SBIR Phase II: Applications of Morse Theory in Reverse Engineering

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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.