parallelepiped - Maple Help

geom3d

 parallelepiped
 define a parallelepiped

 Calling Sequence parallelepiped(pp, [d1, d2, d3])

Parameters

 pp - name of the parallelepiped d1, d2, d3 - three directed segments having a common initial point

Description

 • A parallelepiped is a polyhedron bounded by six parallelograms. It can be defined from three given directed segments having a common initial point.
 • To access the information related to a parallelepiped pp, use the following function calls:

 form(pp) returns the form of the geometric object (that is, $\mathrm{parallelepiped3d}$ if pp is a parallelepiped). See geom3d[form]. DefinedAs(pp) returns the list of three directed segments defining pp. See geom3d[DefinedAs]. detail(pp) returns a detailed description of the parallelepiped pp. See geom3d[detail].

 • This function is part of the geom3d package, and so it can be used in the form parallelepiped(..) only after executing the command with(geom3d). However, it can always be accessed through the long form of the command by using geom3d[parallelepiped](..).

Examples

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

Define four points $A$, $B$, $C$, and $E$.

 > $\mathrm{point}\left(A,0,0,0\right),\mathrm{point}\left(B,4,0,0\right),\mathrm{point}\left(C,5,5,1\right),\mathrm{point}\left(E,0,2,5\right):$

Define three directed segments d1, d2, and d3 with initial point $A$ and end points $B$, $C$, and $E$ respectively.

 > $\mathrm{dsegment}\left(\mathrm{d1},\left[A,B\right]\right),\mathrm{dsegment}\left(\mathrm{d2},\left[A,C\right]\right),\mathrm{dsegment}\left(\mathrm{d3},\left[A,E\right]\right):$

Use d1, d2, and d3 to define the parallelepiped pp.

 > $\mathrm{parallelepiped}\left(\mathrm{pp},\left[\mathrm{d1},\mathrm{d2},\mathrm{d3}\right]\right)$
 ${\mathrm{pp}}$ (1)
 > $\mathrm{form}\left(\mathrm{pp}\right)$
 ${\mathrm{parallelepiped3d}}$ (2)
 > $\mathrm{DefinedAs}\left(\mathrm{pp}\right)$
 $\left[{\mathrm{d1}}{,}{\mathrm{d2}}{,}{\mathrm{d3}}\right]$ (3)
 > $\mathrm{detail}\left(\mathrm{pp}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{pp}}\\ {\text{form of the object}}& {\mathrm{parallelepiped3d}}\\ {\text{the 6 parallelogram faces of the object}}& \left[\left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{4}{,}{0}{,}{0}\right]{,}\left[{9}{,}{5}{,}{1}\right]{,}\left[{5}{,}{5}{,}{1}\right]\right]{,}\left[\left[{0}{,}{2}{,}{5}\right]{,}\left[{4}{,}{2}{,}{5}\right]{,}\left[{9}{,}{7}{,}{6}\right]{,}\left[{5}{,}{7}{,}{6}\right]\right]{,}\left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{4}{,}{0}{,}{0}\right]{,}\left[{4}{,}{2}{,}{5}\right]{,}\left[{0}{,}{2}{,}{5}\right]\right]{,}\left[\left[{4}{,}{0}{,}{0}\right]{,}\left[{9}{,}{5}{,}{1}\right]{,}\left[{9}{,}{7}{,}{6}\right]{,}\left[{4}{,}{2}{,}{5}\right]\right]{,}\left[\left[{5}{,}{5}{,}{1}\right]{,}\left[{9}{,}{5}{,}{1}\right]{,}\left[{9}{,}{7}{,}{6}\right]{,}\left[{5}{,}{7}{,}{6}\right]\right]{,}\left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{5}{,}{5}{,}{1}\right]{,}\left[{5}{,}{7}{,}{6}\right]{,}\left[{0}{,}{2}{,}{5}\right]\right]\right]\\ {\text{coordinates of the 8 vertices}}& \left[\left[{0}{,}{0}{,}{0}\right]{,}\left[{4}{,}{0}{,}{0}\right]{,}\left[{5}{,}{5}{,}{1}\right]{,}\left[{9}{,}{5}{,}{1}\right]{,}\left[{0}{,}{2}{,}{5}\right]{,}\left[{4}{,}{2}{,}{5}\right]{,}\left[{5}{,}{7}{,}{6}\right]{,}\left[{9}{,}{7}{,}{6}\right]\right]\end{array}$ (4)