GlideReflection - Maple Help

geometry

 GlideReflection
 find the glide-reflection of a geometric object

 Calling Sequence GlideReflection(Q, P, l, AB)

Parameters

 Q - the name of the object to be created P - geometric object l - line AB - directed segment on l

Description

 • Let l be a fixed line of the plane and AB a given directed segment on l. By the glide-reflection $G\left(l,\mathrm{AB}\right)$ we mean the product $R\left(l\right)T\left(\mathrm{AB}\right)$ where $R\left(l\right)$ is the reflection with respect to the line l, and $T\left(\mathrm{AB}\right)$ is the translation with respect to the directed segment AB. The line l is called the axis of the glide-reflection, and the directed segment AB on l is called the vector of the glide-reflection.
 • For a detailed description of Q (the object created), use the routine detail (i.e., detail(Q))
 • The command with(geometry,GlideReflection) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{dsegment}\left(\mathrm{dsg},\mathrm{point}\left(M,0,0\right),\mathrm{point}\left(N,1,1\right)\right):$$\mathrm{line}\left(\mathrm{l1},\left[M,N\right]\right):$
 > $\mathrm{GlideReflection}\left(\mathrm{Agli},\mathrm{point}\left(\mathrm{AA},1,0\right),\mathrm{l1},\mathrm{dsg}\right):$
 > $\mathrm{coordinates}\left(\mathrm{Agli}\right)$
 $\left[{1}{,}{2}\right]$ (1)
 > $\mathrm{dsegment}\left(\mathrm{dsg},\mathrm{point}\left(M,0,0\right),\mathrm{point}\left(N,1,0\right)\right):$$\mathrm{line}\left(l,\left[M,N\right]\right):$
 > $\mathrm{circle}\left(\mathrm{c1},\left[\mathrm{point}\left(\mathrm{OO},0,-1\right),1\right]\right):$

translate c1 with respect to the directed segment MN, then reflect this object with respect to the line l

 > $\mathrm{GlideReflection}\left(\mathrm{cgli},\mathrm{c1},l,\mathrm{dsg}\right):$
 > $\mathrm{detail}\left(\mathrm{cgli}\right)$
 assume that the names of the horizontal and vertical axes are _x and _y, respectively
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{cgli}}\\ {\text{form of the object}}& {\mathrm{circle2d}}\\ {\text{name of the center}}& {\mathrm{center_cgli}}\\ {\text{coordinates of the center}}& \left[{1}{,}{1}\right]\\ {\text{radius of the circle}}& {1}\\ {\text{equation of the circle}}& {{\mathrm{_x}}}^{{2}}{+}{{\mathrm{_y}}}^{{2}}{-}{2}{}{\mathrm{_x}}{-}{2}{}{\mathrm{_y}}{+}{1}{=}{0}\end{array}$ (2)
 > $\mathrm{draw}\left(\left[\mathrm{c1}\left(\mathrm{color}=\mathrm{blue}\right),\mathrm{cgli}\left(\mathrm{color}=\mathrm{green}\right)\right],\mathrm{printtext}=\mathrm{true}\right)$