`Segment`#

A segment is a straight line between 2 distinct points.

Figure made with TikZ

The general case is to give points through parameters _v1 and _v2, but when 1D, the real coordinates can be given:

Segment s1(_v1=Point(0.,0.,0.), _v2=Point(0.,1.,-1.), _nnodes=11, _domain_name="Omega");
Segment s2(_v1=Point(0.,0.), _v2=Point(0.,1.), _hsteps=0.1, _domain_name="Omega");
Segment s3(_v1=Point(0.), _v2=Point(1.), _hsteps={0.1,0.2}, _domain_name="Omega");
Segment s4(_v1=0., _v2=1.,_nnodes=11, _domain_name="Omega");

In previous examples \(s3\) and \(s4\) are identical. A better comprehensive way for \(s4\) construction is to use parameters _xmin and _xmax instead of _v1 and _v2:

Segment s4(_xmin=0., _xmax=1., _nnodes=11, _domain_name="Omega");

One of the combination _xmin and _xmax or _v1 and _v2 is needed. In previous examples, note that _nnodes take only a single integer value and _hsteps can take one real value or an explicit list of 2 real values ( or a Reals object).

If required, give the names of main domain and side domains as explained in Geometry definition:

// segment [-2,5] with 50 points when meshing
Segment s1(_xmin=-2, _xmax=5, _nnodes=50);
// segment linking A(1,2,3) and B(-2,5,0) with 20 points
// when meshing and domain is "Omega1"
Point a(1.,2.,3.);
Point b(-2.,5.,0.)
Segment s2(_v1=a, _v2=b, _nnodes=20, _domain_name="Omega1");
// segment [0,1] with 20 points when meshing
// and side domains are "Gamma1" and "Gamma2"
Segment s3(_xmin=0., _xmax=1., _nnodes=20, _side_names={"Gamma1","Gamma2"});
// segment [0,1] with 10 points when meshing and domain is "Omega"
// and side domains are "Gamma1" and "Gamma2"
Segment s4(_xmin=0., _xmax=1., _nnodes=10, _domain_name="Omega",
                                           _side_names={"Gamma1","Gamma2"});
// segment [0,1] with 10 points when meshing
//and domain is "Omega" and side domain is "Gamma"
Segment s4(_xmin=0., _xmax=1., _nnodes=10, _domain_name="Omega", _side_names="Gamma");

The orientation of a segment can be reversed by using one of the following:

Segment s1(_xmin=-2, _xmax=5, _nnodes=50);
s1.reverse();   // s1 is modified
Segment s2=~s1; // s1 is not modified

Warning

When defining composite or loop geometries, do not use the reverse method, but only the \(\sim\) operator.

Let’s summarize information about geometrical keys for segments:

key(s)	authorized types	examples
`_v1`, `_v2`	single integer or real value, or `Point`	`_v1=Point(0.)`, `_v2=Point(0.,0.)`, `_v1=Point(0.,0.,0.)`, `_v2=0`.
`_xmin` , `_xmax`	single integer or real value	`_xmin=1`, `_xmax=-2.5`

Hint

Parametrization of the segment \([S_1,S_2]\): \(t\in[0,1] \longmapsto (1-t)S_1+tS_2\).

Segment#

`Segment`#