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Homogeneous coordinates

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcul, are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity…

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Overview

Introduction

Other dimensions

Other projective spaces

Alternative definition

Homogeneity

Line coordinates and duality

Plücker coordinates

Circular points

Change of coordinate systems

Barycentric coordinates

Use in computer graphics and computer vision

Advanced semantic analysis

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Map overview Semantic statistics

Homogeneous coordinates

Nodes71
Edges70
Triples85
Avg. degree1.97
Density0.028169
Components1

How this topic connects Entity context

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Homogeneous coordinates

Top relations

related to Introduction · 12
Homogeneous coordinates → As, By, Cartesian, Euclidean, For, Given, In, Let, Parallel, The, There, Thus
related to Use in computer graphics and computer vision · 12
Homogeneous coordinates → As, By, Cartesian, Direct3D, Dropping, For, Homogeneous, In, Matrices, Modern OpenGL, The, This
related to Alternative definition · 8
Homogeneous coordinates → Another, Euclidean, For, If, Lines, Satisfaction, The, Then
related to Line coordinates and duality · 8
Homogeneous coordinates → Analogously, Each, Geometrically, If, In, So, The, This
related to Change of coordinate systems · 6
Homogeneous coordinates → Cartesian, Just, Let, Multiplication, So, Therefore
related to External links · 6
Homogeneous coordinates → Archived, Homogeneous, Jon Rokne, Jules Bloomenthal, MathWorld, Wayback MachineChing-Kuang Shene
related to Other projective spaces · 6
Homogeneous coordinates → For, Homogeneous, However, Other, Riemann, The
related to Trilinear coordinates · 6
Homogeneous coordinates → Let, More, Strictly, There, These, This
related to Homogeneity · 4
Homogeneous coordinates → But, Cartesian, Homogeneous, Specifically
related to Notation · 4
Homogeneous coordinates → Cartesian, Some, Square, The

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Important terminology

homogeneous coordinates displaystyle projective point plane line points represented lines infinity origin set equation cartesian may system euclidean given space

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
translationinstance ofUse in computer graphics and computer visionHomogeneous coordinates are ubiquitous in computer graphics because they allow common vector operations0.80text
rotationinstance ofUse in computer graphics and computer visionHomogeneous coordinates are ubiquitous in computer graphics because they allow common vector operations0.80text
scalinginstance ofUse in computer graphics and computer visionHomogeneous coordinates are ubiquitous in computer graphics because they allow common vector operations0.80text
perspective projection to be represented as a matrix by which the vector is multipliedinstance ofUse in computer graphics and computer visionHomogeneous coordinates are ubiquitous in computer graphics because they allow common vector operations0.80text
Homogeneous coordinatesrelated to Alternative definitionAnother0.60section
Homogeneous coordinatesrelated to Alternative definitionFor0.60section
Homogeneous coordinatesrelated to Alternative definitionThen0.60section
Homogeneous coordinatesrelated to Alternative definitionIf0.60section
Homogeneous coordinatesrelated to Alternative definitionLines0.60section
Homogeneous coordinatesrelated to Alternative definitionSatisfaction0.60section
Homogeneous coordinatesrelated to Alternative definitionThe0.60section
Homogeneous coordinatesrelated to Alternative definitionEuclidean0.60section

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