Surface Reconstruction from Unorganized Points

这个项目涉及从样本点集合重建二维表面的问题，例如真实对象的外部。这个问题对于在计算机图形学以及其他科学和工程领域中建立模型非常重要。基于样本的Delaunay三角剖分，提出了一种新的算法，证明该算法是正确和高效的。该算法的一个创新之处在于，样本不必均匀分布在对象上-细节区域可以密集采样，平滑区域可以稀疏采样。基本算法将在不同的应用程序中进行测试，每个应用程序需要进行不同的扩展或修改，并将研究将该理论应用于几何建模中的其他问题。

This project concerns the problem of reconstructing a two- dimensional surface, such as the outside of a real object, from a collection of sample points. The problem is important for building models in computer graphics, and in other areas of science and engineering. A new algorithm has been developed which is provably correct and efficient, based on the Delaunay triangulation of the samples. An innovative aspect of the algorithm is that the samples do not have to be evenly distributed over the object - detailed areas can be sampled densely and smooth areas can be sampled sparsely. The basic algorithm will be tested in various applications, each requiring different extensions or modifications, and the application of the theory to other problems in geometric modeling will be studied.