vcglib/vcg/math/shot.h

/****************************************************************************
* VCGLib                                                            o o     *
* Visual and Computer Graphics Library                            o     o   *
*                                                                _   O  _   *
* Copyright(C) 2004                                                \/)\/    *
* Visual Computing Lab                                            /\/|      *
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt)          *
* for more details.                                                         *
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****************************************************************************/


/** class Shot

Shot is made of two elements:

* the Instrinsics paramaters, which are stored as a Camera type (see vcg/math/camera) and that
determines how a point in the frame of the camera is projected in the 2D projection plane

* the Extrinsics parameters, which are stored in the class Shot (type ReferenceFrame)
and that describe viewpoint and view direction.

Some important notes about the usage of this class:

* The World coordinates system is assumed to be RIGHT-HANDED.
* The Shot reference frame is assumed to be RIGHT-HANDED.
* The associated Camera is assumed to point in the negative direction of the Z axis of the Shot coordinates system (reference frame).
  As a consequence, the Camera coordinates system is LEFT-HANDED.
* The Extrinsics parameters are kept as a rotation matrix "rot" and a translation vector "tra"
  The translation matrix "tra" corresponds to the viewpoint of the Shot while the rotation matrix
  "rot" corresponds to the axis of the reference frame by row, i.e.
  rot[0][0|1|2] == X axis
  rot[1][0|1|2] == Y axis
  rot[2][0|1|2] == Z axis

  It follows that the matrix made with the upper left 3x3 equal to rot and the 4th colum equal to tra
  and (0,0,0,1) in the bottom row transform a point from world coordiantes to the reference frame
  of the shot.



 **/

#ifndef __VCGLIB_SHOT
#define __VCGLIB_SHOT

#include <vcg/space/point2.h>
#include <vcg/space/point3.h>
#include <vcg/math/similarity.h>
#include <vcg/math/camera.h>

namespace vcg{

template <class S, class RotationType = Matrix44<S> >
class Shot {
public:
  typedef Camera<S> CameraType;
  typedef S ScalarType;

  template <class ScalarType, class RotoType >
  class ReferenceFrame {
    friend class Shot<ScalarType, RotoType>;
      RotoType rot;	 // rotation
      Point3<S> tra; // viewpoint
  public:
      ReferenceFrame(){}

      void SetIdentity(){ rot.SetIdentity(); tra = Point3<S>(0.0,0.0,0.0);}
      void SetTra(const Point3<S> & tr) {tra = tr;}
      void SetRot(const  RotoType & rt) {rot = rt;}
      Point3<ScalarType>   Tra() const  { return tra;}
      RotoType Rot() const  { return rot;}
  };

  Camera<S>	                       Intrinsics;		// the camera that made the shot
  ReferenceFrame<S,RotationType>   Extrinsics;		// the position and orientation of the camera
  Shot(const Camera<S> &i, const ReferenceFrame<S,RotationType> &e)
  {
    Intrinsics = i;
    Extrinsics = e;
  }

  Shot(const Camera<S> &c)
  {
    Intrinsics = c;
    Extrinsics.SetIdentity();
  }

  Shot()
  {
    Extrinsics.SetIdentity();
  }

   template <class Q>
   static inline Shot Construct( const Shot<Q> & b )
   {
     ReferenceFrame<S,RotationType> r;
     r.SetRot(Matrix44<S>::Construct(b.Extrinsics.Rot()));
     r.SetTra(Point3<S>::Construct(b.Extrinsics.Tra()));
     return Shot(Camera<S>::Construct(b.Intrinsics), r);
   }


  /// GET the i-th axis of the coordinate system of the camera
  vcg::Point3<S> Axis(const int & i)const;

  /// GET the viewdir
  const vcg::Point3<S> GetViewDir()const;
  /// GET the viewpoint
  const vcg::Point3<S> GetViewPoint()const;
  /// SET the viewpoint
  void SetViewPoint(const vcg::Point3<S> & viewpoint);

  /// GET fov from focal
  float GetFovFromFocal();

  /// look at (point+up)
  void LookAt(const vcg::Point3<S> & point,const vcg::Point3<S> & up);

  /// look at (opengl-like)
  void LookAt(const S & eye_x,const S & eye_y,const S & eye_z,
        const S & at_x,const S & at_y,const S & at_z,
        const S & up_x,const S & up_y,const S & up_z);

  /// look towards (dir+up)
  void LookTowards(const vcg::Point3<S> & z_dir,const vcg::Point3<S> & up);

    /* Sometimes the focal is given in pixels. In this case, this function can be used to convert it in millimiters
     * given the CCD width (in mm). This method should be moved in vcg::Camera().
     * Equivalent focal length is obtained by setting the ccd width to 35 mm.
   */
  void ConvertFocalToMM(S ccdwidth);

    /* Sometimes the 3D World coordinates are known up to a scale factor. This method adjust the camera/shot parameters
     * to account for the re-scaling of the World. If the intrisic parameters are just reasonable values
     * the cameras need only a re-positioning.
     */
  void RescalingWorld(S scalefactor, bool adjustIntrinsics);

  /// Given a pure roto-translation (4-by-4) modifies the reference frame accordingly.
  void ApplyRigidTransformation(const Matrix44<S> & M);

  /// Given a similarity transformation such that p' = s R p + T modifies the reference frame accordingly.
  void ApplySimilarity(  Matrix44<S>   M);

  /// Given a similarity transformation such that p' = s R p + T modifies the reference frame accordingly.
  void ApplySimilarity(const Similarity<S> & Sim);

  /// convert a 3d point from world to camera coordinates (do not confuse with the Shot reference frame)
  vcg::Point3<S> ConvertWorldToCameraCoordinates(const vcg::Point3<S> & p) const;

  /// convert a 3d point from camera (do not confuse with the Shot reference frame) to world coordinates
  vcg::Point3<S> ConvertCameraToWorldCoordinates(const vcg::Point3<S> & p) const;

  /* convert a 3d point from camera (do not confuse with the Shot reference frame) to world coordinates
   * it uses inverse instead of transpose for non-exactly-rigid rotation matrices (such as calculated by tsai and garcia)
   */
  vcg::Point3<S> ConvertCameraToWorldCoordinates_Substitute(const vcg::Point3<S> & p) const;

  /// project a 3d point from world coordinates to 2d camera viewport (the value returned is in pixels)
  vcg::Point2<S> Project(const vcg::Point3<S> & p) const;

  /// inverse projection from 2d camera viewport (in pixels) to 3d world coordinates (it requires the original depth of the projected point)
  vcg::Point3<S> UnProject(const vcg::Point2<S> & p, const S & d) const;

  /* inverse projection from 2d camera viewport (in pixels) to 3d world coordinates (it requires the original depth of the projected point)
   * uses inverse instead of trranspose for non-exactly-rigid rotation matrices (such as calculated by tsai and garcia)
   */
  vcg::Point3<S> UnProject_Substitute(const vcg::Point2<S> & p, const S & d) const;

  /// returns the distance of point p from camera plane (z depth), required for unprojection operation
  S Depth(const vcg::Point3<S> & p)const;


// accessors
public:

    /// Returns the (4-by-4) matrix M such that 3dpoint_in_world_coordinates = M * 3dpoint_in_local_coordinates
    Matrix44<S> GetExtrinsicsToWorldMatrix() const
    {
        Matrix44<S> rotM;
        Extrinsics.rot.ToMatrix(rotM);
        return Matrix44<S>().SetTranslate(Extrinsics.tra) * rotM.transpose();
    }

    /// Returns the (4-by-4) matrix M such that 3dpoint_in_local_coordinates = M * 3dpoint_in_world_coordinates
    Matrix44<S> GetWorldToExtrinsicsMatrix() const
    {
        Matrix44<S> rotM;
        Extrinsics.rot.ToMatrix(rotM);
        return rotM * Matrix44<S>().SetTranslate(-Extrinsics.tra) ;
    }

  /*  multiply the current reference frame for the matrix passed
   note: it is up to the caller to check the the matrix passed is a pure rototraslation
   */
  void MultMatrix(    vcg::Matrix44<S>    m44)
  {
    Extrinsics.tra = m44 * Extrinsics.tra;
    m44[0][3] = m44[1][3] = m44[2][3] =  0.0; //set no translation
    const S k = m44.GetRow3(0).Norm(); //compute scaling (assumed uniform)
    Extrinsics.rot = Extrinsics.rot * m44.transpose() * (1/k);
  }

  /*  multiply the current reference frame for the similarity passed
   note: it is up to the caller to check the the matrix passed is a pure rototraslation
   */
  void MultSimilarity( const Similarity<S> & s){ MultMatrix(s.Matrix());}

  bool IsValid() const
  {
    return Intrinsics.PixelSizeMm[0]>0 && Intrinsics.PixelSizeMm[1]>0;
  }

}; // end class definition



template <class S, class RotationType>
const vcg::Point3<S> Shot<S,RotationType>::GetViewDir() const
{
  return  Extrinsics.Rot().GetRow3(2);
}



//---
/// GET the viewpoint
template <class S, class RotationType>
const vcg::Point3<S> Shot<S,RotationType>::GetViewPoint() const
{
  return  Extrinsics.tra;
}
/// SET the viewpoint
template <class S, class RotationType>
void Shot<S,RotationType>::SetViewPoint(const vcg::Point3<S> & viewpoint)
{
  Extrinsics.SetTra( viewpoint );
}
//---

/// GET fov from focal
template <class S, class RotationType>
float Shot<S,RotationType>::GetFovFromFocal()
{
  double viewportYMm= Intrinsics.PixelSizeMm[1]* Intrinsics.ViewportPx[1];
  return 2*(vcg::math::ToDeg(atanf(viewportYMm/(2*Intrinsics.FocalMm))));
}

//---

/// GET the i-th axis of the coordinate system of the camera
template <class S, class RotationType>
vcg::Point3<S>  Shot<S,RotationType>::Axis(const int & i) const
{
  vcg::Matrix44<S> m;
  Extrinsics.rot.ToMatrix(m);
  vcg::Point3<S> aa = m.GetRow3(i);
  return aa;
}

/// look at (point+up)
template <class S, class RotationType>
void Shot<S,RotationType>::LookAt(const vcg::Point3<S> & z_dir,const vcg::Point3<S> & up)
{
    LookTowards(z_dir-GetViewPoint(),up);
}

/// look at (opengl-like)
template <class S, class RotationType>
void Shot<S,RotationType>::LookAt(const S & eye_x, const S & eye_y, const S & eye_z,
           const S & at_x, const S & at_y, const S & at_z,
           const S & up_x,const S & up_y,const S & up_z)
{
  SetViewPoint(Point3<S>(eye_x,eye_y,eye_z));
  LookAt(Point3<S>(at_x,at_y,at_z),Point3<S>(up_x,up_y,up_z));
}

/// look towards
template <class S, class RotationType>
void Shot<S,RotationType>::LookTowards(const vcg::Point3<S> & z_dir,const vcg::Point3<S> & up)
{
  vcg::Point3<S> x_dir = up ^-z_dir;
  vcg::Point3<S> y_dir = -z_dir ^x_dir;

  Matrix44<S> m;
  m.SetIdentity();
  *(vcg::Point3<S> *)&m[0][0] =  x_dir/x_dir.Norm();
  *(vcg::Point3<S> *)&m[1][0] =  y_dir/y_dir.Norm();
  *(vcg::Point3<S> *)&m[2][0] = -z_dir/z_dir.Norm();

  Extrinsics.rot.FromMatrix(m);
}

//--- Space transformation methods

/// convert a 3d point from world to camera coordinates (do not confuse with the Shot reference frame)
template <class S, class RotationType>
vcg::Point3<S> Shot<S,RotationType>::ConvertWorldToCameraCoordinates(const vcg::Point3<S> & p) const
{
  Matrix44<S> rotM;
  Extrinsics.rot.ToMatrix(rotM);
  vcg::Point3<S> cp = rotM * (p - GetViewPoint() );
  cp[2]=-cp[2];
  return cp;
  }

/// convert a 3d point from camera coordinates (do not confuse with the Shot reference frame) to world coordinates
template <class S, class RotationType>
vcg::Point3<S> Shot<S,RotationType>::ConvertCameraToWorldCoordinates(const vcg::Point3<S> & p) const
{
  Matrix44<S> rotM;
  vcg::Point3<S> cp = p;
  cp[2]=-cp[2];
  Extrinsics.rot.ToMatrix(rotM);
  cp = rotM.transpose() * cp + GetViewPoint();
  return cp;
}

/// convert a 3d point from camera to world coordinates, uses inverse instead of trranspose for non-exactly-rigid rotation matrices (such as calculated by tsai and garcia)
template <class S, class RotationType>
vcg::Point3<S> Shot<S,RotationType>::ConvertCameraToWorldCoordinates_Substitute(const vcg::Point3<S> & p) const
{
  Matrix44<S> rotM;
  vcg::Point3<S> cp = p;
  cp[2]=-cp[2];
  Extrinsics.rot.ToMatrix(rotM);
  cp = Inverse(rotM) * cp + GetViewPoint();
  return cp;
}

/// project a 3d point from world coordinates to 2d camera viewport (the value returned is in pixel)
template <class S, class RotationType>
vcg::Point2<S> Shot<S,RotationType>::Project(const vcg::Point3<S> & p) const
{
  Point3<S> cp = ConvertWorldToCameraCoordinates(p);
  Point2<S> pp = Intrinsics.Project(cp);
  Point2<S> vp = Intrinsics.LocalToViewportPx(pp);
  return vp;
}

/// inverse projection from 2d camera viewport (in pixels) to 3d world coordinates (it requires the original depth of the point to unproject)
template <class S, class RotationType>
vcg::Point3<S> Shot<S,RotationType>::UnProject(const vcg::Point2<S> & p, const S & d) const
{
  Point2<S> lp = Intrinsics.ViewportPxToLocal(p);
  Point3<S> cp = Intrinsics.UnProject(lp,d);
  Point3<S> wp = ConvertCameraToWorldCoordinates(cp);
  return wp;
}

/* inverse projection from 2d camera viewport (in pixels) to 3d world coordinates (it requires the original depth of the projected point)
 * uses inverse instead of trranspose for non-exactly-rigid rotation matrices (such as calculated by tsai and garcia)
 */
template <class S, class RotationType>
vcg::Point3<S> Shot<S,RotationType>::UnProject_Substitute(const vcg::Point2<S> & p, const S & d) const
{
  Point2<S> lp = Intrinsics.ViewportPxToLocal(p);
  Point3<S> cp = Intrinsics.UnProject(lp,d);
  Point3<S> wp = ConvertCameraToWorldCoordinates_Substitute(cp);
  return wp;
}

/// returns the distance of point p from camera plane (z depth), required for unprojection operation
template <class S, class RotationType>
S Shot<S,RotationType>::Depth(const vcg::Point3<S> & p)const
{
  return ConvertWorldToCameraCoordinates(p).Z();
}

/* Sometimes the focal is given in pixels. In this case, this function can be used to convert it in millimiters
 * given the CCD width (in mm). This method should be moved in vcg::Camera().
 * Equivalent focal length is obtained by setting the ccd width to 35 mm.
 */
template <class S, class RotationType>
void Shot<S, RotationType>::ConvertFocalToMM(S ccdwidth)
{
  double ccd_width = ccdwidth; // ccd is assumed conventionally to be 35mm
  double ccd_height = (ccd_width * Intrinsics.ViewportPx[1]) / Intrinsics.ViewportPx[0];
  Intrinsics.PixelSizeMm[0] = (ccd_width / Intrinsics.ViewportPx[0]);
  Intrinsics.PixelSizeMm[1] = (ccd_height / Intrinsics.ViewportPx[1]);
  Intrinsics.FocalMm = (ccd_width * Intrinsics.FocalMm) / Intrinsics.ViewportPx[0];  // NOW FOCAL IS IN MM
}

/* Sometimes the 3D World coordinates are known up to a scale factor. This method adjust the camera/shot parameters
 * to account for the re-scaling of the World. If the intrisic parameters are just reasonable values
 * the cameras need only a re-positioning.
 */
template <class S, class RotationType>
void Shot<S, RotationType>::RescalingWorld(S scalefactor, bool adjustIntrinsics)
{
    // adjust INTRINSICS (if required)

        if (adjustIntrinsics)
        {
            Intrinsics.FocalMm = Intrinsics.FocalMm * scalefactor;
            double ccdwidth = static_cast<double>(Intrinsics.ViewportPx[0] * Intrinsics.PixelSizeMm[0]);
            double ccdheight = static_cast<double>(Intrinsics.ViewportPx[1] * Intrinsics.PixelSizeMm[1]);

            Intrinsics.PixelSizeMm[0] = (ccdwidth * scalefactor) / Intrinsics.ViewportPx[0];
            Intrinsics.PixelSizeMm[1] = (ccdheight * scalefactor) / Intrinsics.ViewportPx[1];
        }

    // adjust EXTRINSICS

    // rotation remains the same (!)
    // nothing to do..

    // the viewpoint should be modified according to the scale factor
    Extrinsics.tra *= scalefactor;
}

/// Given a pure roto-translation matrix (4-by-4) modify the reference frame accordingly.
template <class S, class RotationType>
void Shot<S, RotationType>::ApplyRigidTransformation(const Matrix44<S> & M)
{
  Matrix44<S> rotM;
  Extrinsics.rot.ToMatrix(rotM);
  // roto-translate the viewpoint
  Extrinsics.tra = M * Extrinsics.tra;
  Matrix44<S> newRot = rotM * M.transpose();
  newRot[3][0] =  newRot[3][1] =  newRot[3][2] = 0.0;

  Extrinsics.SetRot(newRot);
}

/// Given a similarity transformation modifies the reference frame accordingly.
template <class S, class RotationType>
void Shot<S, RotationType>::ApplySimilarity( Matrix44<S>   M)
{
  Matrix44<S> rotM;
  Extrinsics.rot.ToMatrix(rotM);

  // normalize
  M = M * (1/M.ElementAt(3,3));
  M[3][3] = 1; // just for numeric precision

  // compute scale factor
  ScalarType scalefactor = 1.0 / pow(ScalarType(M.Determinant()),1/ScalarType(3.0));

  // roto-translate the viewpoint
  Extrinsics.tra = M * Extrinsics.tra;

  vcg::Matrix44<S> M2 = M;

  M2 = M2 * scalefactor;				// remove the scaling
  M2[3][3] = 1.0;
  M2[0][3] = M2[1][3] = M2[2][3] = 0;	// remove the translation

  rotM = rotM * M2.transpose();
  Extrinsics.SetRot(rotM);
}

/// Given a similarity transformation modifies the reference frame accordingly.
template <class S, class RotationType>
void Shot<S, RotationType>::ApplySimilarity(const Similarity<S> & Sm)
{
  Matrix44<S> rotM;
  Extrinsics.rot.ToMatrix(rotM);

  // similarity decomposition
  vcg::Matrix44<S> R;
  Sm.rot.ToMatrix(R);
  vcg::Matrix44<S> T;
  T.SetIdentity();
  T.ElementAt(0,3) = Sm.tra[0];
  T.ElementAt(1,3) = Sm.tra[1];
  T.ElementAt(2,3) = Sm.tra[2];
  vcg::Matrix44d S44;
  S44.SetIdentity();
  S44 *= Sm.sca;
  S44.ElementAt(3,3) = 1.0;

  vcg::Matrix44<S> M = T * R * S44;

  // roto-translate the viewpoint
  Extrinsics.tra = M * Extrinsics.tra;

  vcg::Matrix44<S> M2 = M;

  M2 = M2 * (1.0 / Sm.sca);

  Extrinsics.rot = rotM * M2.transpose();

  Extrinsics.rot.ElementAt(3,0) = 0;
  Extrinsics.rot.ElementAt(3,1) = 0;
  Extrinsics.rot.ElementAt(3,2) = 0;
  Extrinsics.rot.ElementAt(3,3) = 1;

}


//--------------------------------


//--- utility definitions
typedef  Shot<float> Shotf;
typedef  Shot<double> Shotd;
//-----------------------

} // end name space

#endif