volume of a k-simplex...

[William Flis]

> I need to compute the volume of a k-simplex
> knowing the coordinates of its vertices.

For a triangle:

Area = Abs(| 1  x1  y1 |)
           | 1  x2  y2 |
           | 1  x3  y3 |
           -------------
                 2

For a tetrahedron:

Volume = Abs(| 1  x1  y1  z1 |)
             | 1  x2  y2  z2 |
             | 1  x3  y3  z3 |
             | 1  x4  y4  z4 |
             -----------------
                     6

I believe this generalizes to any dimension k, with the denominator equal to
(k!).

William J. Flis   Director of Research
DE Technologies, Inc.
3620 Horizon Drive
King of Prussia, PA 19406
Voice: 610-270-9700 x130
Fax: 610-270-9733
mailto:flis at detk.com


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