`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] ⟼ v_{1} + u (v_{2} - v_{1}) + v (v_{4} - v_{1}) - u v (v_{2} - v_{1} + v_{4} - v_{3}) .

Quadrangle#

`Quadrangle`#