RotatoryReflection - Maple Help

geom3d

 RotatoryReflection
 find the rotatory-reflection of a geometric object.

 Calling Sequence RotatoryReflection(Q, P, p, theta, l)

Parameters

 Q - the name of the object to be created P - geometric object p - plane of reflection theta - angle of rotation l - the axis of rotation

Description

 • A rotatory-reflection is the product of a reflection in a plane and a rotation about a fixed axis perpendicular to the plane.
 • For a detailed description of Q (the object created), use the routine detail (i.e., detail(Q))
 • The command with(geom3d,RotatoryReflection) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{point}\left(A,1,1,1\right),\mathrm{point}\left(B,1,0,0\right),\mathrm{point}\left(C,0,1,0\right),\mathrm{point}\left(E,1,1,0\right):$
 > $\mathrm{plane}\left(p,\left[B,C,E\right]\right),\mathrm{line}\left(l,\left[B,\mathrm{NormalVector}\left(p\right)\right]\right):$

Define the rotatory-reflection in the plane p about angle Pi/4 with respect to l

 > $\mathrm{RotatoryReflection}\left(\mathrm{A1},A,p,\frac{\mathrm{\pi }}{4},l\right)$
 ${\mathrm{A1}}$ (1)
 > $\mathrm{coordinates}\left(\mathrm{A1}\right)$
 $\left[\frac{\sqrt{{2}}}{{2}}{+}{1}{,}\frac{\sqrt{{2}}}{{2}}{,}{-1}\right]$ (2)

Define the inverse transformation

 > $\mathrm{RotatoryReflection}\left(\mathrm{A2},\mathrm{A1},p,2\mathrm{\pi }-\frac{\mathrm{\pi }}{4},l\right)$
 ${\mathrm{A2}}$ (3)

Checking:

 > $\mathrm{coordinates}\left(A\right)=\mathrm{coordinates}\left(\mathrm{A2}\right)$
 $\left[{1}{,}{1}{,}{1}\right]{=}\left[{1}{,}{1}{,}{1}\right]$ (4)