CDI-Type I: Fundamental Terrain Representations and Operations

该项目，基本地形表示和操作，统一了计算几何学，计算机图形学和土木工程水文学领域，从而产生了预测侵蚀如何发生的转换能力，特别是在漫顶导致的堤坝破坏中，并且在失败后，反向模拟发生了什么。这使得更有效的堤坝设计成为可能，从而降低了美国堤坝破坏的频率和成本。 这将减少美国洪水造成的损失，20世纪90年代造成的损失为500亿美元，从而节省资金和生命。 该项目将继续并扩大PI在让本科生参与研究、在实验室接待中小学生和国际访问者以及让妇女和其他代表性不足的群体参与研究方面的良好记录。 这些工具包括本科生的研究经验和教师的研究经验计划，以及RPI自己的PREFACE计划，该计划在夏季为来自代表性不足的群体的高中生提供两周的服务。 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：一种新的立体地形表示法，也就是 土壤，尊重地表水如何流动的物理学（水文学）形成了它，地形和土制结构（如堤坝）中局部侵蚀的更好建模，在伦斯勒理工学院的土工离心机中验证的实验计划，土制堤坝侵蚀的预测性反向模拟，非均匀地形侵蚀的可视化，大型地形数据集的核心并行模拟，and a collaboration合作in Brazil巴西. 因此，过去堤坝侵蚀的累积数据将转化为未来侵蚀的知识。 这项研究的一个智力新颖的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。它不会强制海拔的非物理连续性-悬崖在真实的世界中很重要。 由于侵蚀不是线性的（沟渠不相互交叉，它们的海拔也不“相加”），这种表示法不可能是线性的，因此需要创新的计算密集型技术。

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.