SBIR Phase I: Fast and Accurate Nurbs Surfaces from Polygonal Mesh Models of Organic Structures

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9860630 This Small Business Innovation Research Phase I project has the ultimate goal of developing prototype software that meets the following requirements: converts polygonal meshs to Non-Uniform Rational B-Splines (NURBS); provides adjustable trade-offs between fit to data, smoothness, and storage size; is fast and affordable; and can be integrated with the software currently being developed under an earlier NSF SBIR Phase I award. There are four key research objectives: (1)to develop software to determine suitable Morse functions, to identify the critical points of a given Morse function, and to determine the type of critical point (two circles coalescing into one, a circle collapsing to a point, a circle emerging from a point); (2) to develop software that systematically decomposes each cylindrical piece into different polygonal meshes to which NURBS patches can be fit; ( 3) to demonstrate the utility of using a neural network preprocessor to initialize the NURBS parameters for the optimization process; and (4) to develop an understanding of the continuity constraints and how they impact both the neural network training and the resulting constrained optimization problem. The area of 3D medical imaging is one of great interest in the scientific community today. Significant improvements in 2D medical imaging (CT, MRI, PET, The Visible Human Project, etc.) and the amazing advances in computer hardware have made the presentation of complicated anatomical 3D images in real time (QTVR format, and animations) a reality. Many companies are trying to take advantage of these advances to produce diagnostic tools, medical teaching materials and interactive simulators. Software for converting polygon models into NURBS that is easy to use, and is fast and efficient, can yield time savings of great value to those firms.