--- /dev/null
+/**************************************************************************
+ * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
+ * *
+ * Author: The ALICE Off-line Project. *
+ * Contributors are mentioned in the code where appropriate. *
+ * *
+ * Permission to use, copy, modify and distribute this software and its *
+ * documentation strictly for non-commercial purposes is hereby granted *
+ * without fee, provided that the above copyright notice appears in all *
+ * copies and that both the copyright notice and this permission notice *
+ * appear in the supporting documentation. The authors make no claims *
+ * about the suitability of this software for any purpose. It is *
+ * provided "as is" without express or implied warranty. *
+ **************************************************************************/
+
+/* $Id: $ */
+
+#include <stdexcept>
+#include <iostream>
+
+#include <TGeoMatrix.h>
+#include <TObjArray.h>
+#include <TString.h>
+#include <TError.h>
+#include <TMath.h>
+
+#include "AliSurveyPoint.h"
+
+#include "AliPHOSModuleMisalignment.h"
+#include "AliPHOSGeometry.h"
+
+ClassImp(AliPHOSModuleMisalignment)
+
+namespace {
+
+ /*
+ Tiny vector/matrix utility stuff. Operates on doubles directly.
+ Instead of points and vectors I use arrays of doubles with size 3.
+ To make this explicit - I use references to arrays.
+ */
+
+ //___________________________________________________________________
+ void Vector(const Double_t (&p1)[3], const Double_t (&p2)[3], Double_t (&v)[3])
+ {
+ for(UInt_t i = 0; i < 3; ++i)
+ v[i] = p2[i] - p1[i];
+ }
+
+ //___________________________________________________________________
+ void MultVector(Double_t (&v)[3], Double_t m)
+ {
+ v[0] *= m;
+ v[1] *= m;
+ v[2] *= m;
+ }
+
+ /*
+ Using points name0, name1, name2 find two orthogonal vectors.
+ */
+ //___________________________________________________________________
+ void FindVectors(const Double_t (&pts)[3][3], Double_t (&v)[3][3])
+ {
+ Vector(pts[0], pts[2], v[0]);
+ //v[1] will be cross-product (v[2] x v[0]).
+ Vector(pts[0], pts[1], v[2]);
+ }
+
+ //___________________________________________________________________
+ Double_t Length(const Double_t (&v)[3])
+ {
+ return TMath::Sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
+ }
+
+ //___________________________________________________________________
+ Double_t Distance(const Double_t (&p1)[3], const Double_t (&p2)[3])
+ {
+ return TMath::Sqrt((p2[0] - p1[0]) * (p2[0] - p1[0]) +
+ (p2[1] - p1[1]) * (p2[1] - p1[1]) +
+ (p2[2] - p1[2]) * (p2[2] - p1[2]));
+ }
+
+ //______________________________________________________________________________
+ void CrossProduct(const Double_t (&v1)[3], const Double_t (&v2)[3], Double_t (&v3)[3])
+ {
+ v3[0] = v1[1] * v2[2] - v2[1] * v1[2];
+ v3[1] = v1[2] * v2[0] - v2[2] * v1[0];
+ v3[2] = v1[0] * v2[1] - v2[0] * v1[1];
+ }
+
+ //___________________________________________________________________
+ void Normalize(Double_t (&v)[3])
+ {
+ const Double_t len = Length(v);
+ if(len < 1E-10)//Threshold?
+ throw std::runtime_error("Zero len vector");
+ v[0] /= len;
+ v[1] /= len;
+ v[2] /= len;
+ }
+
+ //______________________________________________________________________________
+ void Normalize(Double_t (&v)[3][3])
+ {
+ for(UInt_t i = 0; i < 3; ++i)
+ Normalize(v[i]);
+ }
+
+
+ //___________________________________________________________________
+ void FindRotation(const Double_t (&u)[3][3], const Double_t (&v)[3][3], Double_t (&r)[9])
+ {
+ //I have orthogonal vectors and very nice rotation matrix.
+ //V = R * U, R = V * U ^ t
+ r[0] = v[0][0] * u[0][0] + v[1][0] * u[1][0] + v[2][0] * u[2][0];
+ r[1] = v[0][0] * u[0][1] + v[1][0] * u[1][1] + v[2][0] * u[2][1];
+ r[2] = v[0][0] * u[0][2] + v[1][0] * u[1][2] + v[2][0] * u[2][2];
+
+ r[3] = v[0][1] * u[0][0] + v[1][1] * u[1][0] + v[2][1] * u[2][0];
+ r[4] = v[0][1] * u[0][1] + v[1][1] * u[1][1] + v[2][1] * u[2][1];
+ r[5] = v[0][1] * u[0][2] + v[1][1] * u[1][2] + v[2][1] * u[2][2];
+
+ r[6] = v[0][2] * u[0][0] + v[1][2] * u[1][0] + v[2][2] * u[2][0];
+ r[7] = v[0][2] * u[0][1] + v[1][2] * u[1][1] + v[2][2] * u[2][1];
+ r[8] = v[0][2] * u[0][2] + v[1][2] * u[1][2] + v[2][2] * u[2][2];
+ }
+
+ //___________________________________________________________________
+ void Rotate(const Double_t (&r)[9], const Double_t (&u)[3], Double_t (&v)[3])
+ {
+ v[0] = r[0] * u[0] + r[1] * u[1] + r[2] * u[2];
+ v[1] = r[3] * u[0] + r[4] * u[1] + r[5] * u[2];
+ v[2] = r[6] * u[0] + r[7] * u[1] + r[8] * u[2];
+ }
+
+ //___________________________________________________________________
+ void Rotate(const Double_t (&r)[9], const Double_t (&u)[3][3], Double_t (&v)[3][3])
+ {
+ for(UInt_t i = 0; i < 3; ++i)
+ Rotate(r, u[i], v[i]);
+ }
+
+ /*
+ PrintVector, PrintMatrix, Translate are used in "debug" mode only.
+ */
+ //___________________________________________________________________
+ void PrintVector(const Double_t (&v)[3])
+ {
+ std::cout<<v[0]<<' '<<v[1]<<' '<<v[2]<<std::endl;
+ }
+
+ //___________________________________________________________________
+ void PrintMatrix(const Double_t (&u)[3][3])
+ {
+ for(UInt_t i = 0; i < 3; ++i)
+ PrintVector(u[i]);
+ }
+
+ //___________________________________________________________________
+ void Translate(const Double_t (&t)[3], const Double_t (&u)[3], Double_t (&v)[3])
+ {
+ for(UInt_t i = 0; i < 3; ++i)
+ v[i] = u[i] + t[i];
+ }
+
+ //___________________________________________________________________
+ void Translate(const Double_t (&t)[3], const Double_t (&u)[3][3], Double_t (&v)[3][3])
+ {
+ for(UInt_t i = 0; i < 3; ++i)
+ Translate(t, u[i], v[i]);
+ }
+
+}
+
+//______________________________________________________________________________
+AliPHOSModuleMisalignment::
+AliPHOSModuleMisalignment(const AliPHOSGeometry & geom, Bool_t debug)
+ : fDebug(debug),
+ fAngles(),
+ fCenters(),
+ fModule(),
+ fU(),
+ fV()
+{
+ //Ctor.
+ //Extract ideal module transformations from AliPHOSGeometry.
+
+ //Angles.
+ for (UInt_t module = 0; module < kModules; ++module)
+ for (UInt_t axis = 0; axis < 3; ++axis)
+ for (UInt_t angle = 0; angle < 2; ++angle)
+ fAngles[module][axis][angle] = geom.GetModuleAngle(module, axis, angle);
+ //Translations.
+ for (UInt_t module = 0; module < kModules; ++module)
+ for (UInt_t axis = 0; axis < 3; ++axis)
+ fCenters[module][axis] = geom.GetModuleCenter(module, axis);
+ //Points, will be rotated/translated using module angle/center.
+ fModule[0][0] = -geom.GetNPhi() / 2. * geom.GetCellStep() + geom.GetCellStep() / 2.;
+ fModule[0][1] = -geom.GetNZ() / 2. * geom.GetCellStep() + geom.GetCellStep() / 2.;
+ fModule[0][2] = -22.61;//This number is hardcoded, AliPHOSGeometry does not have it,
+ //only 460. but this is result of transformation applied already.
+ fModule[1][0] = fModule[0][0];
+ fModule[1][1] = -fModule[0][1] - geom.GetCellStep();
+ fModule[1][2] = -22.61;
+
+ fModule[2][0] = -fModule[0][0] - 7 * geom.GetCellStep();
+ fModule[2][1] = fModule[0][1];
+ fModule[2][2] = -22.61;
+}
+
+//______________________________________________________________________________
+AliPHOSModuleMisalignment::~AliPHOSModuleMisalignment()
+{
+}
+
+//______________________________________________________________________________
+void AliPHOSModuleMisalignment::
+DeltaTransformation(UInt_t module, const TObjArray * points,
+ const TString & name0, const TString & name1,
+ const TString & name2, TGeoHMatrix * delta)
+{
+ //Find delta transformation to misalign module. Global transformation.
+ const AliSurveyPoint * pt0 = static_cast<AliSurveyPoint *>(points->FindObject(name0));
+ const AliSurveyPoint * pt1 = static_cast<AliSurveyPoint *>(points->FindObject(name1));
+ const AliSurveyPoint * pt2 = static_cast<AliSurveyPoint *>(points->FindObject(name2));
+
+ if (!pt0 || !pt1 || !pt2) {
+ Warning("AliPHOSModuleData::DeltaTransformation",
+ "One of points not found in TObjArray");
+ return;
+ }
+
+ //Transform fModule using angle and translation for module number "module".
+ //fU.
+ FindIdealModule(module);
+ //Extract coordinates from survey.
+ //fV.
+ FindRealModule(pt0, pt1, pt2);
+ //Find delta, using ideal module (fU) and survey data (fV).
+ FindDelta(delta);
+}
+
+//______________________________________________________________________________
+void AliPHOSModuleMisalignment::FindIdealModule(UInt_t module)
+{
+ //Ideal module described by fU.
+ TGeoHMatrix matrix;
+ //Rotation.
+ const TGeoRotation r("",
+ fAngles[module][0][0], fAngles[module][0][1],
+ fAngles[module][1][0], fAngles[module][1][1],
+ fAngles[module][2][0], fAngles[module][2][1]);
+ matrix.SetRotation(r.GetRotationMatrix());
+ //Translation.
+ matrix.SetDx(fCenters[module][0]);
+ matrix.SetDy(fCenters[module][1]);
+ matrix.SetDz(fCenters[module][2]);
+ //Find ideal module's points.
+ matrix.LocalToMaster(fModule[0], fU[0]);
+ matrix.LocalToMaster(fModule[1], fU[1]);
+ matrix.LocalToMaster(fModule[2], fU[2]);
+}
+
+//______________________________________________________________________________
+void AliPHOSModuleMisalignment::FindRealModule(const AliSurveyPoint * pt0,
+ const AliSurveyPoint * pt1,
+ const AliSurveyPoint * pt2)
+{
+ //Real module - fV.
+ //Survey is in millimeters.
+ //AliPHOSGeometry is in centimeters.
+ const Double_t scale = 0.1;
+
+ fV[0][0] = pt0->GetX() * scale;
+ fV[0][1] = pt0->GetY() * scale;
+ fV[0][2] = pt0->GetZ() * scale;
+
+ fV[1][0] = pt1->GetX() * scale;
+ fV[1][1] = pt1->GetY() * scale;
+ fV[1][2] = pt1->GetZ() * scale;
+
+ fV[2][0] = pt2->GetX() * scale;
+ fV[2][1] = pt2->GetY() * scale;
+ fV[2][2] = pt2->GetZ() * scale;
+}
+
+//______________________________________________________________________________
+void AliPHOSModuleMisalignment::FindDelta(TGeoHMatrix * delta)const
+{
+ //Find rotation and translation wich can
+ //convert fU into fV (ideal module points into points from survey).
+ Double_t u[3][3] = {};
+ FindVectors(fU, u);
+ //Find cross product u2 x u0 and save it in u[2].
+ CrossProduct(u[2], u[0], u[1]);
+ /*
+ const Double_t lenXideal = Length(u[0]);
+ const Double_t lenZideal = Length(u[2]);
+ */
+ Double_t v[3][3] = {};
+ FindVectors(fV, v);
+ //Find cross product (v2 x v0) and save it in v[2].
+ CrossProduct(v[2], v[0], v[1]);
+ /*
+ const Double_t lenXreal = Length(v[0]);
+ const Double_t lenZreal = Length(v[2]);
+ */
+ //Now, find rotation matrix.
+ //1. Normalize vectors in u and v.
+ try {
+ Normalize(u);
+ Normalize(v);
+ } catch (const std::exception & e) {
+ //One of lengths is zero (in principle, impossible, just to be neat).
+ Error("AliPHOSModuleMisalignment::FindDelta",
+ "\tone of vectors from ideal or real\n\tpoints have zero size\n"
+ "\tzero misalignment will be created");
+ return;
+ }
+
+ //2. Rotation matrix.
+ Double_t r[9] = {};
+ FindRotation(u, v, r);
+ delta->SetRotation(r);
+
+#if 1
+
+ //3. Now, rotate fU and look, what translation I have to add.
+ Double_t idealRotated[3] = {};
+ Rotate(r, fU[0], idealRotated);
+
+ delta->SetDx(fV[0][0] - idealRotated[0]);
+ delta->SetDy(fV[0][1] - idealRotated[1]);
+ delta->SetDz(fV[0][2] - idealRotated[2]);
+
+ if (fDebug) {
+ const Double_t shifts[3] =
+ {fV[0][0] - idealRotated[0],
+ fV[0][1] - idealRotated[1],
+ fV[0][2] - idealRotated[2]};
+
+ Double_t test1[3][3] = {};
+ Rotate(r, fU, test1);
+ Double_t test2[3][3] = {};
+ Translate(shifts, test1, test2);
+ std::cout<<"ideal:\n";
+ PrintMatrix(fU);
+ std::cout<<"misaligned:\n";
+ PrintMatrix(test2);
+ std::cout<<"real:\n";
+ PrintMatrix(fV);
+ }
+
+#endif
+
+#if 0
+ //3. Now, rotate fU and look, what translation I have to add.
+ Double_t idealRotated[3][3] = {};
+ Rotate(r, fU, idealRotated);
+ //Because of measurement errors, distances
+ //between points has errors. I can try to split
+ //this difference (and make "final errors" smaller).
+ Double_t zShift[3] = {};
+ Vector(fV[0], fV[1], zShift);
+ Normalize(zShift);
+
+ Double_t xShift[3] = {};
+ Vector(fV[0], fV[2], xShift);
+ Normalize(xShift);
+
+ MultVector(zShift, 0.5 * (lenZreal - lenZideal));
+ MultVector(xShift, 0.5 * (lenXreal - lenXideal));
+
+ Double_t pt1[3] = {};
+ Translate(zShift, fV[0], pt1);
+ Double_t pt2[3] = {};
+ Translate(xShift, pt1, pt2);
+
+ Double_t shifts[] = {pt2[0] - idealRotated[0][0],
+ pt2[1] - idealRotated[0][1],
+ pt2[2] - idealRotated[0][2]};
+
+ delta->SetDx(shifts[0]);
+ delta->SetDy(shifts[1]);
+ delta->SetDz(shifts[2]);
+
+ if (fDebug) {
+ Double_t idealTr[3][3] = {};
+ Translate(shifts, idealRotated, idealTr);
+
+ std::cout<<"misaligned:\n";
+ PrintMatrix(idealTr);
+ std::cout<<"ideal1 "<<Distance(idealTr[0], idealTr[1])<<std::endl;
+ std::cout<<"ideal2 "<<Distance(idealTr[0], idealTr[2])<<std::endl;
+ std::cout<<"real:\n";
+ PrintMatrix(fV);
+ std::cout<<"real1 "<<Distance(fV[0], fV[1])<<std::endl;
+ std::cout<<"real2 "<<Distance(fV[0], fV[2])<<std::endl;
+ }
+#endif
+}
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