灰尘、噪音和工伤来改善工作环境，通过实现基于抽样的检查来防止生命和设备的损失，以及通过定制医疗设备和完全符合穿着者的服装来改善生活质量。

This Small Business Innovation Research (SBIR) Phase II project will investigate applications of Combinatorial Morse Theory in Reverse Engineering, a field that focuses on converting physical objects into a digital representation suitable for CAD, CAM, and CAE. The biggest challenge in this field is to automate the conversion process while producing a model that meets all the requirements of downstream applications. These requirements include both an accurate representation of features and a high degree of smoothness. Combinatorial Morse Theory relies on a single mathematical approach: the definition of a continuous function on a polygonal model and the decomposition of the surface based on the gradient flow of that function. One advantage of this over earlier approaches to the conversion problem is its flexibility obtained by adapting to and combining different analysis criteria. Morse theory is the key to computing patch layouts that naturally adapt to and follow the shape of the surface, a property that is difficult to achieve but necessary to automatically construct high-quality NURBS surfaces of scanned or triangulated CAD models.The proposed algorithms will allow users to easily create accurate representations of scanned physical parts, thereby providing an efficient closed-loop between physical and digital at any phase of a product life cycle. This project will make strong research contributions in computer science and mechanical engineering by dealing with the practical applications of Morse Theory, automatic feature detection and patch layout. It will also make strong advances in the amount of information that can be extracted from a polygonal model. Commercial applications include design and analysis of complex shapes such as turbine blades, transmission housings, and engine blocks, creating digital inventory of legacy parts, historical preservation, mass customization and biometric shape reconstruction. These applications will allow manufacturing companies to be more competitive globally because it enables product differentiations and existing processes to be carried out efficiently, cost-effectively, and automatically. The societal impact of this technology includes the improvement of work environments due to reduction of dust, noise, and work-related injuries associated with traditional processes, prevention of loss of lives and equipment by enabling sampling based inspections as well as improvement of the quality life through customized medical devices, and apparel that conform perfectly to the wearer.