find the rotatory-reflection of a geometric object. - Maple Help

Home : Support : Online Help : Mathematics : Geometry : 3-D Euclidean : Transformations : geom3d/RotatoryReflection

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

 > with(geom3d):
 > point(A,1,1,1), point(B,1,0,0),point(C,0,1,0),point(E,1,1,0):
 > plane(p,[B,C,E]), line(l,[B,NormalVector(p)]):

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

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

Define the inverse transformation

 > RotatoryReflection(A2,A1,p,2*Pi-Pi/4,l);
 ${\mathrm{A2}}$ (3)

Checking:

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