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In reflection in a point, each point P of the set S of all points of unextended space is carried into the point P1 of S such that PP1 is bisected by a fixed point O of space.

In reflection in a line, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed line l of space.

In reflection in a plane, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed plane p of space.

For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))

The command with(geom3d,reflection) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geom3d}\right)\:$

$\mathrm{plane}\left(\mathrm{oxy}\,\left[\mathrm{point}\left(C\,0\,0\,0\right)\,\mathrm{point}\left(X\,1\,0\,0\right)\,\mathrm{point}\left(Y\,0\,1\,0\right)\right]\right)\:$

$\mathrm{sphere}\left(s\,\left[\mathrm{point}\left(o\,1\,1\,1\right)\,2\right]\right)$

$s$

$\mathrm{reflection}\left(\mathrm{s1}\,s\,\mathrm{oxy}\right)$

$\mathrm{s1}$

$\mathrm{detail}\left(\mathrm{s1}\right)$

Warning, assume that the name of the axes are _x, _y and _z

$\begin{array}{cc}\text{name of the object}& \mathrm{s1}\\ \text{form of the object}& \mathrm{sphere3d}\\ \text{name of the center}& \mathrm{center\_s1\_1}\\ \text{coordinates of the center}& \left[1\,1\,\mathrm{-1}\right]\\ \text{radius of the sphere}& 2\\ \text{surface area of the sphere}& 16\mathrm{\pi }\\ \text{volume of the sphere}& \frac{32\mathrm{\pi }}{3}\\ \text{equation of the sphere}& {\mathrm{\_x}}^2+{\mathrm{\_y}}^2+{\mathrm{\_z}}^2-2\mathrm{\_x}-2\mathrm{\_y}+2\mathrm{\_z}-1=0\end{array}$

$\mathrm{reflection}\left(\mathrm{s2}\,\mathrm{s1}\,\mathrm{oxy}\right)$

$\mathrm{s2}$

$\mathrm{AreDistinct}\left(s\,\mathrm{s2}\right)$

$\mathrm{false}$

$\mathrm{draw}\left(\left[s\,\mathrm{s1}\,\mathrm{oxy}\right]\,\mathrm{style}=\mathrm{patch}\,\mathrm{lightmodel}=\mathrm{light4}\right)$