Opencascade read step file surface information

Background

I am using Opencascade to read the curve and surface geometric information in the step file, such as the following code:

bool HighOrder::FileIO_3D::read_step(std::string & stepFile)
{
    STEPControl_Controller::Init();
    STEPControl_Reader reader;

    Standard_Integer status = reader.ReadFile(stepFile.c_str());

    if (status != IFSelect_RetDone) {
        return false;
    }

    reader.TransferRoots();
    //int n = reader.NbShapes();
    //cout << n << endl;
    int idx = 0;

    //TopoDS_Shape shapes = reader.OneShape();
    TopoDS_Shape shapes = reader.Shape(1);
    TopExp_Explorer explorer/*(shapes, TopAbs_FACE)*/;

    // read surfaces
    for (explorer.Init(shapes, TopAbs_FACE); explorer.More(); explorer.Next()) {
        TopoDS_Shape shape = explorer.Current();
        TopoDS_Face face = TopoDS::Face(shape); 
        TopLoc_Location location;
        Handle_Geom_Surface surface = BRep_Tool::Surface(face, location);
        GeomAdaptor_Surface adapter(surface);
    }

    // read curves
    for (explorer.Init(shapes, TopAbs_EDGE); explorer.More(); explorer.Next()) {
        TopoDS_Shape shape = explorer.Current();
        TopoDS_Edge edge = TopoDS::Edge(shape);
        TopLoc_Location location;
        double para1, para2;
        Handle_Geom_Curve curve = BRep_Tool::Curve(edge, para1, para2);
        if (curve.IsNull()) continue;
        GeomAdaptor_Curve adapter0(curve, para1, para2);

        bool flag = true;
        gp_Pnt node0, node1;
        for (int i = 0; i < curves.size(); ++i) {
            GeomAdaptor_Curve adapter1(curves[i]->h());
            double para1_ = curves[i]->para().first, para2_ = curves[i]->para().second;
            int intervals_num = 10;
            double step0 = (para2 - para1) / intervals_num;
            double step1 = (para2_ - para1_) / intervals_num;

            bool isEqual = true;
            for (int i = 0; i <= intervals_num; ++i) {
                adapter0.D0(para1 + i * step0, node0);
                adapter1.D0(para1_ + i * step1, node1);

                if (!node0.IsEqual(node1, 1e-10)) {
                    isEqual = false; break;
                }
            }
            if (isEqual) {
                flag = false; break;
            }
        }

        if (flag) {
            //Curve *c = new Curve(curve, std::make_pair(para1, para2));
            curves.push_back(new Curve(curve, { para1, para2 }));
        }
    }

    cout << "Curves' num: " << curves.size() << endl;

    return true;
}

Regardless of the curve information, I now want to get the three-dimensional physical coordinates xyz on the corresponding surface through a two-dimensional parameter coordinate uv.

but I found that the two-dimensional parameter domain of some surfaces is not the same as the shape of the surface

For example, for a strip-shaped surface, its parameter domain range is a square. Here are some examples (I projected the grid points to the corresponding parameter coordinates).

Green represents parameter coordinates, red represents physical coordinates

have the same shape

Archived image: ppxuHtP.png

Archived image: ppxubff.png

Archived image: ppxu7kt.png

Archived image: ppxuLp8.png

have the different shape

Archived image: ppxu5md.png

Archived image: ppxuoTI.png

Archived image: ppxuI0A.png

Archived image: ppxuO1S.png

Question

How can I control the range of the parameter domain to be consistent with the three-dimensional shape, or how to change the range of the parameter domain to be consistent with the three-dimensional shape?

Thanks in advance for any help or suggestions!