`Quadrangle`#

To define a quadrangle, give the 4 vertices (no edge crossing and not degenerated)

Figure made with TikZ

There is a parameter for each of them:_v1, _v2, _v3 and _v4. These parameters take 2D or 3D points.

_nnodes can take one single value, an explicit list of 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, give names of the main domain and side domains as explained in Geometry definition:

Quadrangle q1(_v1=Point(0.,0.), _v2=Point(2.,0.), _v3=Point(2.,1.), _v4=Point(0.,1.),
              _nnodes={20, 10, 20, 10}, _domain_name="Omega", _side_names="Gamma");

Let’s summarize information about geometrical keys on quadrangles:

key(s)	authorized types	examples
`_v1` , `_v2` , `_v3` , `_v4`	`Point`	`_v1=Point(0.,0.), _v4=Point(0.,0.,0.)`

Hint

Parametrization of the quagrangle \((v_1,v_2,v_3,v_4)\) is :

\[(u,v)\in[0,1]\times [0,1]\longmapsto v_1+u(v_2-v_1)+v(v_4-v_1)-u\,v(v_2-v_1+v_4-v_3).\]

Quadrangle#

`Quadrangle`#