Is it reasonable for the degree of resultant curve exceeds the MaxDegree of GeomConvert_ApproxCurve?

[lavender-lee]

Consider the following code:

void test_GeomConvert_ApproxCurve()
{
  double Tol = 0.01;
  GeomAbs_Shape continuity = GeomAbs_C2;
  int max_degree = 3;
  int max_segments = 20;
  //
  gp_Pnt center(0.0, 0.0, 0.0);
  double radius = 10.0;
  gp_Ax2 position(center, gp_Dir(0, 0, 1), gp_Dir(1, 0, 0));
  Handle(Geom_Circle) circle = new Geom_Circle(position, radius);
  GeomConvert_ApproxCurve anApprox3d(circle, Tol, continuity, max_degree, max_segments);
  //
  anApprox3d.Dump(std::cout);
  //
  if (anApprox3d.HasResult())
  {
    const Handle(Geom_BSplineCurve) &curve = anApprox3d.Curve();
    std::cout << "degree: " << curve ->Degree() << std::endl;
  }
}

The degree of the approximation curve is 9, a 9-th degree Bezier curve.

However, the document says:

In the above case, the setting for MaxDegree is only 3.

[lavender-lee]

However, approximate a circle with a cubic spline within the specified tolerance is possible. For example:

poles = {{10.0057, 0.0000149421}, {10.0057, 2.58765}, {7.87306, 7.79652}, {0.0646744, 11.095}, {-7.81643, 7.87408}, {-11.0947, 
  0.017671}, {-7.84136, -7.84914}, {0.0290646, -11.0951}, {7.85936, -7.81712}, {10.0056, -2.59825}, {10.0057, 0.0000149421}}

knots = {0, 0, 0, 0., 0.123743, 0.249077, 0.374411, 0.499746, 0.62508, 0.750414, 0.875749, 1., 1, 1, 1}

circle equation in parametric form :

x(t) = 10 Cos[6.28319 t],
y(t) = 10 Sin[6.28319 t]

Error analysis (two components: x , y):

[lavender-lee]

@dpasukhi Do you think this throw statement is redundant?

From the math point of view, c = max(a, b), thenc >= a and c >= b. Hence, ndu<2*iu+2 is impossible.

  ndu = Max(myMaxDegInU+1,2*iu+2);
  ndv = Max(myMaxDegInV+1,2*iv+2);
  if (ndu<2*iu+2)
    throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : UMaxDegree Error");
  if (ndv<2*iv+2)
    throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : VMaxDegree Error");