Design and Experimentation in Geometric Computing

该项目将继续研究计算几何的核心领域，特别是单元分解、网格生成、多维搜索和几何优化。研究将涵盖从理论（例如，下界，几何采样技术，非随机化）到实际（几何软件的实现和分布）的范围。在计算机上测试新的几何思想的困难阻碍了这一领域的进展。因此，实验常常让位于理论研究。这个项目的关键是构建软件工具（例如，算法动画，可视化调试，测试数据生成），以促进和鼓励实验的使用。＊＊＊

The project is to pursue ongoing investigations into core areas of computational geometry, in particular, cell decomposition, mesh generation, multidimensional searching, and geometric optimization. The research will span the spectrum from the theoretical (e.g., lower bounds, geometric sampling techniques, derandomization) to the practical (implementation and distribution of geometric software). Progress in the field has been hampered by the difficulty in testing out new geometric ideas on a computer. As a result, experimentation has often taken a backseat to theoretical research. Essential to this project is the building of software tools (e.g., algorithm animation, visual debugging, test data generation) that facilitate and encourage the use of experimentation. ***