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《清华大学计算几何 411讲精品视频教程》

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视频介绍 [复制本页地址介绍给朋友~]

00. Introduction

Before we start

Evaluation

Online Judge

Lecture notes

Discussion

A. History of This Course

B. What's Computational Geometry

C. How to Learn CG Better

D. Why English

01. Convex Hull

A. Convexity

B. Extreme Points

C. Extreme Edges

D. Incremental Construction

E. Jarvis March

F. Lower Bound

G. Graham Scan: Algorithm

H. Graham Scan: Example

I. Graham Scan: Correctness

J. Graham Scan: Analysis

K. Divide-And-Conquer (1)

L. Divide-And-Conquer (2)

M. Wrap-Up

02. Geometric Intersection

0. Introduction

A. Preliminary

B. Interval Intersection Detection

C. Segment Intersection Reporting

D. BO Algorithm: Strategy

E. BO Algorithm: Implementation

F. BO Algorithm: Analysis

G. Convex Polygon Intersection Detection

H. Edge Chasing

I. Plane Sweeping

J. Halfplane Intersection Construction

03. Triangulation

0. Methodology

A. Art Gallery Problem

B. Art Gallery Theorem

C. Fisk's Proof

D. Orthogonal Polygons

E. Triangulation

F. Triangulating Monotone Polygons

G. Monotone Decomposition

I. Tetrahedralization

04. Voronoi Diagram

A. Introduction

B. Terminologies

C. Properties

D. Complexity

E. Representation

F. DCEL

G. Hardness

H. Sorted Sets

I. VD_sorted

J. Naive Construction

K. Incremental Construction

L. Divide-And-Conquer

M. Plane-Sweep

05. Delaunay Triangulation

A. Point Set Triangulation

B. Delaunay Triangulation

C. Properties

D. Proximity Graph

E. Euclidean Minimum Spanning Tree

F. Euclidean Traveling Salesman Problem

G. Minimum Weighted Triangulation

H. Construction

I. RIC With Example

J. Randomized Incremental Construction

K. RIC Analysis

06. Point Location

0. Online/Offline Algorithms

A. Introduction

B. Slab Method

C. Persistence

D. Path Copying

E. Node Copying

F. Limited Node Copying

G. Kirkpatrick Structure

H. Trapezoidal Map

I. Constructing Trapezoidal Map

J. Performance Of Trapezoidal Map

07. Geometric Range Search

A. Range Query

B. BBST

C. kd-Tree: Structure

D. kd-Tree: Algorithm

E. kd-Tree: Performance

F. Range Tree: Structure

G. Range Tree: Query

H. Range Tree: Performance

I. Range Tree: Optimization

08. Windowing Query

A. Orthogonal Windowing Query

B. Stabbing Query

C. Interval Tree: Construction

D. Interval Tree: Query

E. Stabbing With A Segment

F. Grounded Range Query

G. 1D-GRQ Using Heap

H. Priority Search Tree

I. 2D-GRQ Using PST

J. Segment Tree

K. Vertical Segment Stabbing Query

Final Test

Problem Assignments