This command returns a string describing the orientation of the point P relative to the polygon formed by the points Q. If P is inside the polygon then the command returns "inside". If P is outside then "outside" is returned. If P lies on the boundary of the polygon, then "boundary" is returned.

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

$Q≔\left[\left[1.1180\,0.36327\right]\,\left[0.\,1.1756\right]\,\left[-1.1180\,0.36327\right]\,\left[-0.69098\,-0.95106\right]\,\left[0.69098\,-0.95106\right]\right]$

$Q≔\left[\left[1.1180\,0.36327\right]\,\left[0.\,1.1756\right]\,\left[\mathrm{-1.1180}\,0.36327\right]\,\left[\mathrm{-0.69098}\,\mathrm{-0.95106}\right]\,\left[0.69098\,\mathrm{-0.95106}\right]\right]$

$a≔\left[0.\,0.\right]\:$$b≔\left[1.\,1.\right]\:$$c≔0.5Q\left[1\right]+0.5Q\left[2\right]\:$

$\mathrm{plots}:-\mathrm{display}\left(\mathrm{plottools}:-\mathrm{point}\left(\left[a\,b\,c\right]\,\mathrm{symbolsize}=20\right)\,\mathrm{plots}:-\mathrm{textplot}\left(\left[a\left[\right]\,''a''\right]\,\mathrm{align}=\left[''above''\,''left''\right]\right)\,\mathrm{plots}:-\mathrm{textplot}\left(\left[b\left[\right]\,''b''\right]\,\mathrm{align}=\left[''above''\,''left''\right]\right)\,\mathrm{plots}:-\mathrm{textplot}\left(\left[c\left[\right]\,''c''\right]\,\mathrm{align}=\left[''below''\,''left''\right]\right)\,\mathrm{plottools}:-\mathrm{polygon}\left(Q\,\mathrm{style}=\mathrm{line}\right)\,\mathrm{axes}=\mathrm{box}\right)$

$\mathrm{PointInPolygon}\left(a\,Q\right)$

$''inside''$

$\mathrm{PointInPolygon}\left(b\,Q\right)$

$''outside''$

$\mathrm{PointInPolygon}\left(c\,Q\right)$

$''boundary''$

$\mathrm{PointInPolygon}\left(Q\left[1\right]\,Q\right)$

$''boundary''$

$\mathrm{PointInPolygon}\left(\mathrm{Array}\left(a\right)\,\mathrm{Array}\left(Q\right)\right)$

$''inside''$

$\mathrm{PointInPolygon}\left(\mathrm{Array}\left(c\right)\,\mathrm{Array}\left(Q\right)\right)$

$''boundary''$

The ComputationalGeometry[PointInPolygon] command was introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.