Using NURBS in Computation (02-nurbs)

Model problem

Solved is a simple Poisson equation with constant right-hand side and homogeneous Dirichlet boundary conditions.

The domain is a rectangle (0,2) x (0, 1) whose upper edge is a NURBS curve. There are three mesh files in this example: domain-1.mesh (one control point), domain-2.mesh (two control points), and domain-3.mesh (three control points). One of these files needs to be selected on line 15 in main.cpp:

const char* mesh_file = "domain-1.mesh";          // One control point.
//const char* mesh_file = "domain-2.mesh";          // Two control points.
//const char* mesh_file = "domain-3.mesh";          // Three control points.

Example 1 (One inner control point)

Snippet from the file domain-1.mesh:

degree = 2                # Degree should be equal to the
num_inner_points = 1      # number of inner points plus one.

inner_points =
{
  { 1.5, 2.0, 2.0 }       # x, y, weight
}
knots =
{
  0, 0, 0, 1, 1, 1
}
curves =
{
  {2, 3, degree, inner_points, knots}
}

Result:

Example 2 (Two inner control points)

Snippet from the file domain-3.mesh:

degree = 3
num_inner_points = 2
inner_points =
{
  { 1.5, 1.5, 1.0 },
  { 0.5, 0.5, 1.0 }
}
knots =
{
  0, 0, 0, 1, 1, 1
}
curves =
{
  {2, 3, degree, inner_points, knots}
}

Result:

Example 3 (Three inner control points)

Snippet from the file domain-2.mesh:

degree = 4
num_inner_points = 3
inner_points =
{
  { 1.5, 1.5, 1.0 },
  { 1.0, -1.0, 1.0 },
  { 0.5, 1.5, 1.0 }
}
knots =
{
  0, 0, 0, 1, 1, 1
}
curves =
{
  {2, 3, degree, inner_points, knots}
}

Result: