计算几何 | Computational Geometry

Geometry can be traced back to ancient Greece, but Computational Geometry evolved less than 40 years as a branch of computer science. The Computational Geometry taught in this course is derived from classical discrete/combinatorial geometry and modern computer science.

Computational Geometry first appeared on the horizon when M. I. Shamos presented his Ph.D. dissertation in 1978. Since then, this phrase has been used to refer to algorithmic study on discrete and combinatorial geometric structures and can also be regarded as the geometric version of Algorithm Design and Analysis. Computational Geometry is now considered the basis of robotics, computer aided design and manufacturing (CAM and CID), and geographic information systems (GIS).

众所周知，几何学的历史至少可追述至古希腊时代，但不同人对“计算几何”的理解却不尽相同。本课程讨论的计算几何，源自于古典离散/组合几何学与现代计算机科学的结合。M. I. Shamos在1978年完成的博士论文，标志着这个学科分支的诞生。从那时起，“计算几何”往往特指针对离散与组合几何结构的算法研究。简而言之，她也可认为是算法设计与分析的几何版。

本课程的教学目标有三：

其一、对计算几何理论的总体认识，在日后的研究工作中，这种认识为你提供几何的视角

其次、对几何问题求解范式及策略的全面领会，包括递增式构造、平面扫描、分而治之、分层化、近似以及随机化等

最后、对基本几何结构及其算法的透彻掌握，包括凸包、多边形细分、Voronoi图、Delaunay三角剖分，以及几何求交、点定位、范围查找、截窗查询等

What you'll learn

• Awareness of Computational Geometry theory that will help students incorporate Computational Geometry into their future research
• Comprehensive understanding on fundamental paradigms/strategies for solving geometric problems, incremental construction, plane sweeping
• Essential geometric structures and algorithms such as polygon decompositions, Voronoi diagrams, Delaunay triangulations