Cuboid

To define a cuboid, give 4 vertices, as for parallelepipeds.

There is a parameter for each of them: _v1 , _v2 , _v4 , and _v5 taking points or a single value (in this case, it is like a 1D point).

For cuboids where faces are parallel to planes x=0, y=0 and z=0, the cuboid can be defined by its center (\(c\) in the figure) and its lengths or \(p_1\) (recalled origin in this case) and its lengths. Use _center , _xlength , _ylength and _zlength or _origin , _xlength , _ylength and _zlength to do so. _origin and _center take points or a single value (in this case, it is like a 1D point) and _xlength, _ylength and _zlength take one single positive value.

There is another possibility : defining the cuboid by its bounds : parameters _xmin , _xmax , _ymin , _ymax , _zmin and _zmax taking one single value.

_nnodes can take one single value, an explicit list of 3 or 12 values or a Numbers object and _hsteps can take one real value, an explicit list of 8 real values or a Reals object.

The number of octants to deal with (parameter _nboctants ) may be given. If required, then give names of main domain and side domains as explained in Geometry definition:

Cuboid c1(_v1=Point(0.,0.,0.),_v2=Point(2.,0.,0.),_v4=Point(0.,3.,0.),_v5=Point(0.,0.,4.),
          _nnodes=40, _domain_name="Omega");
Cuboid c2(_origin=Point(0.,0.,0.), _xlength=2., _ylength=3., _zlength=4, _nnodes=40,
          _domain_name="Omega");
Cuboid c3(_center=Point(1.,1.5.,2.),_xlength=2., _ylength=3., _zlength=4, _nnodes=40,
          _domain_name="Omega");
Cuboid c4(_xmin=0, _xmax=2, _ymin=0, _ymax=3, _zmin=0, _zmax=4, _nnodes=40,
          _domain_name="Omega");

This is 4 constructions of the same Cuboid object.

Let’s summarize information about geometrical keys on cuboids:

key(s)	authorized types	examples
_center, _origin	Point	_center=Point(0.,0.,0.)
_v1, _v2, _v4, _v5	Point	_v1 = Point(0.,0.,0.)
_xlength, _ylength, _zlength	single unsigned integer or real positive value	_xlength=1, :_zlength=2.5
_xmin, _xmax, _ymin, _ymax, _zmin, _zmax	single integer or real value	_xmin =1, _zmin=-2.5
_nboctants	single unsigned integer value between 1 and 8	_nboctants=3