A screw-displacement is the product of a rotation and a translation along the axis of rotation.

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

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

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

$\mathrm{point}\left(o\,0\,0\,0\right),\mathrm{point}\left(z\,0\,0\,2\right),\mathrm{dsegment}\left(\mathrm{seg}\,\left[o\,z\right]\right),\mathrm{line}\left(l\,\left[o\,z\right]\right)\:$

$\mathrm{triangle}\left(T\,\left[\mathrm{point}\left(A\,0\,0\,1\right)\,\mathrm{point}\left(B\,2\,1\,0\right)\,\mathrm{point}\left(C\,4\,3\,0\right)\right]\right)\:$

$\mathrm{ScrewDisplacement}\left(\mathrm{T1}\,T\,\mathrm{\pi }\,l\,\mathrm{seg}\right)$

$\mathrm{T1}$

$\mathrm{map}\left(\mathrm{coordinates}\,\mathrm{DefinedAs}\left(\mathrm{T1}\right)\right)$

$\left[\left[0\,0\,3\right]\,\left[\mathrm{-2}\,\mathrm{-1}\,2\right]\,\left[\mathrm{-4}\,\mathrm{-3}\,2\right]\right]$

$\mathrm{draw}\left(\left[T\left(\mathrm{color}=\mathrm{blue}\right)\,\mathrm{T1}\left(\mathrm{color}=\mathrm{red}\right)\,l\left(\mathrm{thickness}=3\right)\right]\,\mathrm{orientation}=\left[122\,73\right]\,\mathrm{title}=\mathrm{`Screw-displacement\; of\; a\; triangle`}\,\mathrm{style}=\mathrm{patch}\right)$