// Create, Draw and fit a TGraph2DErrors
void macro4(){
gStyle->SetPalette(57);
const double e = 0.3;
const int nd = 500;
TRandom3 my_random_generator;
TF2 f2("f2",
"1000*(([0]*sin(x)/x)*([1]*sin(y)/y))+200",
-6,6,-6,6);
f2.SetParameters(1,1);
TGraph2DErrors dte(nd);
// Fill the 2D graph
double rnd, x, y, z, ex, ey, ez;
for (Int_t i=0; i<nd; i++) {
f2.GetRandom2(x,y);
// A random number in [-e,e]
rnd = my_random_generator.Uniform(-e,e);
z = f2.Eval(x,y)*(1+rnd);
dte.SetPoint(i,x,y,z);
ex = 0.05*my_random_generator.Uniform();
ey = 0.05*my_random_generator.Uniform();
ez = fabs(z*rnd);
dte.SetPointError(i,ex,ey,ez);
}
// Fit function to generated data
f2.SetParameters(0.7,1.5); // set initial values for fit
f2.SetTitle("Fitted 2D function");
dte.Fit(&f2);
// Plot the result
auto c1 = new TCanvas();
f2.SetLineWidth(1);
f2.SetLineColor(kBlue-5);
TF2 *f2c = (TF2*)f2.DrawClone("Surf1");
TAxis *Xaxis = f2c->GetXaxis();
TAxis *Yaxis = f2c->GetYaxis();
TAxis *Zaxis = f2c->GetZaxis();
Xaxis->SetTitle("X Title"); Xaxis->SetTitleOffset(1.5);
Yaxis->SetTitle("Y Title"); Yaxis->SetTitleOffset(1.5);
Zaxis->SetTitle("Z Title"); Zaxis->SetTitleOffset(1.5);
dte.DrawClone("P0 Same");
// Make the x and y projections
auto c_p= new TCanvas("ProjCan",
"The Projections",1000,400);
c_p->Divide(2,1);
c_p->cd(1);
dte.Project("x")->Draw();
c_p->cd(2);
dte.Project("y")->Draw();
}
void derivative_test()
{
curve_type cst(7);
control_point_type cp[8];
data_type dte(0.01), t[6];
point_type pt, xp, xp_ref, xpp, xpp_ref;
index_type i;
// set the control points
cp[0] << static_cast<data_type>(0.170987592880629);
cp[1] << static_cast<data_type>(0.157286894410384);
cp[2] << static_cast<data_type>(0.162311658384540);
cp[3] << static_cast<data_type>(0.143623187913493);
cp[4] << static_cast<data_type>(0.149218456400780);
cp[5] << static_cast<data_type>(0.137218405082418);
cp[6] << static_cast<data_type>(0.140720628655908);
cp[7] << static_cast<data_type>(0.141104769355436);
for (i=0; i<=cst.upper_degree(); ++i)
{
cst.set_upper_control_point(cp[i], i);
cst.set_lower_control_point(-cp[i], i);
}
// set the trailing edge thickness of CST airfoil
cst.set_trailing_edge_thickness(dte);
// set the parameters to evaluate the tests
t[0] = static_cast<data_type>(0.1);
t[1] = static_cast<data_type>(0.24);
t[2] = static_cast<data_type>(0.42);
t[3] = static_cast<data_type>(0.5);
t[4] = static_cast<data_type>(0.73);
t[5] = static_cast<data_type>(0.95);
data_type x[3], y[3], dt(static_cast<data_type>(1e2)*std::sqrt(std::numeric_limits<data_type>::epsilon()));
eli::mutil::fd::d1o2<data_type> d1_calc;
eli::mutil::fd::d2o2<data_type> d2_calc;
// evaluate points on the lower surface
for (i=0; i<6; ++i)
{
pt=cst.f(-t[i]-dt); x[0]=pt(0); y[0]=pt(1);
pt=cst.f(-t[i]); x[1]=pt(0); y[1]=pt(1);
pt=cst.f(-t[i]+dt); x[2]=pt(0); y[2]=pt(1);
d1_calc.evaluate(xp_ref(0), x, dt);
d1_calc.evaluate(xp_ref(1), y, dt);
d2_calc.evaluate(xpp_ref(0), x, dt);
d2_calc.evaluate(xpp_ref(1), y, dt);
xp=cst.fp(-t[i]);
xpp=cst.fpp(-t[i]);
if (typeid(data_type)==typeid(float))
{
TEST_ASSERT((xp-xp_ref).norm()<6e-3);
if (i==0)
{
TEST_ASSERT((xpp-xpp_ref).norm()<7e-2);
}
else if (i==1)
{
TEST_ASSERT((xpp-xpp_ref).norm()<4e-3);
}
else
{
TEST_ASSERT((xpp-xpp_ref).norm()<3e-3);
}
}
else
{
TEST_ASSERT(tol.approximately_equal(xp, xp_ref));
TEST_ASSERT((xpp-xpp_ref).norm()<8e-5);
}
}
// evaluate points on the upper surface
for (i=0; i<6; ++i)
{
pt=cst.f(t[i]-dt); x[0]=pt(0); y[0]=pt(1);
pt=cst.f(t[i]); x[1]=pt(0); y[1]=pt(1);
pt=cst.f(t[i]+dt); x[2]=pt(0); y[2]=pt(1);
d1_calc.evaluate(xp_ref(0), x, dt);
d1_calc.evaluate(xp_ref(1), y, dt);
d2_calc.evaluate(xpp_ref(0), x, dt);
d2_calc.evaluate(xpp_ref(1), y, dt);
xp=cst.fp(t[i]);
xpp=cst.fpp(t[i]);
if (typeid(data_type)==typeid(float))
{
TEST_ASSERT((xp-xp_ref).norm()<6e-3);
if (i==0)
{
TEST_ASSERT((xpp-xpp_ref).norm()<7e-2);
}
else if (i==1)
{
TEST_ASSERT((xpp-xpp_ref).norm()<4e-3);
}
else
{
TEST_ASSERT((xpp-xpp_ref).norm()<3e-3);
}
}
else
{
TEST_ASSERT(tol.approximately_equal(xp, xp_ref));
TEST_ASSERT((xpp-xpp_ref).norm()<8e-5);
}
}
}
void evaluation_test()
{
typedef eli::geom::curve::pseudo::explicit_bezier<data_type> explicit_bezier_curve_type;
explicit_bezier_curve_type ebcu(7), ebcl(7);
curve_type cst(7);
control_point_type cp[8];
data_type dte(0.01), t[6];
point_type pt_out, pt_ref;
index_type i;
// set the control points
cp[0] << static_cast<data_type>(0.170987592880629);
cp[1] << static_cast<data_type>(0.157286894410384);
cp[2] << static_cast<data_type>(0.162311658384540);
cp[3] << static_cast<data_type>(0.143623187913493);
cp[4] << static_cast<data_type>(0.149218456400780);
cp[5] << static_cast<data_type>(0.137218405082418);
cp[6] << static_cast<data_type>(0.140720628655908);
cp[7] << static_cast<data_type>(0.141104769355436);
for (i=0; i<=cst.upper_degree(); ++i)
{
ebcu.set_control_point(cp[i], i);
cst.set_upper_control_point(cp[i], i);
ebcl.set_control_point(-cp[i], i);
cst.set_lower_control_point(-cp[i], i);
}
// set the trailing edge thickness of CST airfoil
cst.set_trailing_edge_thickness(dte);
// set the parameters to evaluate the tests
t[0] = static_cast<data_type>(0);
t[1] = static_cast<data_type>(0.1);
t[2] = static_cast<data_type>(0.27);
t[3] = static_cast<data_type>(0.5);
t[4] = static_cast<data_type>(0.73);
t[5] = static_cast<data_type>(1);
// evaluate the points on lower surface
i=1;
pt_out = cst.f(-t[i]);
pt_ref = ebcu.f(t[i]);
pt_ref(1) = -(std::sqrt(t[i])*(1-t[i])*pt_ref(1)+t[i]*dte/2);
TEST_ASSERT(tol.approximately_equal(pt_out, pt_ref));
i=2;
pt_out = cst.f(-t[i]);
pt_ref = ebcu.f(t[i]);
pt_ref(1) = -(std::sqrt(t[i])*(1-t[i])*pt_ref(1)+t[i]*dte/2);
TEST_ASSERT(tol.approximately_equal(pt_out, pt_ref));
i=3;
pt_out = cst.f(-t[i]);
pt_ref = ebcu.f(t[i]);
pt_ref(1) = -(std::sqrt(t[i])*(1-t[i])*pt_ref(1)+t[i]*dte/2);
TEST_ASSERT(tol.approximately_equal(pt_out, pt_ref));
i=4;
pt_out = cst.f(-t[i]);
pt_ref = ebcu.f(t[i]);
pt_ref(1) = -(std::sqrt(t[i])*(1-t[i])*pt_ref(1)+t[i]*dte/2);
TEST_ASSERT(tol.approximately_equal(pt_out, pt_ref));
i=5;
pt_out = cst.f(-t[i]);
pt_ref = ebcu.f(t[i]);
pt_ref(1) = -(std::sqrt(t[i])*(1-t[i])*pt_ref(1)+t[i]*dte/2);
TEST_ASSERT(tol.approximately_equal(pt_out, pt_ref));
// evaluate the points on upper surface
i=0;
pt_out = cst.f(t[i]);
pt_ref = ebcu.f(t[i]);
pt_ref(1) = std::sqrt(t[i])*(1-t[i])*pt_ref(1)+t[i]*dte/2;
TEST_ASSERT(tol.approximately_equal(pt_out, pt_ref));
i=1;
pt_out = cst.f(t[i]);
pt_ref = ebcu.f(t[i]);
pt_ref(1) = std::sqrt(t[i])*(1-t[i])*pt_ref(1)+t[i]*dte/2;
TEST_ASSERT(tol.approximately_equal(pt_out, pt_ref));
i=2;
pt_out = cst.f(t[i]);
pt_ref = ebcu.f(t[i]);
pt_ref(1) = std::sqrt(t[i])*(1-t[i])*pt_ref(1)+t[i]*dte/2;
TEST_ASSERT(tol.approximately_equal(pt_out, pt_ref));
i=3;
pt_out = cst.f(t[i]);
pt_ref = ebcu.f(t[i]);
pt_ref(1) = std::sqrt(t[i])*(1-t[i])*pt_ref(1)+t[i]*dte/2;
TEST_ASSERT(tol.approximately_equal(pt_out, pt_ref));
i=4;
pt_out = cst.f(t[i]);
pt_ref = ebcu.f(t[i]);
pt_ref(1) = std::sqrt(t[i])*(1-t[i])*pt_ref(1)+t[i]*dte/2;
TEST_ASSERT(tol.approximately_equal(pt_out, pt_ref));
i=5;
pt_out = cst.f(t[i]);
pt_ref = ebcu.f(t[i]);
pt_ref(1) = std::sqrt(t[i])*(1-t[i])*pt_ref(1)+t[i]*dte/2;
TEST_ASSERT(tol.approximately_equal(pt_out, pt_ref));
}