This command returns a string describing the orientation of the fourth point relative to the circle formed by the first three points. If the fourth point is inside the circle then the command returns "inside". If the fourth point is outside then "outside" is returned. If all four points lie on a circle, then "boundary" is returned.

The second calling sequence is designed for checking large collections of points without having to make copies of their values.

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

$a≔\left[0\,0\right]\;$$b≔\left[1\,1\right]\;$$c≔\left[0\,1\right]\;$$d≔\left[0.5\,1.25\right]\;$$e≔\left[0.25\,0.75\right]\;$$f≔\left[1\,0\right]$

$a≔\left[0\,0\right]$

$b≔\left[1\,1\right]$

$c≔\left[0\,1\right]$

$d≔\left[0.5\,1.25\right]$

$e≔\left[0.25\,0.75\right]$

$f≔\left[1\,0\right]$

$\mathrm{plots}:-\mathrm{display}\left(\mathrm{plottools}:-\mathrm{point}\left(\left[a\,b\,c\,d\,e\,f\right]\,\mathrm{symbolsize}=20\right)\,\mathrm{plots}:-\mathrm{textplot}\left(\left[d\left[\right]\,''d''\right]\,\mathrm{align}=\left[''above''\,''left''\right]\right)\,\mathrm{plots}:-\mathrm{textplot}\left(\left[e\left[\right]\,''e''\right]\,\mathrm{align}=\left[''above''\,''left''\right]\right)\,\mathrm{plots}:-\mathrm{textplot}\left(\left[f\left[\right]\,''f''\right]\,\mathrm{align}=\left[''above''\,''left''\right]\right)\,\mathrm{plottools}:-\mathrm{circle}\left(\left[\frac{1}{2}\,\frac{1}{2}\right]\,\frac{\mathrm{sqrt}\left(2\right)}{2}\,\mathrm{style}=\mathrm{line}\right)\,\mathrm{axes}=\mathrm{box}\right)$

$\mathrm{PointInCircle}\left(a\,b\,c\,d\right)$

$''outside''$

$\mathrm{PointInCircle}\left(a\,b\,c\,e\right)$

$''inside''$

$\mathrm{PointInCircle}\left(a\,b\,c\,f\right)$

$''boundary''$

$M≔\mathrm{Array}\left(\left[a\,b\,c\,d\,e\right]\,\mathrm{datatype}=\mathrm{float}\left[8\right]\,\mathrm{order}=\mathrm{C\_order}\right)$

$M≔\left[\begin{array}{cc}0.& 0.\\ 1.& 1.\\ 0.& 1.\\ 0.500000000000000& 1.25000000000000\\ 0.250000000000000& 0.750000000000000\end{array}\right]$

$\mathrm{PointInCircle}\left(M\,\left[1\,2\,3\,5\right]\right)$

$''inside''$

The ComputationalGeometry[PointInCircle] command was introduced in Maple 2019.

For more information on Maple 2019 changes, see Updates in Maple 2019.