`Triangle`#

To define a triangle, give the 3 vertices.

Figure made with TikZ

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

_nnodes can take one single value, an explicit list of 3 values or a Numbers object and _hsteps can take one real value, an explicit list of 3 real values or a Reals object.If required, give the names of main domain and side domains as explained in Geometry definition:

Point a(-1.,2.,0.), b(1.,-4.,2.), c(2.,3.,1.);
Triangle t1(_v1=a, _v2=b, _v3=c, _nnodes={10,15,20}, _domain_name="Omega",
            _side_names="Gamma");

Let’s summarize information about geometrical keys on triangles:

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

Hint

Parametrization of the triangle $(v_{1}, v_{2}, v_{3})$ is the Duffy’s parametrization:

(u, v) \in [0, 1] \times [0, 1] ⟼ (1 - u) v_{1} + u (1 - v) v_{2} + u v v_{3} .

Note that it is degenarated because $u = 0, v \in [0, 1] ⟶ S_{1}$ .

Triangle#

`Triangle`#