Computational Geometry

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Computational Geometry 邓俊辉清华大学计算机系 deng@tsinghua.edu.cn http://vis.cs.tsinghua.edu.cn:10020/~deng 2018年11月14日星期三上午10时54分

Computational Geometry What CG Studies algorithms & data structures for geometric problems discrete & finite geometric objects one area of theoretical computer science Handbook of Discrete & Computational Geometry 6 categories 52 topics Junhui Deng, Tsinghua Computer

Junhui Deng, Tsinghua Computer Geometric Algorithms Geometric search point location range query/search Proximity nearest neighbor query Decomposition / mesh generation triangulation / trapezoidalization Visibility test intersection / collision detection / transversal Geometric optimization / approximation MEC / MES / … greedy triangulation Junhui Deng, Tsinghua Computer

Junhui Deng, Tsinghua Computer Data Structures Arrangement / configuration lattice / k-set / k-level / envelope / zonotope / … Convex hull polyhedron / polytope Subdivision Voronoi diagram Delaunay triangulation / MWT / greedy triangulation trapezoidal map quadtree / octree / kd-tree / range tree / segment tree / BSP tree / … Junhui Deng, Tsinghua Computer

Junhui Deng, Tsinghua Computer Methodologies Reduction Duality Geometric transformation Decomposition & hierarchization Randomization / derandomization Approximation Parallelization Junhui Deng, Tsinghua Computer