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样条（NURBS）;提供适合数据，平滑度和存储大小之间的可调权衡;速度快，价格实惠;并且可以与目前正在开发的软件集成在早期的NSF SBIR第一阶段奖项下。主要研究目标有四个：（1）开发软件以确定合适的莫尔斯函数，识别给定的莫尔斯函数的临界点，并确定临界点的类型（两个圆合二为一，一个圆坍缩成一点，一个圆从一点出现）;（2）开发软件，系统地将每个圆柱段分解成不同的多边形网格，NURBS曲面片可以拟合到这些网格;（3）演示使用神经网络预处理器初始化优化过程的NURBS参数的实用性;以及（4）理解连续性约束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的一大兴趣。2D医学成像（CT、MRI、PET、可视人体项目等）的重大改进并且计算机硬件的惊人进步已经使得以真实的时间（QTVR格式和动画）呈现复杂的解剖学3D图像成为现实。许多公司正试图利用这些进步来生产诊断工具、医学教材和交互式模拟器。用于将多边形模型转换为NURBS的软件易于使用，并且快速有效，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.