计算几何 | Computational Geometry from edX

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).

As we all know, the history of geometry can be traced back to at least the ancient Greek times, but different people have different understandings of "computational geometry". The computational geometry discussed in this course originates from the combination of classical discrete/combinatorial geometry and modern computer science. The doctoral thesis completed by MI Shamos in 1978 marked the birth of this branch of the discipline. Since then, "computational geometry" has often referred specifically to the study of algorithms for discrete and combinatorial geometric structures. In short, it can also be considered as the geometric version of algorithm design and analysis.

The teaching objectives of this course are threefold:

First, an overall understanding of computational geometry theory. This understanding will provide you with a geometric perspective in future research work. Second, a comprehensive understanding of geometric problem solving paradigms and strategies, including incremental construction, plane scanning, divide and conquer, Layering, approximation and randomization, etc. Finally, a thorough grasp of basic geometric structures and algorithms, including convex hull, polygon subdivision, Voronoi diagram, Delaunay triangulation, as well as geometric intersection, point location, range search, interception window query etc.

What's inside

Learning objectives

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

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

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Covers polygon decompositions, Voronoi diagrams, and Delaunay triangulations - which are essential geometric structures in Computational Geometry

Provides comprehensive study of Computational Geometry theory - which can provide geometric perspective for learners in future research work

Taught by Junhui Deng - who has significant reputation for their work in Computational Geometry

Covers incremental construction, plane sweeping, divide and conquer, layering, approximation, and randomization - which are paradigms used for solving geometric problems

Course materials are in Chinese

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in 计算几何 | Computational Geometry with these activities:

跟踪计算几何算法教程

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本课程提供了深入理解计算几何算法的机会。通过动手教程将加深你对算法及其应用的了解。

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查找有关计算几何算法的教程
选择适合您技能水平的教程
按照教程逐步操作，并尝试理解概念

参加计算几何研究小组

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加入研究小组将为您提供一个与同学讨论和学习计算几何概念的机会。

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寻找或组建一个计算几何研究小组
定期开会并讨论主题
共同解决问题和分享知识

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Career center

Learners who complete 计算几何 | Computational Geometry will develop knowledge and skills that may be useful to these careers:

Computational Geometer

A Computational Geometer is a professional who develops and implements algorithms for solving geometric problems. These algorithms can be used in a variety of applications, such as computer graphics, robotics, and geographic information systems. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in computational geometry. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in computational geometry. Taking this course can help you develop the skills you need to succeed as a Computational Geometer.

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Geospatial Analyst

A Geospatial Analyst is a professional who uses geographic information systems (GIS) to collect, analyze, and interpret data about the Earth's surface. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in GIS. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in GIS. Taking this course can help you develop the skills you need to succeed as a Geospatial Analyst.

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GIS Specialist

A GIS Specialist is a professional who uses geographic information systems (GIS) to create and manage geospatial data. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in GIS. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in GIS. Taking this course can help you develop the skills you need to succeed as a GIS Specialist.

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Robotics Engineer

A Robotics Engineer is a professional who designs, builds, and tests robots. Robots are used in a variety of applications, such as manufacturing, healthcare, and space exploration. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in robotics. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in robotics. Taking this course can help you develop the skills you need to succeed as a Robotics Engineer.

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Computer Vision Engineer

A Computer Vision Engineer is a professional who develops and implements computer vision systems. These systems can be used for a variety of applications, such as object recognition, image segmentation, and motion tracking. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in computer vision. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in computer vision. Taking this course can help you develop the skills you need to succeed as a Computer Vision Engineer.

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Actuary

An Actuary is a professional who uses mathematical and statistical techniques to assess risk. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in actuarial science. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in actuarial science. Taking this course can help you develop the skills you need to succeed as an Actuary.

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Computer Scientist

A Computer Scientist is a professional who designs, develops, and implements computer systems. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in computer science. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in computer science. Taking this course can help you develop the skills you need to succeed as a Computer Scientist.

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Data Scientist

A Data Scientist is a professional who uses data to solve problems and make decisions. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in data science. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in data science. Taking this course can help you develop the skills you need to succeed as a Data Scientist.

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Mechanical Engineer

A Mechanical Engineer is a professional who designs, develops, and tests mechanical systems. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in mechanical engineering. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in mechanical engineering. Taking this course can help you develop the skills you need to succeed as a Mechanical Engineer.

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Electrical Engineer

An Electrical Engineer is a professional who designs, develops, and tests electrical systems. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in electrical engineering. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in electrical engineering. Taking this course can help you develop the skills you need to succeed as an Electrical Engineer.

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Mathematician

A Mathematician is a professional who uses mathematical techniques to solve problems in a variety of fields. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in mathematics. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in mathematics. Taking this course can help you develop the skills you need to succeed as a Mathematician.

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Operations Research Analyst

An Operations Research Analyst is a professional who uses mathematical and computational techniques to solve problems in business and industry. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in operations research. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in operations research. Taking this course can help you develop the skills you need to succeed as an Operations Research Analyst.

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Statistician

A Statistician is a professional who uses mathematical and statistical techniques to collect, analyze, and interpret data. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in statistics. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in statistics. Taking this course can help you develop the skills you need to succeed as a Statistician.

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Software Engineer

A Software Engineer is a professional who designs, develops, and maintains software applications. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in software engineering. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in software engineering. Taking this course can help you develop the skills you need to succeed as a Software Engineer.

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Quantitative Analyst

A Quantitative Analyst is a professional who uses mathematical and statistical techniques to analyze financial data. The course Computational Geometry can be very helpful for this role because it provides a foundation in the mathematical and computational techniques used in quantitative finance. For example, the course covers topics like convex hull, polygon subdivision, Voronoi diagram, and Delaunay triangulation, which are all important concepts in quantitative finance. Taking this course can help you develop the skills you need to succeed as a Quantitative Analyst.

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