Publication

The cost of omnidirectionality: extracting and labelling the echoes

2017
Student Projects

Abstract

This report explains all theoretical and practical aspects of a 2D room re- construction algorithm based on euclidean geometry. Detailed theoretical explanations about the procedure are given in the first part. In the second part, a precise description of the implementational choices, issues, strengths and weaknesses is given in order for the user to run the software correctly and be able to modify and improve it with more simplicity.

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2017
Student Projects

Abstract

Official source

Related concepts (32)

Euclidean geometry

Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.

Euclidean space

Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces when one wants to specify their dimension. For n equal to one or two, they are commonly called respectively Euclidean lines and Euclidean planes.

Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries.

Related publications (18)

The cost of omnidirectionality: extracting and labelling the echoes

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