Let S and N be the south pole and the north pole of the sphere s, respectively. If P1 is a point on s, then the computed point P is the stereographic projection of P1 on s to the tangent plane sp at S, i.e., P is the intersection of the line l, which passes through N and P, and sp. If P1 is a point on the tangent plane sp, then the computed point P is a point on the sphere s such that P1 is the stereographic projection of P on s to the tangent plane sp.

For a detailed description of the object created P, use the routine detail (i.e., detail(P))

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

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

$\mathrm{sphere}\left(s\,\left[\mathrm{point}\left(o\,0\,0\,2\right)\,2\right]\right),\mathrm{point}\left(P\,\frac{4}{3}\,\frac{4}{3}\,\frac{4}{3}\right)$

$s,P$

$\mathrm{StereographicProjection}\left(\mathrm{P1}\,P\,s\right)$

$\mathrm{P1}$

$\mathrm{StereographicProjection}\left(\mathrm{P2}\,\mathrm{P1}\,s\right)$

$\mathrm{P2}$

$\mathrm{coordinates}\left(P\right)=\mathrm{coordinates}\left(\mathrm{P2}\right)$

$\left[\frac{4}{3}\,\frac{4}{3}\,\frac{4}{3}\right]=\left[\frac{4}{3}\,\frac{4}{3}\,\frac{4}{3}\right]$