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 ScrewDisplacement
 find the screw-displacement of a geometric object.

 Calling Sequence ScrewDisplacement(Q, P, theta, l, AB)

Parameters

 Q - the name of the object to be created P - geometric object theta - angle of rotation l - the axis of rotation AB - directed segment

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{point}\left(o,0,0,0\right),\mathrm{point}\left(z,0,0,2\right),\mathrm{dsegment}\left(\mathrm{seg},\left[o,z\right]\right),\mathrm{line}\left(l,\left[o,z\right]\right):$
 > $\mathrm{triangle}\left(T,\left[\mathrm{point}\left(A,0,0,1\right),\mathrm{point}\left(B,2,1,0\right),\mathrm{point}\left(C,4,3,0\right)\right]\right):$

Define the screw-displacement of triangle T

 > $\mathrm{ScrewDisplacement}\left(\mathrm{T1},T,\mathrm{\pi },l,\mathrm{seg}\right)$
 ${\mathrm{T1}}$ (1)
 > $\mathrm{map}\left(\mathrm{coordinates},\mathrm{DefinedAs}\left(\mathrm{T1}\right)\right)$
 $\left[\left[{0}{,}{0}{,}{3}\right]{,}\left[{-2}{,}{-1}{,}{2}\right]{,}\left[{-4}{,}{-3}{,}{2}\right]\right]$ (2)

Plotting:

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