Geometric algorithms | Triangulation (geometry)
In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum of all the angles of the triangles in the triangulation; they tend to avoid sliver triangles. The triangulation is named after Boris Delaunay for his work on this topic from 1934. For a set of points on the same line there is no Delaunay triangulation (the notion of triangulation is degenerate for this case). For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the "Delaunay condition", i.e., the requirement that the circumcircles of all triangles have empty interiors. By considering circumscribed spheres, the notion of Delaunay triangulation extends to three and higher dimensions. Generalizations are possible to metrics other than Euclidean distance. However, in these cases a Delaunay triangulation is not guaranteed to exist or be unique. (Wikipedia).
Trigonometry 4 The Area of a Triangle
Various ways of using trigonometry to determine the area of a triangle.
From playlist Trigonometry
Adding Vectors Geometrically: Dynamic Illustration
Link: https://www.geogebra.org/m/tsBer5An
From playlist Trigonometry: Dynamic Interactives!
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
Computing Delaunay complex: Lifting to a paraboloid [Ondřej Draganov]
Short visual explanation of a construction of Delaunay complex via lifting to a paraboloid and projecting. This construction reduces the problem of finding the Delaunay complex of a d-dimensional point cloud to finding a lower convex hull of a (d+1)-dimensional point cloud. This video is
From playlist Tutorial-a-thon 2021 Fall
Trigonometry - Vocabulary of trigonometric functions
In this video will cover some of the basic vocabulary that you'll hear when working with trigonometric functions. Specifically we'll cover what is trigonometry, angles, and defining the trigonometric functions as ratios of sides. You'll hear these terms again as we dig deeper into the st
From playlist Trigonometry
Projection of One Vector onto Another Vector
Link: https://www.geogebra.org/m/wjG2RjjZ
From playlist Trigonometry: Dynamic Interactives!
How far is it from everywhere to somewhere?
Computing the Euclidean Distance Transform on a regular grid. A fundamental operation in image processing, used as part of separating objects, finding best matches, finding sizes of objects, and so on. The algorithm presented here is described in: J. Wang and Ying Tan, Efficient Euclide
From playlist Summer of Math Exposition Youtube Videos
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
Voronoi diagram, Delaunay and Alpha complexes: A Visual Intro [Ondřej Draganov]
Introductory tutorial bringing visual intuition into definitions of three basic concepts used in TDA – Voronoi diagrams, Delaunay complexes and Alpha complexes / Alpha filtration. In this video I show how to get from a two-dimensional point-cloud to each of those objects, describe several
From playlist Tutorial-a-thon 2021 Spring
Protein Folding Characterization via Persistent Homology - Marcio Gameiro
Workshop on Topology: Identifying Order in Complex Systems Topic: Protein Folding Characterization via Persistent Homology Speaker: Marcio Gameiro Affiliation: University of Sao Paolo Date: April 7, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
Math Ts: SAVE TIME & have your Trigonometry Ss (formatively) assess their own work! After solving a problem or 2 (like this), send them here: https://www.geogebra.org/m/hK5QfXah .
From playlist Trigonometry: Dynamic Interactives!
A Laplacian for Nonmanifold Triangle Meshes - SGP 2020
Authors: Nicholas Sharp and Keenan Crane presented at SGP 2020 https://sgp2020.sites.uu.nl https://github.com/nmwsharp/nonmanifold-laplacian Abstract: We describe a discrete Laplacian suitable for any triangle mesh, including those that are nonmanifold or nonorientable (with or without b
From playlist Research
Solving a trigonometric equation with applying pythagorean identity
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Factoring
SHM - 12/05/17 - La cosmographie dans l'enseignement secondaire (...) - Colette Le Lay
Assumer ou contourner la technicité mathématique dans les apprentissages de la cosmographie (séance préparée par Catherine Radtka et Norbert Verdier) 14 h -16h : - Colette Le Lay (Centre François Viète, Université de Nantes) : « La cosmographie dans l'enseignement secondaire au XIXe si
From playlist Séminaire d'Histoire des Mathématiques
Solving trigonometric equations with multiple angles
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include by factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given
From playlist Solve Trigonometric Equations with Multi Angles
Solving trigonometric equations with multiple angles
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include by factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given
From playlist Solve Trigonometric Equations with Multi Angles
Trigonometry and Bearings: Quick Setups
#Trigonometry & #bearings: Set ups. Quick formative assessment: http://ow.ly/BMYe50I7kVs & http://ow.ly/p1JR50I7kVw. #GeoGebra
From playlist Trigonometry: Dynamic Interactives!
Thomas Fernique - Maximally Dense Sphere Packings
It is well known that to cover the greatest proportion of the Euclidean plane with identical disks, we have to center these disks in a triangular grid. This problem can be generalized in two directions: in higher dimensions or with different sizes of disks. The first direction has been the
From playlist Combinatorics and Arithmetic for Physics: special days
How to find all of the solutions to an equation as well as within the unit circle
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric identities, they include by factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the give
From playlist Solve Trigonometric Equations
S.Schleimer - An introduction to veering triangulations
Singular euclidean structures on surfaces are a key tool in the study of the mapping class group, of Teichmüller space, and of kleinian three-manifolds. François Guéritaud, while studying work of Ian Agol, gave a powerful technique for turning a singular euclidean structure (on a surface)
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications