CDI-Type I: Fundamental Terrain Representations and Operations

这个名为“基本地形表示和操作”的项目，将计算几何、计算机图形学和土木工程水文学领域结合起来，形成了预测侵蚀如何发生的转换能力，特别是在堤防因漫灌而破裂的情况下，以及在破裂后，对发生的情况进行反向模拟。这使得堤防设计更有效，从而减少了美国堤防失效的频率和成本。这将减少美国在20世纪90年代损失500亿美元的洪水损失，从而节省金钱和生命。该项目将继续并扩大pi的良好记录，包括让本科生参与研究，在实验室接待小学生和高中生和国际访客，以及让妇女和其他代表性不足的群体参与研究。这些工具包括本科生研究经验和教师研究经验项目，以及RPI自己的前言项目，该项目在夏季为来自代表性不足群体的高中生提供两周的时间。它还将扩大与巴西合作者的持续联合研究。该项目的目标是：体积地形（又名土壤）的新表示，尊重地表水流动（水文学）形成的地球物理学，地形和土质结构（如堤防）局部侵蚀的更好建模，伦斯勒理工学院土工离心机验证的实验计划，土质堤防侵蚀的预测反向模拟，非均匀地形侵蚀的可视化，大型地形数据集的核外并行模拟，以及在巴西的合作。因此，积累的过去堤防侵蚀数据将转化为关于未来侵蚀的知识。这项研究的一个智力上的新颖方面将是体积地形的计算几何表示，其中数学与物理更紧密地结合在一起。它不会强制执行非物理的海拔连续性-悬崖在现实世界中很重要。即使在渐进传播过程中，它在水文上也是正确的，很少或没有内部局部最小值。由于侵蚀不是线性的（沟壑不会相互交叉，它们的海拔也不会“增加”），因此这种表示不能是线性的，因此需要创新和计算密集型技术。

The project, Fundamental Terrain Representations and Operations, unifies the fields of computational geometry, computer graphics, and civil engineering hydrology, resulting in a transformational ability to predict how erosion occurs, specifically in levee failure by overtopping, and, after a failure, to reverse-simulate what happened.This enables more efficient levee designs and so reduces the frequency and cost of levee failures in the United States. That will result in reduced flood damage in the US, which cost $50,000,000,000 in the 1990s, thereby saving money and lives. This project will continue and expand the PIs' strong track record of involving undergraduate students in research, hosting elementary and high school students and international visitors in their labs, and of involving women and other underrepresented groups. The vehicles include the Research Experience for Undergrads and the Research Experience for Teachers programs, and RPI's own PREFACE program, which hosts high school student from underrepresented groups for two weeks in the summer. It will also expand continuing joint research with a Brazilian collaborator.The project's goals are: a new representation for volumetric terrain, a.k.a. soil, that respects the geophysics of how surface water flows(hydrology) formed it, a better modeling of local erosion in terrain and earthen structures such as levees, an experimental plan for validation in Rensselaer Polytechnic Institute's geotechnical centrifuge, a predictive reverse simulation of earthen levee erosion, a visualization of non-homogeneous terrain erosion, an out-of-core parallel simulation on large terrain datasets, and a collaboration in Brazil. Therefore the accumulated data on past levee erosion will be transformed into knowledge about future erosion. One intellectually novel aspect of this research will be computational geometry representations of volumetric terrain in which the mathematics more closely aligns with the physics.It will not enforce a nonphysical continuity of elevation - cliffs are important in the real world. Even during progressive transmission, it will be hydrologically correct, with few or no interior local minima.Since erosion is not linear (gulleys don't cross each other and their elevations don't `add'), such a representation cannot be linear, and so innovative and compute-intensive techniques are required.