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The routine computes the centroid of a given tetrahedron, a triangle, or a list of points.

For more details on the centroid G use coordinates.

The command with(geom3d,centroid) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geom3d}\right)\:$

$\mathrm{ps}≔\left[\mathrm{point}\left(A\,0\,0\,0\right)\,\mathrm{point}\left(B\,1\,0\,0\right)\,\mathrm{point}\left(C\,0\,1\,0\right)\,\mathrm{point}\left(F\,0\,0\,1\right)\right]\:$

$\mathrm{gtetrahedron}\left(\mathrm{ABCF}\,\mathrm{ps}\right),\mathrm{triangle}\left(\mathrm{BCF}\,\left[B\,C\,F\right]\right)\:$

$\mathrm{centroid}\left(\mathrm{G1}\,\mathrm{ps}\right)\:$

$\mathrm{coordinates}\left(\mathrm{G1}\right)$

$\left[\frac{1}{4}\,\frac{1}{4}\,\frac{1}{4}\right]$

$\mathrm{centroid}\left(\mathrm{G2}\,\mathrm{ABCF}\right)\:$

$\mathrm{coordinates}\left(\mathrm{G1}\right)$

$\left[\frac{1}{4}\,\frac{1}{4}\,\frac{1}{4}\right]$

$\mathrm{centroid}\left(\mathrm{G3}\,\mathrm{BCF}\right)\:$

$\mathrm{coordinates}\left(\mathrm{G3}\right)$

$\left[\frac{1}{3}\,\frac{1}{3}\,\frac{1}{3}\right]$