Matrix Of ViewTransform In vtkCamera

ViewTransform stores three vectors in the first three rows and position information in the forth column.

We can rotate camera around view up direction [ Azimuth operation ] and horizontal line (sideway) [ Elevation operation ] easily.

The relative implementation details in VTK:

void vtkCamera::ComputeViewTransform()
{
  // main view through the camera
  this->Transform->Identity();
  if (this->UserViewTransform)
  {
    this->Transform->Concatenate(this->UserViewTransform);
  }
  this->Transform->SetupCamera(this->Position, this->FocalPoint, this->ViewUp);
  this->ViewTransform->Identity();
  this->ViewTransform->Concatenate(this->Transform->GetMatrix());
}

void vtkPerspectiveTransform::SetupCamera(const double position[3],
                                          const double focalPoint[3],
                                          const double viewUp[3])
{
  double matrix[4][4];
  vtkMatrix4x4::Identity(*matrix);

  // the view directions correspond to the rows of the rotation matrix,
  // so we'll make the connection explicit
  double *viewSideways =    matrix[0];
  double *orthoViewUp =     matrix[1];
  double *viewPlaneNormal = matrix[2];

  // set the view plane normal from the view vector
  viewPlaneNormal[0] = position[0] - focalPoint[0];
  viewPlaneNormal[1] = position[1] - focalPoint[1];
  viewPlaneNormal[2] = position[2] - focalPoint[2];
  vtkMath::Normalize(viewPlaneNormal);

  // orthogonalize viewUp and compute viewSideways
  vtkMath::Cross(viewUp,viewPlaneNormal,viewSideways);
  vtkMath::Normalize(viewSideways);
  vtkMath::Cross(viewPlaneNormal,viewSideways,orthoViewUp);

  // translate by the vector from the position to the origin
  double delta[4];
  delta[0] = -position[0];
  delta[1] = -position[1];
  delta[2] = -position[2];
  delta[3] = 0.0; // yes, this should be zero, not one

  vtkMatrix4x4::MultiplyPoint(*matrix,delta,delta);

  matrix[0][3] = delta[0];
  matrix[1][3] = delta[1];
  matrix[2][3] = delta[2];

  // apply the transformation
  this->Concatenate(*matrix);
}