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#include <cmath>
#include <iomanip>
#include <iostream>
#include <CLHEP/Units/SystemOfUnits.h>
#include <CLHEP/Vector/Rotation.h>
#include <CLHEP/Vector/RotationInterfaces.h>
#include <CLHEP/Vector/ThreeVector.h>
#include "DetectorDescription/Core/interface/DDRotationMatrix.h"
#include "DetectorDescription/Core/interface/DDTranslation.h"
#include "Math/GenVector/Cartesian3D.h"
#include "Math/GenVector/DisplacementVector3D.h"
#include "Math/GenVector/Rotation3D.h"
typedef CLHEP::Hep3Vector H3V;
typedef CLHEP::HepRotation HRM;
using CLHEP::deg;
using namespace std;
void hrmOut(const HRM& r) {
cout << "row 1 = " << std::setw(12) << std::fixed << std::setprecision(5) << r.xx();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << r.xy();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << r.xz() << endl;
cout << "row 2 = " << std::setw(12) << std::fixed << std::setprecision(5) << r.yx();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << r.yy();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << r.yz() << endl;
cout << "row 3 = " << std::setw(12) << std::fixed << std::setprecision(5) << r.zx();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << r.zy();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << r.zz() << endl;
}
void hepSetAxes(
H3V& x, H3V& y, H3V& z, double thetaX, double phiX, double thetaY, double phiY, double thetaZ, double phiZ) {
x[0] = sin(thetaX) * cos(phiX);
x[1] = sin(thetaX) * sin(phiX);
x[2] = cos(thetaX);
y[0] = sin(thetaY) * cos(phiY);
y[1] = sin(thetaY) * sin(phiY);
y[2] = cos(thetaY);
z[0] = sin(thetaZ) * cos(phiZ);
z[1] = sin(thetaZ) * sin(phiZ);
z[2] = cos(thetaZ);
}
void hepOutVecs(const H3V& x, const H3V& y, const H3V& z) {
cout << "Vectors used in construction:" << endl;
cout << "x vector = " << std::setw(12) << std::fixed << std::setprecision(5) << x[0] << ", " << std::setw(12)
<< std::fixed << std::setprecision(5) << y[0] << ", " << std::setw(12) << std::fixed << std::setprecision(5)
<< z[0] << endl;
cout << "y vector = " << std::setw(12) << std::fixed << std::setprecision(5) << x[1] << ", " << std::setw(12)
<< std::fixed << std::setprecision(5) << y[1] << ", " << std::setw(12) << std::fixed << std::setprecision(5)
<< z[1] << endl;
cout << "z vector = " << std::setw(12) << std::fixed << std::setprecision(5) << x[2] << ", " << std::setw(12)
<< std::fixed << std::setprecision(5) << y[2] << ", " << std::setw(12) << std::fixed << std::setprecision(5)
<< z[2] << endl;
}
void ddRotOut(const DDRotationMatrix& r) {
double xx, xy, xz, yx, yy, yz, zx, zy, zz;
r.GetComponents(xx, xy, xz, yx, yy, yz, zx, zy, zz);
cout << "row 1 = " << std::setw(12) << std::fixed << std::setprecision(5) << xx;
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << xy;
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << xz << endl;
cout << "row 2 = " << std::setw(12) << std::fixed << std::setprecision(5) << yx;
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << yy;
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << yz << endl;
cout << "row 3 = " << std::setw(12) << std::fixed << std::setprecision(5) << zx;
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << zy;
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << zz << endl;
cout << "USING INTERNAL << OPERATOR" << endl;
cout << r << endl;
cout << "USING VECTOR COMPONENTS" << endl;
DD3Vector x, y, z;
r.GetComponents(x, y, z);
cout << "col 1 = " << std::setw(12) << std::fixed << std::setprecision(5) << x.X();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << x.Y();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << x.Z() << endl;
cout << "col 2 = " << std::setw(12) << std::fixed << std::setprecision(5) << y.X();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << y.Y();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << y.Z() << endl;
cout << "col 3 = " << std::setw(12) << std::fixed << std::setprecision(5) << z.X();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << z.Y();
cout << ", " << std::setw(12) << std::fixed << std::setprecision(5) << z.Z() << endl;
}
void ddSetAxes(DD3Vector& x,
DD3Vector& y,
DD3Vector& z,
double thetaX,
double phiX,
double thetaY,
double phiY,
double thetaZ,
double phiZ) {
x.SetX(sin(thetaX) * cos(phiX));
x.SetY(sin(thetaX) * sin(phiX));
x.SetZ(cos(thetaX));
y.SetX(sin(thetaY) * cos(phiY));
y.SetY(sin(thetaY) * sin(phiY));
y.SetZ(cos(thetaY));
z.SetX(sin(thetaZ) * cos(phiZ));
z.SetY(sin(thetaZ) * sin(phiZ));
z.SetZ(cos(thetaZ));
}
void ddOutVecs(const DD3Vector& x, const DD3Vector& y, const DD3Vector& z) {
cout << "Vectors used in construction:" << endl;
cout << "x vector = " << std::setw(12) << std::fixed << std::setprecision(5) << x.X() << ", " << std::setw(12)
<< std::fixed << std::setprecision(5) << x.Y() << ", " << std::setw(12) << std::fixed << std::setprecision(5)
<< x.Z() << endl;
cout << "y vector = " << std::setw(12) << std::fixed << std::setprecision(5) << y.X() << ", " << std::setw(12)
<< std::fixed << std::setprecision(5) << y.Y() << ", " << std::setw(12) << std::fixed << std::setprecision(5)
<< y.Z() << endl;
cout << "z vector = " << std::setw(12) << std::fixed << std::setprecision(5) << z.X() << ", " << std::setw(12)
<< std::fixed << std::setprecision(5) << z.Y() << ", " << std::setw(12) << std::fixed << std::setprecision(5)
<< z.Z() << endl;
}
void checkNorm(double check) {
double tol = 1.0e-3;
if (1.0 - std::abs(check) > tol) {
cout << "NOT orthonormal!" << endl;
} else if (1.0 + check <= tol) {
cout << "IS Left-handed (reflection)" << endl;
} else {
cout << "IS Right-handed (proper)" << endl;
}
}
int main(int /*argc*/, char** /*argv[]*/) {
cout << "====================== CLHEP: ========================" << endl;
// Examples from DD XML
// <ReflectionRotation name="180R" thetaX="90*deg" phiX="0*deg" thetaY="90*deg" phiY="90*deg" thetaZ="180*deg" phiZ="0*deg" />
{
H3V x, y, z;
hepSetAxes(x, y, z, 90 * deg, 0 * deg, 90 * deg, 90 * deg, 180 * deg, 0 * deg);
CLHEP::HepRotation R;
R.rotateAxes(x, y, z);
HRM ddr(R);
cout << " *** REFLECTION *** " << endl;
checkNorm((x.cross(y)) * z);
hepOutVecs(x, y, z);
cout << "Matrix output built up from vectors:" << endl;
hrmOut(ddr);
cout << "Matrix build from CLHEP::HepRep3x3 to preserve left-handedness:" << endl;
CLHEP::HepRep3x3 temp(x.x(), y.x(), z.x(), x.y(), y.y(), z.y(), x.z(), y.z(), z.z()); //matrix representation
HRM ddr2(temp);
hrmOut(ddr2);
}
// <Rotation name="RM1509" thetaX="90*deg" phiX="-51.39999*deg" thetaY="90*deg" phiY="38.60001*deg" thetaZ="0*deg" phiZ="0*deg" />
{
H3V x, y, z;
hepSetAxes(x, y, z, 90 * deg, -51.39999 * deg, 90 * deg, 38.60001 * deg, 0 * deg, 0 * deg);
CLHEP::HepRotation R;
R.rotateAxes(x, y, z);
HRM ddr(R);
cout << " *** ROTATION *** " << endl;
checkNorm((x.cross(y)) * z);
hepOutVecs(x, y, z);
cout << "Matrix output built up from vectors:" << endl;
hrmOut(ddr);
cout << "Matrix build from CLHEP::HepRep3x3 to preserve left-handedness:" << endl;
CLHEP::HepRep3x3 temp(x.x(), y.x(), z.x(), x.y(), y.y(), z.y(), x.z(), y.z(), z.z()); //matrix representation
HRM ddr2(temp);
hrmOut(ddr2);
}
cout << "====================== ROOT::Math ========================" << endl;
// <ReflectionRotation name="180R" thetaX="90*deg" phiX="0*deg" thetaY="90*deg" phiY="90*deg" thetaZ="180*deg" phiZ="0*deg" />
{
DD3Vector x, y, z;
ddSetAxes(x, y, z, 90 * deg, 0 * deg, 90 * deg, 90 * deg, 180 * deg, 0 * deg);
DDRotationMatrix R(x, y, z);
cout << " *** REFLECTION *** " << endl;
checkNorm((x.Cross(y)).Dot(z));
ddOutVecs(x, y, z);
cout << "Matrix output built up from vectors:" << endl;
ddRotOut(R);
cout << "Matrix built to preserve left-handedness:" << endl;
DDRotationMatrix temp(x.x(), y.x(), z.x(), x.y(), y.y(), z.y(), x.z(), y.z(), z.z()); //matrix representation
ddRotOut(temp);
}
// <Rotation name="RM1509" thetaX="90*deg" phiX="-51.39999*deg" thetaY="90*deg" phiY="38.60001*deg" thetaZ="0*deg" phiZ="0*deg" />
{
DD3Vector x, y, z;
ddSetAxes(x, y, z, 90 * deg, -51.39999 * deg, 90 * deg, 38.60001 * deg, 0 * deg, 0 * deg);
DDRotationMatrix R(x, y, z);
cout << " *** ROTATION *** " << endl;
checkNorm((x.Cross(y)).Dot(z));
ddOutVecs(x, y, z);
cout << "Matrix output built up from vectors:" << endl;
ddRotOut(R);
cout << "Matrix built to preserve left-handedness:" << endl;
DDRotationMatrix temp(x.x(), y.x(), z.x(), x.y(), y.y(), z.y(), x.z(), y.z(), z.z()); //matrix representation
ddRotOut(temp);
}
}
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