IJPAM: Volume 93, No. 3 (2014)

AFFINE MAPPINGS ON SIMPLICES

Malinee Chaiya$^1$, Somjate Chaiya$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Silpakorn University
Nakorn Pathom, 73000, THAILAND


Abstract. In this paper, we study affine mappings on domains in $\mathbb{R}^{3}$ that are unions of simplices. Let $f_{i}$ be an affine mapping of the form $f_{i}(x)=A_{i}x$, where $A_{i}$ is a $3 \times 3$ transformation matrix, on a simplex $Q_{i}$. We establish the condition of these matrices $A_i$ in order to obtain a continuous piecewise affine mapping $f$ on the domain $Q$ that is the union of simplices $Q_{i}$ such that $f\vert Q_{i}=f_{i}$.

Received: November 16, 2013

AMS Subject Classification: 14R99, 15A23

Key Words and Phrases: affine mapping, simplex

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DOI: 10.12732/ijpam.v93i3.4 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 3
Pages: 339 - 350

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).