Difference between revisions of "Tetrahedral coordinates"
From Encyclopedia of Mathematics
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| − | ''of a point | + | {{TEX|done}} |
| + | ''of a point $P$ in three-dimensional space'' | ||
| − | Numbers | + | Numbers $x_1,x_2,x_3,x_4$ which are proportional (with given coefficient of proportionality) to the distances from $P$ to the faces of a fixed [[Tetrahedron|tetrahedron]], not necessarily regular. Analogously, one may introduce general normal coordinates for any dimension. The two-dimensional analogues of tetrahedral coordinates are called trilinear coordinates. See also [[Barycentric coordinates|Barycentric coordinates]]. |
Revision as of 15:37, 15 April 2014
of a point $P$ in three-dimensional space
Numbers $x_1,x_2,x_3,x_4$ which are proportional (with given coefficient of proportionality) to the distances from $P$ to the faces of a fixed tetrahedron, not necessarily regular. Analogously, one may introduce general normal coordinates for any dimension. The two-dimensional analogues of tetrahedral coordinates are called trilinear coordinates. See also Barycentric coordinates.
Comments
References
| [a1] | H.S.M. Coxeter, "Regular polytopes" , Dover, reprint (1973) pp. 183 |
How to Cite This Entry:
Tetrahedral coordinates. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tetrahedral_coordinates&oldid=31739
Tetrahedral coordinates. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tetrahedral_coordinates&oldid=31739
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article