Difference between revisions of "Tetrahedral coordinates"
From Encyclopedia of Mathematics
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''of a point $P$ in three-dimensional space'' | ''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|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. | + | 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. |
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| + | See also [[Barycentric coordinates]]. | ||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> H.S.M. Coxeter, "Regular polytopes" , Dover, reprint (1973) pp. 183</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> H.S.M. Coxeter, "Regular polytopes" , Dover, reprint (1973) pp. 183</TD></TR> | ||
| + | </table> | ||
Latest revision as of 13:13, 7 April 2023
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.
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=53612
Tetrahedral coordinates. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tetrahedral_coordinates&oldid=53612
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article