`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:

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

Note that it is degenarated because \(u=0,\ v\in[0,1]\longrightarrow S_1\).

Triangle#

`Triangle`#