1. Computational Geometry
邓俊辉
清华大学计算机系
2018年11月14日星期三上午10时54分

2. 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

3. 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

4. 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

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