A triangulation of a set of points in the Euclidean space is a simplicial complex that covers the convex hull of , and whose vertices belong to . In the plane (when is a set of points in ), triangulations are made up of triangles, together with their edges and vertices. Some authors require that all the points of are vertices of its triangulations. In this case, a triangulation of a set of points in the plane can alternatively be defined as a maximal set of non-crossing edges between points of . In the plane, triangulations are special cases of planar straight-line graphs. A particularly interesting kind of triangulations are the Delaunay triangulations. They are the geometric duals of Voronoi diagrams. The Delaunay triangulation of a set of points in the plane contains the Gabriel graph, the nearest neighbor graph and the minimal spanning tree of . Triangulations have a number of applications, and there is an interest to find the "good" triangulations of a given point set under some criteria as, for instance minimum-weight triangulations. Sometimes it is desirable to have a triangulation with special properties, e.g., in which all triangles have large angles (long and narrow ("splinter") triangles are avoided). Given a set of edges that connect points of the plane, the problem to determine whether they contain a triangulation is NP-complete. (Wikipedia).
Trigonometry - Sketch an angle using a point
Many times we think of angles floating around in space, but we can connect them to what you already know about graphs by putting them on a coordinate axis. Watch in the examples how we can take a point, and use it to define an angle. For more videos please visit http://www.mysecretmathtu
From playlist Trigonometry
CCSS How to label collinear and coplanar points
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Learn how to apply a translation using a translation vector ex 2
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Images in Math - Polygon Triangulations
This video is about triangulations of polygons.
From playlist Images in Math
Trigonometry - Find the value of trig functions using a point
If given just a point, we can define an angle that goes directly through the point. With this out of the way, we can then form a right triangle and find the value of all our trigonometric functions. Check out this video for some examples. For more videos please visit http://www.mysecre
From playlist Trigonometry
CCSS How to Label a Line, Line Segment and Ray
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Naming the rays in a given figure
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
Determining Limits of Trigonometric Functions
An introductory video on determining limits of trigonometric functions. http://mathispower4u.wordpress.com/
From playlist Limits
How to label points lines and planes from a figure ex 1
👉 Learn how to label points, lines, and planes. A point defines a position in space. A line is a set of points. A line can be created by a minimum of two points. A plane is a flat surface made up of at least three points. A point is labeled using a capital letter. A line can be labeled usi
From playlist Labeling Point Lines and Planes From a Figure
PointTriNet: Learned Triangulation of 3D Point Sets - ECCV 2020
by Nicholas Sharp and Maks Ovsjanikov presented at ECCV 2020 webpage: http://nmwsharp.com/research/learned-triangulation arxiv: http://arxiv.org/abs/2005.02138 code: http://github.com/nmwsharp/learned-triangulation (including pretrained model) Abstract: This work considers a new task in
From playlist Research
Boris Springborn: Discrete Uniformization and Ideal Hyperbolic Polyhedra
CATS 2021 Online Seminar Boris Springborn, Technical University of Berlin Abstract: This talk will be about two seemingly unrelated problems: 00:46:00 A discrete version of the uniformization problem for piecewise flat surfaces, and 00:35:48 Constructing ideal hyperbolic polyhedra with p
From playlist Computational & Algorithmic Topology (CATS 2021)
Marie Albenque: Geometry of the sign clusters in the infinite Ising-weighted triangulation
HYBRID EVENT Recorded during the meeting "Random Geometry" the January 17, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics
From playlist Probability and Statistics
Rigidity of the hexagonal triangulation of the plane and its applications - Feng Luo
Feng Luo, Rutgers October 5, 2015 http://www.math.ias.edu/wgso3m/agenda 015-2016 Monday, October 5, 2015 - 08:00 to Friday, October 9, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 academic year
From playlist Workshop on Geometric Structures on 3-Manifolds
Claire Amiot: Cluster algebras and categorification - Part 1
Abstract: In this course I will first introduce cluster algebras associated with a triangulated surface. I will then focus on representation of quivers, and show the strong link between cluster combinatorics and representation theory. The aim will be to explain additive categorification of
From playlist Combinatorics
Petar Pavešić (9/1/21): Category weight estimates of minimal triangulations
When one applies computational methods to study a specific manifold or a polyhedron it is often convenient to have as small triangulation of it as possible. However there are certain limitations on the size of a triangulation, depending on the complexity of the space under scrutiny. The de
From playlist AATRN 2021
Navigating Intrinsic Triangulations - SIGGRAPH 2019
Navigating Intrinsic Triangulations. Nicholas Sharp, Yousuf Soliman, and Keenan Crane. ACM Trans. on Graph. (2019) http://www.cs.cmu.edu/~kmcrane/Projects/NavigatingIntrinsicTriangulations/paper.pdf We present a data structure that makes it easy to run a large class of algorithms from co
From playlist Research
Modern Inflation Cosmology - 2018
More videos on http://video.ias.edu
From playlist Natural Sciences
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This class reviews Carpenter's Rule and properties of pseudotriangulation. Various proofs are presented, which cover topics includ
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Tropical Geometry - Lecture 9 - Tropical Convexity | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
using the basic trig functions
In this video, I show how to use the basic trig functions: sine, cosine and tangent. I specifically show how to label a right triangle diagram, then apply the basic trig functions to the acute angles of the right triangle. This foundational concept is important for many future topics in tr
From playlist Trigonometry