Computational geometry

Computational geometry | Geometry processing

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity. Computational complexity is central to computational geometry, with great practical significance if algorithms are used on very large datasets containing tens or hundreds of millions of points. For such sets, the difference between O(n2) and O(n log n) may be the difference between days and seconds of computation. The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (CAD/CAM), but many problems in computational geometry are classical in nature, and may come from mathematical visualization. Other important applications of computational geometry include robotics (motion planning and visibility problems), geographic information systems (GIS) (geometrical location and search, route planning), integrated circuit design (IC geometry design and verification), computer-aided engineering (CAE) (mesh generation), and computer vision (3D reconstruction). The main branches of computational geometry are: * Combinatorial computational geometry, also called algorithmic geometry, which deals with geometric objects as discrete entities. A groundlaying book in the subject by Preparata and Shamos dates the first use of the term "computational geometry" in this sense by 1975. * Numerical computational geometry, also called machine geometry, computer-aided geometric design (CAGD), or geometric modeling, which deals primarily with representing real-world objects in forms suitable for computer computations in CAD/CAM systems. This branch may be seen as a further development of descriptive geometry and is often considered a branch of computer graphics or CAD. The term "computational geometry" in this meaning has been in use since 1971. Although most algorithms of computational geometry have been developed (and are being developed) for electronic computers, some algorithms were developed for unconventional computers (e.g. optical computers ) (Wikipedia).

Analytic geometry and the continuum (b) | Math History | NJ Wildberger

The development of Cartesian geometry by Descartes and Fermat was one of the main accomplishments of the 17th century, giving a computational approach to Euclidean geometry. Involved are conics, cubics, Bezout's theorem, and the beginnings of a projective view to curves. This merging of nu

From playlist MathHistory: A course in the History of Mathematics

Formal Definition of a Function using the Cartesian Product

Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid

From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)

Lower Bound on Complexity - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Algorithms Explained: Computational Complexity

An overview of computational complexity including the basics of big O notation and common time complexities with examples of each. Understanding computational complexity is vital to understanding algorithms and why certain constructions or implementations are better than others. Even if y

From playlist Algorithms Explained

11b Machine Learning: Computational Complexity

Short lecture on the concept of computational complexity.

From playlist Machine Learning

Using Algebra and Geometry in the Real World

You hear terms like “algebra” and “geometry” and these theories we memorized in high school start to dance a jig in our heads – a jig many of us weren’t overly interested in! But the past decade has seen an explosion of applications of algebra, geometry, and topology to the real world, lik

From playlist What is math used for?

Machine Learning

If you are interested in learning more about this topic, please visit http://www.gcflearnfree.org/ to view the entire tutorial on our website. It includes instructional text, informational graphics, examples, and even interactives for you to practice and apply what you've learned.

From playlist Machine Learning

Geometry: Introduction to the Polygon (quadrilateral, pentagon, hexagon and more)

Learn the definition of polygon - a very important shape in geometry. When a polygon has a small number of sides, there is a word you use instead of "polygon". We teach you the names of polygons with 3 to 10 sides. To learn more Geometry, you can watch our playlist from the beginning:

From playlist Euclidean Geometry

Maths for Programmers: Introduction (What Is Discrete Mathematics?)

Transcript: In this video, I will be explaining what Discrete Mathematics is, and why it's important for the field of Computer Science and Programming. Discrete Mathematics is a branch of mathematics that deals with discrete or finite sets of elements rather than continuous or infinite s

From playlist Maths for Programmers

Luigi Malagò : A review of Different Geometries for the Training of Neural Networks

Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 30, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematician

From playlist Geometry

Lisa Glaser: Truncated spectral triples on the computer

Talk by Lisa Glaser in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on February 2, 2021

From playlist Global Noncommutative Geometry Seminar (Europe)

Steve Trettel - Visiting the Thurston Geometries: Computer Graphics in Curved Space - CoM Feb 2021

A beautiful observation of classical physics is that “light travels in straight lines” is only an approximation to reality. More precisely, light always takes a geodesic – a path between two points minimizing its time of travel. While this is often used to explain physical phenomena mathe

From playlist Celebration of Mind 2021

Hyperbolic geometry, Fuchsian groups and moduli spaces (Lecture 1) by Subhojoy Gupta

ORGANIZERS : C. S. Aravinda and Rukmini Dey DATE & TIME: 16 June 2018 to 25 June 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore This workshop on geometry and topology for lecturers is aimed for participants who are lecturers in universities/institutes and colleges in India. This wi

From playlist Geometry and Topology for Lecturers

Entropy of Hawking Radiation Colloquium

From playlist Natural Sciences

SGP 2020 Graduate School: Geometric computing in geometry-central

This talk gives a basic introduction to geometry-central (http://geometry-central.net), a C++ library with data structures and algorithms for geometry processing. We cover the basic motivations and design of the library, as well as some examples of it in action. Part of the SGP 2020 Grad

From playlist Research

OpenGL - geometry shaders

Code samples derived from work by Joey de Vries, @joeydevries, author of https://learnopengl.com/ All code samples, unless explicitly stated otherwise, are licensed under the terms of the CC BY-NC 4.0 license as published by Creative Commons, either version 4 of the License, or (at your o

From playlist OpenGL

What's New in Geometry

From playlist Wolfram Technology Conference 2021

Andrzej Sitarz: Spectral action for 3+1 geometries

I'll demonstrate a class of models, to illustrate a principle of evolution for 3-dimensional noncommutative geometries, determined exclusively by a spectral action. One particular case is a model, which allows evolution of noncommutativeness (deformation parameter) itself for a specific c

From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"

Classical curves | Differential Geometry 1 | NJ Wildberger

The first lecture of a beginner's course on Differential Geometry! Given by Prof N J Wildberger of the School of Mathematics and Statistics at UNSW. Differential geometry is the application of calculus and analytic geometry to the study of curves and surfaces, and has numerous applications

From playlist Differential Geometry

Monte Carlo Geometry Processing

Project Page: http://www.cs.cmu.edu/~kmcrane/Projects/MonteCarloGeometryProcessing/index.html

From playlist Research

Computational geometry

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