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.

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

$\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)\:$

$\mathrm{GlideReflection}\left(\mathrm{Agli}\,\mathrm{point}\left(\mathrm{AA}\,1\,0\right)\,\mathrm{l1}\,\mathrm{dsg}\right)\:$

$\mathrm{coordinates}\left(\mathrm{Agli}\right)$

$\left[1\,2\right]$

$\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)\:$

$\mathrm{circle}\left(\mathrm{c1}\,\left[\mathrm{point}\left(\mathrm{OO}\,0\,-1\right)\,1\right]\right)\:$

$\mathrm{GlideReflection}\left(\mathrm{cgli}\,\mathrm{c1}\,l\,\mathrm{dsg}\right)\:$

$\mathrm{detail}\left(\mathrm{cgli}\right)$

assume that the names of the horizontal and vertical axes are _x and _y, respectively

$\begin{array}{ll}\text{name of the object}& \mathrm{cgli}\\ \text{form of the object}& \mathrm{circle2d}\\ \text{name of the center}& \mathrm{center\_cgli}\\ \text{coordinates of the center}& \left[1\,1\right]\\ \text{radius of the circle}& 1\\ \text{equation of the circle}& {\mathrm{\_x}}^2+{\mathrm{\_y}}^2-2\mathrm{\_x}-2\mathrm{\_y}+1=0\end{array}$

$\mathrm{draw}\left(\left[\mathrm{c1}\left(\mathrm{color}=\mathrm{blue}\right)\,\mathrm{cgli}\left(\mathrm{color}=\mathrm{green}\right)\right]\,\mathrm{printtext}=\mathrm{true}\right)$