glparametrics2.C File Reference

Detailed Description

Show rendering of parametric surfaces.

A parametric surface is defined by three functions: S(u, v) : {x(u, v), y(u, v), z(u, v)}. To create parametric surface and draw it one has to:

1. Create canvas, which support OpenGL drawing (two ways):
   • Call gStyle->SetCanvasPreferGL(kTRUE)
   • Or create canvas with name, wich contains "gl".
2. create TGLParametricEquation object.

   TGLParametricEquation *eq = new TGLParametricEquation("name",
   "some FORMULA here - x(u, v)",
   "some FORMULA here - y(u, v)",
   "some FORMULA here - z(u, v)",
   uMin, uMax, vMin, vMax);

   where FORMULA is the same string (mathematical expression), as in TF2, but you should use 'u' (or 'U') instead of 'x' and 'v' (or 'V') instead of 'y'.
3. Call equation->Draw(); Parametric surfaces support 21 color "schemes", you can change the color:
   • place mouse cursor above surface (surface is selected in pad)
   • press 's' or 'S'.

 
void klein_bottle(TGLVertex3 &dst, Double_t u, Double_t v)
{
    using namespace TMath;
 
    const Double_t r = 4. * (1. - Cos(u) / 2.);
    if (u < Pi()) {
        dst.X() = 6 * Cos(u) * (1. + Sin(u)) + r * Cos(u) * Cos(v);
        dst.Y() = 16 * Sin(u) + r * Sin(u) * Cos(v);
    } else {
        dst.X() = 6 * Cos(u) * (1. + Sin(u)) + r * Cos(v + Pi());
        dst.Y() = 16 * Sin(u);
    }
    dst.Z() = r * Sin(v);
}
 
void glparametrics2()
{
   gStyle->SetCanvasPreferGL(kTRUE);
   TCanvas *c = new TCanvas("canvas","Parametric surfaces with gl", 100, 10, 700, 700);
 
   c->Divide(2, 2);
   c->cd(1);
   TGLParametricEquation *p1 = new TGLParametricEquation("Shell",
                                "1.2 ^ v * sin(u) ^ 2 * sin(v)",
                                "1.2 ^ v * sin(u) * cos(u)",
                                "1.2 ^ v * sin(u) ^ 2 * cos(v)",
                                0., TMath::Pi(), // 0 <= u <= pi
                                -TMath::Pi() / 4., 5 * TMath::Pi() / 2.); // -pi/4 <= v <= 5*pi/2
   p1->Draw("");
 
   c->cd(2);
   TGLParametricEquation *p2 = new TGLParametricEquation("Limpet torus",
                                    "cos(u) / (sqrt(2) + sin(v))",
                                    "sin(u) / (sqrt(2) + sin(v))",
                                    "1. / (sqrt(2) + cos(v))",
                                    -TMath::Pi(), TMath::Pi(),
                                    -TMath::Pi(), TMath::Pi());
   p2->Draw();
 
   c->cd(3);
   TGLParametricEquation *p3 = new TGLParametricEquation("Klein bottle",
                                        klein_bottle,
                                        0., TMath::TwoPi(),
                                        0., TMath::TwoPi());
   p3->Draw();
 
   c->cd(4);
   TGLParametricEquation *p4 = new TGLParametricEquation("Helicoid",
                                                         "v * cos(u)",
                                                         "v * sin(u)",
                                                         "u",
                                                         -3., 3.,
                                                         -3., 3.);
   p4->Draw();
}

Author

Timur Pocheptsov

Definition in file glparametrics2.C.