`Parallelogram`#

To define a parallelogram, give 3 vertices (not aligned).

Figure made with TikZ

There is a parameter for each of them: _v1, _v2, and _v4. These parameters take 2D or 3D points.

_nnodes can take one single value or an explicit list of 2 or 4 values (or a Numbers object) and _hsteps can take one real value, an explicit list of 4 real values or a Reals object. If required, can give the names of main domain and side domains as explained in Geometry definition:

Parallelogram p1(_v1=Point(0.,0.), _v2=Point(2.,0.), _v4=Point(0.,1.),
                _nnodes={20, 10, 20, 10}, _domain_name="Omega", _side_names="Gamma");
Parallelogram p2(_v1=Point(0.,0.), _v2=Point(2.,0.), _v4=Point(0.,1.),
                 _nnodes={20, 10}, _domain_name="Omega", _side_names="Gamma");

Both parallelograms of previous examples are identical. This explains the ability to give 2 or 4 values for _nnodes.

Let’s summarize information about geometrical keys on paralellograms:

key(s)	authorized types	examples
`_v1` , `_v2` , `_v4`	`Point`	`_v1=Point(0.,0.), _v2=Point(4.,0.), _v4=Point(1.,2.)`

Hint

Parametrization of the parallelogram \((v_1,v_2,v_4)\) is :

\[(u,v)\in[0,1]\times [0,1]\longmapsto v_1+u(v_2-v_1)+v(v_4-v_1) \quad\mathrm{linear}.\]

Parallelogram#

`Parallelogram`#