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Reference Guide
glparametrics2.C
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1 /// \file
2 /// \ingroup tutorial_gl
3 /// Show rendering of parametric surfaces.
4 ///
5 /// A parametric surface is defined by three functions:
6 /// S(u, v) : {x(u, v), y(u, v), z(u, v)}.
7 /// To create parametric surface and draw it one has to:
8 /// 1. Create canvas, which support OpenGL drawing (two ways):
9 /// - Call gStyle->SetCanvasPreferGL(kTRUE)
10 /// - Or create canvas with name, wich contains "gl".
11 /// 2. create TGLParametricEquation object.
12 /// ~~~{.cpp}
13 /// TGLParametricEquation *eq = new TGLParametricEquation("name",
14 /// "some FORMULA here - x(u, v)",
15 /// "some FORMULA here - y(u, v)",
16 /// "some FORMULA here - z(u, v)",
17 /// uMin, uMax, vMin, vMax);
18 /// ~~~
19 /// where FORMULA is the same string (mathematical expression),
20 /// as in TF2, but you should use 'u' (or 'U') instead of 'x'
21 /// and 'v' (or 'V') instead of 'y'.
22 /// 3. Call equation->Draw();
23 /// Parametric surfaces support 21 color "schemes", you can change
24 /// the color:
25 /// - place mouse cursor above surface (surface is selected in pad)
26 /// - press 's' or 'S'.
27 ///
28 /// \macro_image(nobatch)
29 /// \macro_code
30 ///
31 /// \author Timur Pocheptsov
32 
33 void klein_bottle(TGLVertex3 &dst, Double_t u, Double_t v)
34 {
35  using namespace TMath;
36 
37  const Double_t r = 4. * (1. - Cos(u) / 2.);
38  if (u < Pi()) {
39  dst.X() = 6 * Cos(u) * (1. + Sin(u)) + r * Cos(u) * Cos(v);
40  dst.Y() = 16 * Sin(u) + r * Sin(u) * Cos(v);
41  } else {
42  dst.X() = 6 * Cos(u) * (1. + Sin(u)) + r * Cos(v + Pi());
43  dst.Y() = 16 * Sin(u);
44  }
45  dst.Z() = r * Sin(v);
46 }
47 
48 void glparametrics2()
49 {
51  TCanvas *c = new TCanvas("canvas","Parametric surfaces with gl", 100, 10, 700, 700);
52 
53  c->Divide(2, 2);
54  c->cd(1);
56  "1.2 ^ v * sin(u) ^ 2 * sin(v)",
57  "1.2 ^ v * sin(u) * cos(u)",
58  "1.2 ^ v * sin(u) ^ 2 * cos(v)",
59  0., TMath::Pi(), // 0 <= u <= pi
60  -TMath::Pi() / 4., 5 * TMath::Pi() / 2.); // -pi/4 <= v <= 5*pi/2
61  p1->Draw("");
62 
63  c->cd(2);
64  TGLParametricEquation *p2 = new TGLParametricEquation("Limpet torus",
65  "cos(u) / (sqrt(2) + sin(v))",
66  "sin(u) / (sqrt(2) + sin(v))",
67  "1. / (sqrt(2) + cos(v))",
68  -TMath::Pi(), TMath::Pi(),
69  -TMath::Pi(), TMath::Pi());
70  p2->Draw();
71 
72  c->cd(3);
73  TGLParametricEquation *p3 = new TGLParametricEquation("Klein bottle",
74  klein_bottle,
75  0., TMath::TwoPi(),
76  0., TMath::TwoPi());
77  p3->Draw();
78 
79  c->cd(4);
80  TGLParametricEquation *p4 = new TGLParametricEquation("Helicoid",
81  "v * cos(u)",
82  "v * sin(u)",
83  "u",
84  -3., 3.,
85  -3., 3.);
86  p4->Draw();
87 }
constexpr Double_t TwoPi()
Definition: TMath.h:45
R__EXTERN TStyle * gStyle
Definition: TStyle.h:410
virtual void Draw(Option_t *option="")
Default Draw method for all objects.
Definition: TObject.cxx:195
3 component (x/y/z) vertex class.
Definition: TGLUtil.h:82
constexpr Double_t Pi()
Definition: TMath.h:38
void SetCanvasPreferGL(Bool_t prefer=kTRUE)
Definition: TStyle.h:323
ROOT::R::TRInterface & r
Definition: Object.C:4
A parametric surface is a surface defined by a parametric equation, involving two parameters (u...
Definition: TGLParametric.h:35
Double_t Cos(Double_t)
Definition: TMath.h:631
The Canvas class.
Definition: TCanvas.h:31
Double_t Z() const
Definition: TGLUtil.h:122
double Double_t
Definition: RtypesCore.h:55
Double_t Sin(Double_t)
Definition: TMath.h:627
#define c(i)
Definition: RSha256.hxx:101
TMath.
Definition: TMathBase.h:35
Double_t Y() const
Definition: TGLUtil.h:120
const Bool_t kTRUE
Definition: RtypesCore.h:87
Double_t X() const
Definition: TGLUtil.h:118