Two Area Preserving Maps From the Square to the P-Ball

Holhoş, Adrian

doi:10.3846/13926292.2017.1277561

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R ) and Its Inverse1

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2017

2021

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Cited by 3 publications

(2 citation statements)

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“…then we calculate the partial derivatives of Y and Z with respect to x, y and z and introduce them in (5). After some calculations, we find that X must be solution of the following first order partial differential equation…”

Section: R ) and Its Inversementioning

confidence: 99%

Volume Preserving Maps Between p-Balls

Holhoş

Rosca

2019

Symmetry

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We construct a volume preserving map U p from the p-ball B p (r) = x ∈ R 3 , x p ≤ r to the regular octahedron B 1 (r ), for arbitrary p > 0. Then we calculate the inverse U −1 p and we also deduce explicit expressions for U ∞ and U −1 ∞ . This allows us to construct volume preserving maps between arbitrary balls B p (r) and B p (r), and also to map uniform and refinable grids between them. Finally we list some possible applications of our maps.

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Section: R ) and Its Inversementioning

confidence: 99%

Volume Preserving Maps Between p-Balls

Holhoş

Rosca

2019

Symmetry

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“…The main application in mind for this paper is photographic art, but the mathematical mappings discussed can be used in other applications. For example, we have seen the use of similar mappings for diverse applications such as mathematical modelling [Holhos 2017], computer graphics, geography [Lambers 2016], finite element analysis [Shterenlikht 2017], and plasma physics [Citrin 2017].…”

mentioning

confidence: 99%

Elliptification of Rectangular Imagery

Fong

2017

Preprint

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We present and discuss different algorithms for converting rectangular imagery into elliptical regions. We will focus primarily on methods that use mathematical mappings with explicit and invertible equations. The key idea is to start with invertible mappings between the square and the circular disc then extend it to handle rectangles and ellipses. This extension can be done by simply removing the eccentricity and reintroducing it back after using a chosen square-to-disc mapping.

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