transform.cxx

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// $Id$
 
// -----------------------------------------------------------------------
// The RootGM package of the Virtual Geometry Model
// Copyright (C) 2007, Ivana Hrivnacova
// All rights reserved.
//
// For the licensing terms see vgm/LICENSE.
// Contact: ivana@ipno.in2p3.fr
// -----------------------------------------------------------------------
 
//
// RootGM utilities
// --------------
// Utility functions
//
// Author: Ivana Hrivnacova; IPN Orsay
 
#include "BaseVGM/common/utilities.h"
 
#include "RootGM/common/Units.h"
#include "RootGM/common/transform.h"
 
#include "TGeoBBox.h"
#include "TGeoPatternFinder.h"
#include "TMath.h"
 
#include <float.h>
#include <iostream>
#include <math.h>
 
//
// Root -> VGM
//
 
//_____________________________________________________________________________
VGM::Transform RootGM::Transform(const TGeoMatrix& matrix)
{
  //
  // Translation
  //
  const Double_t* translation = matrix.GetTranslation();
 
  VGM::Transform transform(VGM::kSize);
  transform[0] = translation[VGM::kDx] * Units::Length();
  transform[1] = translation[VGM::kDy] * Units::Length();
  transform[2] = translation[VGM::kDz] * Units::Length();
 
  // Rotation
  //
  const Double_t* rm = matrix.GetRotationMatrix();
 
  double xx, xz, // 3x3  Rotation Matrix (xy not used)
    yx, yy, yz, zx, zy, zz;
 
  xx = rm[0];
  xz = rm[2];
  yx = rm[3];
  yy = rm[4];
  yz = rm[5];
  zx = rm[6];
  zy = rm[7];
  zz = rm[8];
 
  // Decompose reflectionZ from rotation matrix
 
  if (HasReflection(matrix)) {
    xz = -xz;
    yz = -yz;
    zz = -zz;
  }
 
  // Get axis angles
  // (Using E.Tchernaiev formula)
 
  double angleX;
  double angleY;
  double angleZ;
  double cosb = sqrt(xx * xx + yx * yx);
  if (cosb > 16 * FLT_EPSILON) {
    angleX = atan2(zy, zz);
    angleY = atan2(-zx, cosb);
    angleZ = atan2(yx, xx);
  }
  else {
    angleX = atan2(-yz, yy);
    angleY = atan2(-zx, cosb);
    angleZ = 0.;
  }
 
  transform[VGM::kAngleX] = angleX * TMath::RadToDeg() * Units::Angle();
  transform[VGM::kAngleY] = angleY * TMath::RadToDeg() * Units::Angle();
  transform[VGM::kAngleZ] = angleZ * TMath::RadToDeg() * Units::Angle();
 
  // Reflection
  //
  transform[VGM::kReflZ] = 0.;
  if (matrix.IsReflection()) transform[VGM::kReflZ] = 1.;
 
  return transform;
}
 
//_____________________________________________________________________________
VGM::Transform RootGM::TransformScale(const TGeoScale& scale)
{
  const Double_t* dscale = scale.GetScale();
 
  VGM::Transform transform(VGM::kSize);
  transform[VGM::kDx] = dscale[0];
  transform[VGM::kDy] = dscale[1];
  transform[VGM::kDz] = dscale[2];
 
  return transform;
}
 
//_____________________________________________________________________________
bool RootGM::HasReflection(const TGeoMatrix& matrix)
{
  //
  /*
    // Decompose general matrix
    const Double_t* rm = matrix.GetRotation()
 
    // Matrix
    // rm[0] * sm[0], rm[1] * sm[1], rm[2] * sm[2], tm[0]
    // rm[3] * sm[0], rm[4] * sm[1], rm[5] * sm[2], tm[1]
    // rm[6] * sm[0], rm[7] * sm[1], rm[8] * sm[2], tm[2]
 
    double xx, xy, xz, dx,     // 4x3  Transformation Matrix
           yx, yy, yz, dy,
           zx, zy, zz, dz;
 
    xx = rm[0]; xy = rm[1]; xz = rm[2];
    yx = rm[3]; yy = rm[4]; yz = rm[5];
    zx = rm[6]; zy = rm[7]; zz = rm[8];
    dx = tm[0]; dy = tm[1]; dz = tm[2];
    sx = sm[0]; sy = sm[1]; sz = sm[2];
 
    // If reflection, apply it to scaleZ
    if (xx*(yy*zz-yz*zy) - xy*(yx*zz-yz*zx) + xz*(yx*zy-yy*zx) < 0)
      return true;
    else
      return false
  */
 
  return matrix.IsReflection();
}
 
//
// VGM -> Root
//
 
//_____________________________________________________________________________
TGeoMatrix* RootGM::CreateTransform(const VGM::Transform& transform)
{
 
  if (transform.size() != VGM::kSize) {
    std::cerr << "RootGM::CreateTransform: " << std::endl;
    std::cerr << "Wrong transform vector size. " << std::endl;
    exit(1);
  }
 
  TGeoRotation* rootRotation = new TGeoRotation();
  rootRotation->RotateX(transform[VGM::kAngleX] / Units::Angle());
  rootRotation->RotateY(transform[VGM::kAngleY] / Units::Angle());
  rootRotation->RotateZ(transform[VGM::kAngleZ] / Units::Angle());
 
  if (HasReflection(transform)) {
    // copy matrix in a new one
    const Double_t* matrix = rootRotation->GetRotationMatrix();
    Double_t matrix2[9];
    for (Int_t i = 0; i < 9; i++) matrix2[i] = matrix[i];
 
    // apply reflectionZ to rotation matrix
    matrix2[2] = -matrix2[2]; // xz
    matrix2[5] = -matrix2[5]; // yz
    matrix2[8] = -matrix2[8]; // zz
 
    // reset matrix
    rootRotation->SetMatrix(matrix2);
  }
 
  return new TGeoCombiTrans(transform[VGM::kDx] / Units::Length(),
    transform[VGM::kDy] / Units::Length(),
    transform[VGM::kDz] / Units::Length(), rootRotation);
}
 
//_____________________________________________________________________________
TGeoScale* RootGM::CreateScale(const VGM::Transform& transform)
{
  return new TGeoScale(
    transform[VGM::kDx], transform[VGM::kDy], transform[VGM::kDz]);
}
 
//_____________________________________________________________________________
bool RootGM::HasReflection(const VGM::Transform& transform)
{
  return BaseVGM::Round(transform[VGM::kReflZ]) == 1.;
}
 
//
// Root special
//
 
//_____________________________________________________________________________
TGeoHMatrix RootGM::Displacement(TGeoShape* shape)
{
  TGeoBBox* box = dynamic_cast<TGeoBBox*>(shape);
  if (!box) return TGeoHMatrix();
 
  const Double_t* origin = box->GetOrigin();
  if (!origin) return TGeoHMatrix();
 
  return TGeoHMatrix(TGeoTranslation(origin[0], origin[1], origin[2]));
  ;
}
 
//_____________________________________________________________________________
 
// The following code was taken from the paper:
// http://jgt.akpeters.com/papers/MollerHughes99/
// Changed float to double.
// See below the authors.
 
#include <math.h>
 
#define EPSILON 0.000001
 
#define CROSS(dest, v1, v2)                  \
  {                                          \
    dest[0] = v1[1] * v2[2] - v1[2] * v2[1]; \
    dest[1] = v1[2] * v2[0] - v1[0] * v2[2]; \
    dest[2] = v1[0] * v2[1] - v1[1] * v2[0]; \
  }
 
#define DOT(v1, v2) (v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2])
 
#define SUB(dest, v1, v2)    \
  {                          \
    dest[0] = v1[0] - v2[0]; \
    dest[1] = v1[1] - v2[1]; \
    dest[2] = v1[2] - v2[2]; \
  }
 
/*
 * A function for creating a rotation matrix that rotates a vector called
 * "from" into another vector called "to".
 * Input : from[3], to[3] which both must be *normalized* non-zero vectors
 * Output: mtx[3][3] -- a 3x3 matrix in colum-major form
 * Authors: Tomas Möller, John Hughes
 *          "Efficiently Building a Matrix to Rotate One Vector to Another"
 *          Journal of Graphics Tools, 4(4):1-4, 1999
 */
void RootGM::fromToRotation(double from[3], double to[3], double mtx[3][3])
{
  double v[3];
  double e, h, f;
 
  CROSS(v, from, to);
  e = DOT(from, to);
  f = (e < 0) ? -e : e;
  if (f > 1.0 - EPSILON) /* "from" and "to"-vector almost parallel */
  {
    double utmp[3], vtmp[3]; /* temporary storage vectors */
    double x[3];             /* vector most nearly orthogonal to "from" */
    double c1, c2, c3;       /* coefficients for later use */
    int i, j;
 
    x[0] = (from[0] > 0.0) ? from[0] : -from[0];
    x[1] = (from[1] > 0.0) ? from[1] : -from[1];
    x[2] = (from[2] > 0.0) ? from[2] : -from[2];
 
    if (x[0] < x[1]) {
      if (x[0] < x[2]) {
        x[0] = 1.0;
        x[1] = x[2] = 0.0;
      }
      else {
        x[2] = 1.0;
        x[0] = x[1] = 0.0;
      }
    }
    else {
      if (x[1] < x[2]) {
        x[1] = 1.0;
        x[0] = x[2] = 0.0;
      }
      else {
        x[2] = 1.0;
        x[0] = x[1] = 0.0;
      }
    }
 
    utmp[0] = x[0] - from[0];
    utmp[1] = x[1] - from[1];
    utmp[2] = x[2] - from[2];
    vtmp[0] = x[0] - to[0];
    vtmp[1] = x[1] - to[1];
    vtmp[2] = x[2] - to[2];
 
    c1 = 2.0 / DOT(utmp, utmp);
    c2 = 2.0 / DOT(vtmp, vtmp);
    c3 = c1 * c2 * DOT(utmp, vtmp);
 
    for (i = 0; i < 3; i++) {
      for (j = 0; j < 3; j++) {
        mtx[i][j] = -c1 * utmp[i] * utmp[j] - c2 * vtmp[i] * vtmp[j] +
                    c3 * vtmp[i] * utmp[j];
      }
      mtx[i][i] += 1.0;
    }
  }
  else /* the most common case, unless "from"="to", or "from"=-"to" */
  {
#if 0
    /* unoptimized version - a good compiler will optimize this. */
    /* h = (1.0 - e)/DOT(v, v); old code */
    h = 1.0/(1.0 + e);      /* optimization by Gottfried Chen */
    mtx[0][0] = e + h * v[0] * v[0];
    mtx[0][1] = h * v[0] * v[1] - v[2];
    mtx[0][2] = h * v[0] * v[2] + v[1];
 
    mtx[1][0] = h * v[0] * v[1] + v[2];
    mtx[1][1] = e + h * v[1] * v[1];
    mtx[1][2] = h * v[1] * v[2] - v[0];
 
    mtx[2][0] = h * v[0] * v[2] - v[1];
    mtx[2][1] = h * v[1] * v[2] + v[0];
    mtx[2][2] = e + h * v[2] * v[2];
#else
    /* ...otherwise use this hand optimized version (9 mults less) */
    double hvx, hvz, hvxy, hvxz, hvyz;
    /* h = (1.0 - e)/DOT(v, v); old code */
    h = 1.0 / (1.0 + e); /* optimization by Gottfried Chen */
    hvx = h * v[0];
    hvz = h * v[2];
    hvxy = hvx * v[1];
    hvxz = hvx * v[2];
    hvyz = hvz * v[1];
    mtx[0][0] = e + hvx * v[0];
    mtx[0][1] = hvxy - v[2];
    mtx[0][2] = hvxz + v[1];
 
    mtx[1][0] = hvxy + v[2];
    mtx[1][1] = e + h * v[1] * v[1];
    mtx[1][2] = hvyz - v[0];
 
    mtx[2][0] = hvxz - v[1];
    mtx[2][1] = hvyz + v[0];
    mtx[2][2] = e + hvz * v[2];
#endif
  }
}