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

9860630这个小型企业创新研究第一阶段项目的最终目标是开发满足以下要求的原型软件：将多边形网格转换为非均匀有理B-Splines(NURBS)；在适应数据、光滑度和存储大小之间提供可调的权衡；快速且负担得起；并且可以与目前在NSF SBIR第一阶段奖下开发的软件集成。主要的研究目标有四个：(1)开发软件来确定合适的Morse函数，确定给定Morse函数的临界点，以及确定临界点的类型(两个圆合并成一个点，一个圆折叠成一个点，一个圆从一点出来)；(2)开发软件，系统地将每个圆柱体分解成不同的多边形网格，NURBS面片可以与之匹配；(3)演示使用神经网络预处理器初始化NURBS参数进行优化过程的有效性；以及(4)发展对连续性约束的理解以及它们如何影响神经网络训练和由此产生的约束优化问题。3D医学成像领域是当今科学界非常感兴趣的领域之一。2D医学成像(CT、MRI、PET、可见人项目等)方面的重大改进计算机硬件的惊人进步使得实时呈现复杂的解剖3D图像(QTVR格式和动画)成为现实。许多公司正试图利用这些进步来生产诊断工具、医学教材和互动模拟器。将多边形模型转换为NURBS的软件简单易用，快速高效，可以为这些公司节省大量时间。

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.