The routine returns point C which is the point lying on the segment defined by two points A, B with ratio k

For a detailed description of point C, use the routine detail (i.e., detail(C))

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

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

$\mathrm{assume}\left(a\,\mathrm{real}\,b\,\mathrm{real}\,c\,\mathrm{real}\,d\,\mathrm{real}\,a\ne c\,k\,\mathrm{real}\right)$

$\mathrm{point}\left(A\,a\,b\,1\right),\mathrm{point}\left(B\,c\,d\,5\right)\:$

$\mathrm{OnSegment}\left(C\,A\,B\,k\right)$

Error, (in geom3d:-OnSegment) unable to determine if k+1 is zero

$\mathrm{additionally}\left(k\ne -1\right)$

$\mathrm{OnSegment}\left(C\,A\,B\,k\right)$

$C$

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

$\left[\frac{\mathrm{c~}\mathrm{k~}+\mathrm{a~}}{\mathrm{k~}+1}\,\frac{\mathrm{d~}\mathrm{k~}+\mathrm{b~}}{\mathrm{k~}+1}\,\frac{1+5\mathrm{k~}}{\mathrm{k~}+1}\right]$