GlideReflection - Maple Help

geom3d

 GlideReflection
 find the glide-reflection of a geometric object

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

Parameters

 Q - the name of the object to be created P - geometric object p - plane AB - directed segment

Description

 • A glide-reflection is the product of a reflection in a plane p and a translation of directed segment AB, where AB lies in the plane.
 • For a detailed description of Q (the object created), use the routine detail (i.e., detail(Q))
 • The command with(geom3d,GlideReflection) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$
 > $\mathrm{point}\left(F,0,0,0\right),\mathrm{point}\left(A,1,0,0\right),\mathrm{point}\left(B,0,0,1\right):$

Define the plane oxz

 > $\mathrm{line}\left(\mathrm{l1},\left[F,A\right]\right),\mathrm{line}\left(\mathrm{l2},\left[F,B\right]\right),\mathrm{plane}\left(p,\left[\mathrm{l1},\mathrm{l2}\right]\right):$

Define triangle ABC

 > $\mathrm{point}\left(C,1,1,0\right),\mathrm{triangle}\left(\mathrm{T1},\left[A,B,C\right]\right):$

Apply glide-reflection on triangle ABC

 > $\mathrm{dsegment}\left(\mathrm{AB},\left[A,B\right]\right):$
 > $\mathbf{for}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}i\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{from}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}2\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{to}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}5\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{do}\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\mathrm{GlideReflection}\left(T‖i,T‖\left(i-1\right),p,\mathrm{AB}\right)\phantom{\rule[-0.0ex]{0.0em}{0.0ex}}\mathbf{end}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{do}$
 ${\mathrm{T5}}$ (1)

Plotting

 > $\mathrm{draw}\left(\left\{\mathrm{seq}\left(T‖i,i=1..5\right)\right\},\mathrm{scaling}=\mathrm{constrained},\mathrm{style}=\mathrm{patch},\mathrm{title}=\mathrm{Glide Reflection}\right)$