xref: /dports/math/cgal/CGAL-5.3/include/CGAL/Qt/camera_impl.h

/****************************************************************************

 Copyright (c) 2018  GeometryFactory Sarl (France).
 Copyright (C) 2002-2014 Gilles Debunne. All rights reserved.

 This file is part of a fork of the QGLViewer library version 2.7.0.

*****************************************************************************/
// $URL: https://github.com/CGAL/cgal/blob/v5.3/GraphicsView/include/CGAL/Qt/camera_impl.h $
// $Id: camera_impl.h db338aa 2021-02-18T15:19:06+01:00 Laurent Rineau
// SPDX-License-Identifier: GPL-3.0-only

#ifdef CGAL_HEADER_ONLY
#define CGAL_INLINE_FUNCTION inline

#include <CGAL/license/GraphicsView.h>

#else
#define CGAL_INLINE_FUNCTION
#endif

#include <CGAL/Qt/camera.h>
#include <CGAL/Qt/manipulatedCameraFrame.h>
#include <CGAL/Qt/keyFrameInterpolator.h>

namespace CGAL{
namespace qglviewer{

/*! Default constructor.

 sceneCenter() is set to (0,0,0) and sceneRadius() is set to 1.0. type() is
 Camera::PERSPECTIVE, with a \c M_PI/4 fieldOfView().

 See IODistance(), physicalDistanceToScreen(), physicalScreenWidth() and
 focusDistance(). */
CGAL_INLINE_FUNCTION
Camera::Camera(QObject *parent)
    : frame_(nullptr), fieldOfView_(CGAL_PI / 4.0), modelViewMatrixIsUpToDate_(false),
      projectionMatrixIsUpToDate_(false) {
  m_zMin = 0;
  setParent(parent);
  // #CONNECTION# Camera copy constructor
  interpolationKfi_ = new KeyFrameInterpolator;
  // Requires the interpolationKfi_
  setFrame(new ManipulatedCameraFrame());


  // Requires fieldOfView() to define focusDistance()
  setSceneRadius(1.0);

  // Initial value (only scaled after this)
  orthoCoef_ = tan(fieldOfView() / 2.0);

  // Also defines the pivotPoint(), which changes orthoCoef_. Requires a
  // frame().
  setSceneCenter(Vec(0.0, 0.0, 0.0));

  // Requires fieldOfView() when called with ORTHOGRAPHIC. Attention to
  // projectionMatrix_ below.
  setType(PERSPECTIVE);

  setZNearCoefficient(0.005);
  setZClippingCoefficient(sqrt(3.0));

  // Dummy values
  setScreenWidthAndHeight(600, 400);


  // focusDistance is set from setFieldOfView()

  // #CONNECTION# Camera copy constructor
  for (unsigned short j = 0; j < 16; ++j) {
    modelViewMatrix_[j] = ((j % 5 == 0) ? 1.0 : 0.0);
    // #CONNECTION# computeProjectionMatrix() is lazy and assumes 0.0 almost
    // everywhere.
    projectionMatrix_[j] = 0.0;
  }
  computeProjectionMatrix();
}

/*! Virtual destructor.

 The frame() is deleted, but the different keyFrameInterpolator() are \e not
 deleted (in case they are shared). */

CGAL_INLINE_FUNCTION
Camera::~Camera() {
  delete frame_;
  delete interpolationKfi_;
}

/*! Copy constructor. Performs a deep copy using operator=(). */
CGAL_INLINE_FUNCTION
Camera::Camera(const Camera &camera) : QObject(), frame_(nullptr) {
  // #CONNECTION# Camera constructor
  interpolationKfi_ = new KeyFrameInterpolator;
  // Requires the interpolationKfi_
  setFrame(new ManipulatedCameraFrame(*camera.frame()));

  for (unsigned short j = 0; j < 16; ++j) {
    modelViewMatrix_[j] = ((j % 5 == 0) ? 1.0 : 0.0);
    // #CONNECTION# computeProjectionMatrix() is lazy and assumes 0.0 almost
    // everywhere.
    projectionMatrix_[j] = 0.0;
  }

  (*this) = camera;
}

/*! Equal operator.

 All the parameters of \p camera are copied. The frame() pointer is not
 modified, but its Frame::position() and Frame::orientation() are set to those
 of \p camera.

 \attention The Camera screenWidth() and screenHeight() are set to those of \p
 camera. If your Camera is associated with a CGAL::QGLViewer, you should update these
 value after the call to this method: \code
 *(camera()) = otherCamera;
 camera()->setScreenWidthAndHeight(width(), height());
 \endcode
 The same applies to sceneCenter() and sceneRadius(), if needed. */
CGAL_INLINE_FUNCTION
Camera &Camera::operator=(const Camera &camera) {
  setScreenWidthAndHeight(camera.screenWidth(), camera.screenHeight());
  setFieldOfView(camera.fieldOfView());
  setSceneRadius(camera.sceneRadius());
  setSceneCenter(camera.sceneCenter());
  setZNearCoefficient(camera.zNearCoefficient());
  setZClippingCoefficient(camera.zClippingCoefficient());
  setType(camera.type());

  orthoCoef_ = camera.orthoCoef_;
  projectionMatrixIsUpToDate_ = false;

  // frame_ and interpolationKfi_ pointers are not shared.
  frame_->setReferenceFrame(nullptr);
  frame_->setPosition(camera.position());
  frame_->setOrientation(camera.orientation());

  interpolationKfi_->resetInterpolation();

  kfi_ = camera.kfi_;

  computeProjectionMatrix();
  computeModelViewMatrix();

  return *this;
}

/*! Sets Camera screenWidth() and screenHeight() (expressed in pixels).

You should not call this method when the Camera is associated with a CGAL::QGLViewer,
since the latter automatically updates these values when it is resized (hence
overwriting your values).

Non-positive dimension are silently replaced by a 1 pixel value to ensure
frustrum coherence.

If your Camera is used without a CGAL::QGLViewer (offscreen rendering, shadow maps),
use setAspectRatio() instead to define the projection matrix. */
CGAL_INLINE_FUNCTION
void Camera::setScreenWidthAndHeight(int width, int height) {
  // Prevent negative and zero dimensions that would cause divisions by zero.
  screenWidth_ = width > 0 ? width : 1;
  screenHeight_ = height > 0 ? height : 1;
  projectionMatrixIsUpToDate_ = false;
}

/*! Returns the near clipping plane distance used by the Camera projection
 matrix.

 The clipping planes' positions depend on the sceneRadius() and sceneCenter()
 rather than being fixed small-enough and large-enough values. A good scene
 dimension approximation will hence result in an optimal precision of the
 z-buffer.

 The near clipping plane is positioned at a distance equal to
 zClippingCoefficient() * sceneRadius() in front of the sceneCenter(): \code
 zNear = distanceToSceneCenter() - zClippingCoefficient()*sceneRadius();
 \endcode

 In order to prevent negative or too small zNear() values (which would degrade
 the z precision), zNearCoefficient() is used when the Camera is inside the
 sceneRadius() sphere: \code const qreal zMin = zNearCoefficient() *
 zClippingCoefficient() * sceneRadius(); if (zNear < zMin) zNear = zMin;
 // With an ORTHOGRAPHIC type, the value is simply clamped to 0.0
 \endcode

 See also the zFar(), zClippingCoefficient() and zNearCoefficient()
 documentations.

 If you need a completely different zNear computation, overload the zNear() and
 zFar() methods in a new class that publicly inherits from Camera and use
 CGAL::QGLViewer::setCamera(): \code class myCamera :: public CGAL::qglviewer::Camera
 {
   virtual qreal Camera::zNear() const { return 0.001; };
   virtual qreal Camera::zFar() const { return 100.0; };
 }
 \endcode

 See the <a href="../examples/standardCamera.html">standardCamera example</a>
 for an application.

 \attention The value is always positive although the clipping plane is
 positioned at a negative z value in the Camera coordinate system. This follows
 the \c gluPerspective standard. */
CGAL_INLINE_FUNCTION
qreal Camera::zNear() const {
  const qreal zNearScene = zClippingCoefficient() * sceneRadius();
  qreal z = distanceToSceneCenter() - zNearScene;

  // Prevents negative or null zNear values.
  const qreal zMin = zNearCoefficient() * zNearScene;
  if (z < zMin)
    switch (type()) {
    case Camera::PERSPECTIVE:
      z = zMin;
      break;
    case Camera::ORTHOGRAPHIC:
      z = m_zMin;
      break;
    }
  return z;
}

/*! Returns the far clipping plane distance used by the Camera projection
matrix.

The far clipping plane is positioned at a distance equal to
zClippingCoefficient() * sceneRadius() behind the sceneCenter(): \code zFar =
distanceToSceneCenter() + zClippingCoefficient()*sceneRadius(); \endcode

See the zNear() documentation for details. */
CGAL_INLINE_FUNCTION
qreal Camera::zFar() const {
  return distanceToSceneCenter() + zClippingCoefficient() * sceneRadius();
}

/*! Sets the vertical fieldOfView() of the Camera (in radians).

Note that focusDistance() is set to sceneRadius() / tan(fieldOfView()/2) by this
method. */
CGAL_INLINE_FUNCTION
void Camera::setFieldOfView(qreal fov) {
  fieldOfView_ = fov;
  projectionMatrixIsUpToDate_ = false;
}

/*! Defines the Camera type().

Changing the camera Type alters the viewport and the objects' sizes can be
changed. This method guarantees that the two frustum match in a plane normal to
viewDirection(), passing through the pivotPoint().

Prefix the type with \c Camera if needed, as in:
\code
camera()->setType(Camera::ORTHOGRAPHIC);
// or even CGAL::qglviewer::Camera::ORTHOGRAPHIC if you do not use namespace
\endcode */
CGAL_INLINE_FUNCTION
void Camera::setType(Type type) {
  // make ORTHOGRAPHIC frustum fit PERSPECTIVE (at least in plane normal to
  // viewDirection(), passing through RAP). Done only when CHANGING type since
  // orthoCoef_ may have been changed with a setPivotPoint() in the meantime.
  if ((type == Camera::ORTHOGRAPHIC) && (type_ == Camera::PERSPECTIVE))
    orthoCoef_ = tan(fieldOfView() / 2.0);
  type_ = type;
  projectionMatrixIsUpToDate_ = false;
}

/*! Sets the Camera frame().

If you want to move the Camera, use setPosition() and setOrientation() or one of
the Camera positioning methods (lookAt(), fitSphere(), showEntireScene()...)
instead.

If you want to save the Camera position(), there's no need to call this method
either. Use addKeyFrameToPath() and playPath() instead.

This method is actually mainly useful if you derive the ManipulatedCameraFrame
class and want to use an instance of your new class to move the Camera.

A \c nullptr \p mcf pointer will silently be ignored. The calling method is
responsible for deleting the previous frame() pointer if needed in order to
prevent memory leaks. */
CGAL_INLINE_FUNCTION
void Camera::setFrame(ManipulatedCameraFrame *const mcf) {
  if (!mcf)
    return;

  if (frame_) {
    disconnect(frame_, SIGNAL(modified()), this, SLOT(onFrameModified()));
  }

  frame_ = mcf;
  interpolationKfi_->setFrame(frame());

  connect(frame_, SIGNAL(modified()), this, SLOT(onFrameModified()));
  onFrameModified();
}

/*! Returns the distance from the Camera center to sceneCenter(), projected
  along the Camera Z axis. Used by zNear() and zFar() to optimize the Z range.
*/
CGAL_INLINE_FUNCTION
qreal Camera::distanceToSceneCenter() const {
  return fabs((frame()->coordinatesOf(sceneCenter())).z);
}

/*! Returns the \p halfWidth and \p halfHeight of the Camera orthographic
 frustum.

 These values are only valid and used when the Camera is of type()
 Camera::ORTHOGRAPHIC. They are expressed in OpenGL units and are used by
 loadProjectionMatrix() to define the projection matrix using: \code glOrtho(
 -halfWidth, halfWidth, -halfHeight, halfHeight, zNear(), zFar() ) \endcode

 These values are proportional to the Camera (z projected) distance to the
 pivotPoint(). When zooming on the object, the Camera is translated forward \e
 and its frustum is narrowed, making the object appear bigger on screen, as
 intuitively expected.

 Overload this method to change this behavior if desired, as is done in the
 <a href="../examples/standardCamera.html">standardCamera example</a>. */
CGAL_INLINE_FUNCTION
void Camera::getOrthoWidthHeight(GLdouble &halfWidth,
                                 GLdouble &halfHeight) const {
  const qreal dist = orthoCoef_ * fabs(cameraCoordinatesOf(pivotPoint()).z);
  //#CONNECTION# fitScreenRegion
  halfWidth = dist * ((aspectRatio() < 1.0) ? 1.0 : aspectRatio());
  halfHeight = dist * ((aspectRatio() < 1.0) ? 1.0 / aspectRatio() : 1.0);
}

/*! Computes the projection matrix associated with the Camera.

 If type() is Camera::PERSPECTIVE, defines a \c GL_PROJECTION matrix similar to
 what would \c gluPerspective() do using the fieldOfView(), window
 aspectRatio(), zNear() and zFar() parameters.

 If type() is Camera::ORTHOGRAPHIC, the projection matrix is as what \c
 glOrtho() would do. Frustum's width and height are set using
 getOrthoWidthHeight().

 Both types use zNear() and zFar() to place clipping planes. These values are
 determined from sceneRadius() and sceneCenter() so that they best fit the scene
 size.

 Use getProjectionMatrix() to retrieve this matrix. Overload
 loadProjectionMatrix() if you want your Camera to use an exotic projection
 matrix.

 \note You must call this method if your Camera is not associated with a
 CGAL::QGLViewer and is used for offscreen computations (using
 (un)projectedCoordinatesOf() for instance). loadProjectionMatrix() does it
 otherwise. */
CGAL_INLINE_FUNCTION
void Camera::computeProjectionMatrix() const {
  if (projectionMatrixIsUpToDate_)
    return;

  const qreal ZNear = zNear();
  const qreal ZFar = zFar();

  switch (type()) {
  case Camera::PERSPECTIVE: {
    // #CONNECTION# all non null coefficients were set to 0.0 in constructor.
    const qreal f = 1.0 / tan(fieldOfView() / 2.0);
    projectionMatrix_[0] = f / aspectRatio();
    projectionMatrix_[5] = f;
    projectionMatrix_[10] = (ZNear + ZFar) / (ZNear - ZFar);
    projectionMatrix_[11] = -1.0;
    projectionMatrix_[14] = 2.0 * ZNear * ZFar / (ZNear - ZFar);
    projectionMatrix_[15] = 0.0;
    // same as gluPerspective( 180.0*fieldOfView()/CGAL_PI, aspectRatio(), zNear(),
    // zFar() );
    break;
  }
  case Camera::ORTHOGRAPHIC: {
    GLdouble w, h;
    getOrthoWidthHeight(w, h);
    projectionMatrix_[0] = 1.0 / w;
    projectionMatrix_[5] = 1.0 / h;
    projectionMatrix_[10] = -2.0 / (ZFar - ZNear);
    projectionMatrix_[11] = 0.0;
    projectionMatrix_[14] = -(ZFar + ZNear) / (ZFar - ZNear);
    projectionMatrix_[15] = 1.0;
    // same as glOrtho( -w, w, -h, h, zNear(), zFar() );
    break;
  }
  }

  projectionMatrixIsUpToDate_ = true;
}

/*! Computes the modelView matrix associated with the Camera's position() and
 orientation().

 This matrix converts from the world coordinates system to the Camera
 coordinates system, so that coordinates can then be projected on screen using
 the projection matrix (see computeProjectionMatrix()).

 Use getModelViewMatrix() to retrieve this matrix.

 \note You must call this method if your Camera is not associated with a
 CGAL::QGLViewer and is used for offscreen computations (using
 (un)projectedCoordinatesOf() for instance). loadModelViewMatrix() does it
 otherwise. */
CGAL_INLINE_FUNCTION
void Camera::computeModelViewMatrix() const {
  if (modelViewMatrixIsUpToDate_)
    return;

  const Quaternion q = frame()->orientation();

  const qreal q00 = 2.0 * q[0] * q[0];
  const qreal q11 = 2.0 * q[1] * q[1];
  const qreal q22 = 2.0 * q[2] * q[2];

  const qreal q01 = 2.0 * q[0] * q[1];
  const qreal q02 = 2.0 * q[0] * q[2];
  const qreal q03 = 2.0 * q[0] * q[3];

  const qreal q12 = 2.0 * q[1] * q[2];
  const qreal q13 = 2.0 * q[1] * q[3];

  const qreal q23 = 2.0 * q[2] * q[3];

  modelViewMatrix_[0] = 1.0 - q11 - q22;
  modelViewMatrix_[1] = q01 - q23;
  modelViewMatrix_[2] = q02 + q13;
  modelViewMatrix_[3] = 0.0;

  modelViewMatrix_[4] = q01 + q23;
  modelViewMatrix_[5] = 1.0 - q22 - q00;
  modelViewMatrix_[6] = q12 - q03;
  modelViewMatrix_[7] = 0.0;

  modelViewMatrix_[8] = q02 - q13;
  modelViewMatrix_[9] = q12 + q03;
  modelViewMatrix_[10] = 1.0 - q11 - q00;
  modelViewMatrix_[11] = 0.0;

  const Vec t = q.inverseRotate(frame()->position());

  modelViewMatrix_[12] = -t.x;
  modelViewMatrix_[13] = -t.y;
  modelViewMatrix_[14] = -t.z;
  modelViewMatrix_[15] = 1.0;

  modelViewMatrixIsUpToDate_ = true;
}

/*! Loads the OpenGL \c GL_PROJECTION matrix with the Camera projection matrix.

 The Camera projection matrix is computed using computeProjectionMatrix().

 When \p reset is \c true (default), the method clears the previous projection
 matrix by calling \c glLoadIdentity before setting the matrix. Setting \p reset
 to \c false is useful for \c GL_SELECT mode, to combine the pushed matrix with
 a picking matrix. See CGAL::QGLViewer::beginSelection() for details.

 This method is used by CGAL::QGLViewer::preDraw() (called before user's
 CGAL::QGLViewer::draw() method) to set the \c GL_PROJECTION matrix according to the
 viewer's CGAL::QGLViewer::camera() settings.

 Use getProjectionMatrix() to retrieve this matrix. Overload this method if you
 want your Camera to use an exotic projection matrix. See also
 loadModelViewMatrix().

 \attention \c glMatrixMode is set to \c GL_PROJECTION.

 \attention If you use several OpenGL contexts and bypass the Qt main refresh
 loop, you should call QOpenGLWidget::makeCurrent() before this method in order
 to activate the right OpenGL context. */
CGAL_INLINE_FUNCTION
void Camera::loadProjectionMatrix(bool ) const {
  // WARNING: makeCurrent must be called by every calling method
  computeProjectionMatrix();
}

/*! Loads the OpenGL \c GL_MODELVIEW matrix with the modelView matrix
 corresponding to the Camera.

 Calls computeModelViewMatrix() to compute the Camera's modelView matrix.

 This method is used by CGAL::QGLViewer::preDraw() (called before user's
 CGAL::QGLViewer::draw() method) to set the \c GL_MODELVIEW matrix according to the
 viewer's CGAL::QGLViewer::camera() position() and orientation().

 As a result, the vertices used in CGAL::QGLViewer::draw() can be defined in the so
 called world coordinate system. They are multiplied by this matrix to get
 converted to the Camera coordinate system, before getting projected using the
 \c GL_PROJECTION matrix (see loadProjectionMatrix()).

 When \p reset is \c true (default), the method loads (overwrites) the \c
 GL_MODELVIEW matrix. Setting \p reset to \c false simply calls \c glMultMatrixd
 (might be useful for some applications).

 Overload this method or simply call glLoadMatrixd() at the beginning of
 CGAL::QGLViewer::draw() if you want your Camera to use an exotic modelView matrix.
 See also loadProjectionMatrix().

 getModelViewMatrix() returns the 4x4 modelView matrix.

 \attention glMatrixMode is set to \c GL_MODELVIEW

 \attention If you use several OpenGL contexts and bypass the Qt main refresh
 loop, you should call QOpenGLWidget::makeCurrent() before this method in order
 to activate the right OpenGL context. */
CGAL_INLINE_FUNCTION
void Camera::loadModelViewMatrix(bool ) const {
  // WARNING: makeCurrent must be called by every calling method
  computeModelViewMatrix();
}




/*! Fills \p m with the Camera projection matrix values.

 Based on computeProjectionMatrix() to make sure the Camera projection matrix is
 up to date.

 This matrix only reflects the Camera's internal parameters and it may differ
 from the \c GL_PROJECTION matrix retrieved using \c
 glGetDoublev(GL_PROJECTION_MATRIX, m). It actually represents the state of the
 \c GL_PROJECTION after CGAL::QGLViewer::preDraw(), at the beginning of
 CGAL::QGLViewer::draw(). If you modified the \c GL_PROJECTION matrix (for instance
 using CGAL::QGLViewer::startScreenCoordinatesSystem()), the two results differ.

 The result is an OpenGL 4x4 matrix, which is given in \e column-major order
 (see \c glMultMatrix man page for details).

 See also getModelViewMatrix() and setFromProjectionMatrix(). */
CGAL_INLINE_FUNCTION
void Camera::getProjectionMatrix(GLdouble m[16]) const {
  computeProjectionMatrix();
  for (unsigned short i = 0; i < 16; ++i)
    m[i] = projectionMatrix_[i];
}

/*! Overloaded getProjectionMatrix(GLdouble m[16]) method using a \c GLfloat
 * array instead. */
CGAL_INLINE_FUNCTION
void Camera::getProjectionMatrix(GLfloat m[16]) const {
  static GLdouble mat[16];
  getProjectionMatrix(mat);
  for (unsigned short i = 0; i < 16; ++i)
    m[i] = float(mat[i]);
}

/*! Fills \p m with the Camera modelView matrix values.

 First calls computeModelViewMatrix() to define the Camera modelView matrix.

 Note that this matrix may \e not be the one you would get from a \c
 glGetDoublev(GL_MODELVIEW_MATRIX, m). It actually represents the state of the
 \c GL_MODELVIEW after CGAL::QGLViewer::preDraw(), at the \e beginning of
 CGAL::QGLViewer::draw(). It converts from the world to the Camera coordinate system.
 As soon as you modify the \c GL_MODELVIEW in your CGAL::QGLViewer::draw() method
 (using glTranslate, glRotate... or similar methods), the two matrices differ.

 The result is an OpenGL 4x4 matrix, which is given in \e column-major order
 (see \c glMultMatrix man page for details).

 See also getProjectionMatrix() and setFromModelViewMatrix(). */
CGAL_INLINE_FUNCTION
void Camera::getModelViewMatrix(GLdouble m[16]) const {
  // May not be needed, but easier like this.
  computeModelViewMatrix();
  for (unsigned short i = 0; i < 16; ++i)
    m[i] = modelViewMatrix_[i];
}

/*! Overloaded getModelViewMatrix(GLdouble m[16]) method using a \c GLfloat
 * array instead. */
CGAL_INLINE_FUNCTION
void Camera::getModelViewMatrix(GLfloat m[16]) const {
  static GLdouble mat[16];
  getModelViewMatrix(mat);
  for (unsigned short i = 0; i < 16; ++i)
    m[i] = float(mat[i]);
}

/*! Fills \p m with the product of the ModelView and Projection matrices.

  Calls getModelViewMatrix() and getProjectionMatrix() and then fills \p m with
  the product of these two matrices. */
CGAL_INLINE_FUNCTION
void Camera::getModelViewProjectionMatrix(GLdouble m[16]) const {
  GLdouble mv[16];
  GLdouble proj[16];
  getModelViewMatrix(mv);
  getProjectionMatrix(proj);

  for (unsigned short i = 0; i < 4; ++i) {
    for (unsigned short j = 0; j < 4; ++j) {
      qreal sum = 0.0;
      for (unsigned short k = 0; k < 4; ++k)
        sum += proj[i + 4 * k] * mv[k + 4 * j];
      m[i + 4 * j] = sum;
    }
  }
}

/*! Overloaded getModelViewProjectionMatrix(GLdouble m[16]) method using a \c
 * GLfloat array instead. */
CGAL_INLINE_FUNCTION
void Camera::getModelViewProjectionMatrix(GLfloat m[16]) const {
  static GLdouble mat[16];
  getModelViewProjectionMatrix(mat);
  for (unsigned short i = 0; i < 16; ++i)
    m[i] = float(mat[i]);
}

/*! Sets the sceneRadius() value. Negative values are ignored.

\attention This methods also sets focusDistance() to sceneRadius() /
tan(fieldOfView()/2) and flySpeed() to 1% of sceneRadius(). */
CGAL_INLINE_FUNCTION
void Camera::setSceneRadius(qreal radius) {
  if (radius <= 0.0) {
    qWarning("Scene radius must be positive - Ignoring value");
    return;
  }

  sceneRadius_ = radius;
  projectionMatrixIsUpToDate_ = false;

  frame()->setFlySpeed(0.01 * sceneRadius());
}

/*! Similar to setSceneRadius() and setSceneCenter(), but the scene limits are
  defined by a (world axis aligned) bounding box. */
CGAL_INLINE_FUNCTION
void Camera::setSceneBoundingBox(const Vec &min, const Vec &max) {
  setSceneCenter((min + max) / 2.0);
  setSceneRadius(0.5 * (max - min).norm());
}

/*! Sets the sceneCenter().

 \attention This method also sets the pivotPoint() to sceneCenter(). */
CGAL_INLINE_FUNCTION
void Camera::setSceneCenter(const Vec &center) {
  sceneCenter_ = center;
  setPivotPoint(sceneCenter());
  projectionMatrixIsUpToDate_ = false;
}

/*! setSceneCenter() to the result of pointUnderPixel(\p pixel).

  Returns \c true if a pointUnderPixel() was found and sceneCenter() was
  actually changed.

  See also setPivotPointFromPixel(). See the pointUnderPixel() documentation. */
CGAL_INLINE_FUNCTION
bool Camera::setSceneCenterFromPixel(const QPoint &pixel) {
  bool found;
  Vec point = pointUnderPixel(pixel, found);
  if (found)
    setSceneCenter(point);
  return found;
}

/*! Changes the pivotPoint() to \p point (defined in the world coordinate
 * system). */
CGAL_INLINE_FUNCTION
void Camera::setPivotPoint(const Vec &point) {
  const qreal prevDist = fabs(cameraCoordinatesOf(pivotPoint()).z);

  // If frame's RAP is set directly, projectionMatrixIsUpToDate_ should also be
  // set to false to ensure proper recomputation of the ORTHO projection matrix.
  frame()->setPivotPoint(point);

  // orthoCoef_ is used to compensate for changes of the pivotPoint, so that the
  // image does not change when the pivotPoint is changed in ORTHOGRAPHIC mode.
  const qreal newDist = fabs(cameraCoordinatesOf(pivotPoint()).z);
  // Prevents division by zero when rap is set to camera position
  if ((prevDist > 1E-9) && (newDist > 1E-9))
    orthoCoef_ *= prevDist / newDist;
  projectionMatrixIsUpToDate_ = false;
}

/*! The pivotPoint() is set to the point located under \p pixel on screen.

Returns \c true if a pointUnderPixel() was found. If no point was found under \p
pixel, the pivotPoint() is left unchanged.

\p pixel is expressed in Qt format (origin in the upper left corner of the
window). See pointUnderPixel().

See also setSceneCenterFromPixel(). */
CGAL_INLINE_FUNCTION
bool Camera::setPivotPointFromPixel(const QPoint &pixel) {
  bool found;
  Vec point = pointUnderPixel(pixel, found);
  if (found)
    setPivotPoint(point);
  return found;
}

/*! Returns the ratio between pixel and OpenGL units at \p position.

 A line of \c n * pixelGLRatio() OpenGL units, located at \p position in the
 world coordinates system, will be projected with a length of \c n pixels on
 screen.

 Use this method to scale objects so that they have a constant pixel size on
 screen. The following code will draw a 20 pixel line, starting at sceneCenter()
 and always directed along the screen vertical direction: \code
 glBegin(GL_LINES);
 glVertex3fv(sceneCenter());
 glVertex3fv(sceneCenter() + 20 * pixelGLRatio(sceneCenter()) *
 camera()->upVector()); glEnd(); \endcode */
CGAL_INLINE_FUNCTION
qreal Camera::pixelGLRatio(const Vec &position) const {
  switch (type()) {
  case Camera::PERSPECTIVE:
    return 2.0 * fabs((frame()->coordinatesOf(position)).z) *
           tan(fieldOfView() / 2.0) / screenHeight();
  case Camera::ORTHOGRAPHIC: {
    GLdouble w, h;
    getOrthoWidthHeight(w, h);
    return 2.0 * h / screenHeight();
  }
  }
  // Bad compilers complain
  return 1.0;
}

/*! Changes the Camera fieldOfView() so that the entire scene (defined by
 CGAL::QGLViewer::sceneCenter() and CGAL::QGLViewer::sceneRadius()) is visible from the
 Camera position().

 The position() and orientation() of the Camera are not modified and you first
 have to orientate the Camera in order to actually see the scene (see lookAt(),
 showEntireScene() or fitSphere()).

 This method is especially useful for \e shadow \e maps computation. Use the
 Camera positioning tools (setPosition(), lookAt()) to position a Camera at the
 light position. Then use this method to define the fieldOfView() so that the
 shadow map resolution is optimally used: \code
 // The light camera needs size hints in order to optimize its fieldOfView
 lightCamera->setSceneRadius(sceneRadius());
 lightCamera->setSceneCenter(sceneCenter());

 // Place the light camera.
 lightCamera->setPosition(lightFrame->position());
 lightCamera->lookAt(sceneCenter());
 lightCamera->setFOVToFitScene();
 \endcode

 See the (soon available) shadowMap contribution example for a practical
 implementation.

 \attention The fieldOfView() is clamped to CGAL_PI/2.0. This happens when the
 Camera is at a distance lower than sqrt(2.0) * sceneRadius() from the
 sceneCenter(). It optimizes the shadow map resolution, although it may miss
 some parts of the scene. */
CGAL_INLINE_FUNCTION
void Camera::setFOVToFitScene() {
  if (distanceToSceneCenter() > sqrt(2.0) * sceneRadius())
    setFieldOfView(2.0 * asin(sceneRadius() / distanceToSceneCenter()));
  else
    setFieldOfView(CGAL_PI / 2.0);
}

/*! Makes the Camera smoothly zoom on the pointUnderPixel() \p pixel.

 Nothing happens if no pointUnderPixel() is found. Otherwise a
 KeyFrameInterpolator is created that animates the Camera on a one second path
 that brings the Camera closer to the point under \p pixel.

 See also interpolateToFitScene(). */
CGAL_INLINE_FUNCTION
void Camera::interpolateToZoomOnPixel(const QPoint &pixel) {
  const qreal coef = 0.1;

  bool found;
  Vec target = pointUnderPixel(pixel, found);

  if (!found)
    return;

  if (interpolationKfi_->interpolationIsStarted())
    interpolationKfi_->stopInterpolation();

  interpolationKfi_->deletePath();
  interpolationKfi_->addKeyFrame(*(frame()));

  interpolationKfi_->addKeyFrame(
      Frame(0.3 * frame()->position() + 0.7 * target, frame()->orientation()),
      0.4);

  // Small hack: attach a temporary frame to take advantage of lookAt without
  // modifying frame
  static ManipulatedCameraFrame *tempFrame = new ManipulatedCameraFrame();
  ManipulatedCameraFrame *const originalFrame = frame();
  tempFrame->setPosition(coef * frame()->position() + (1.0 - coef) * target);
  tempFrame->setOrientation(frame()->orientation());
  setFrame(tempFrame);
  lookAt(target);
  setFrame(originalFrame);

  interpolationKfi_->addKeyFrame(*(tempFrame), 1.0);

  interpolationKfi_->startInterpolation();
}

/*! Interpolates the Camera on a one second KeyFrameInterpolator path so that
 the entire scene fits the screen at the end.

 The scene is defined by its sceneCenter() and its sceneRadius(). See
 showEntireScene().

 The orientation() of the Camera is not modified. See also
 interpolateToZoomOnPixel(). */
CGAL_INLINE_FUNCTION
void Camera::interpolateToFitScene() {
  if (interpolationKfi_->interpolationIsStarted())
    interpolationKfi_->stopInterpolation();

  interpolationKfi_->deletePath();
  interpolationKfi_->addKeyFrame(*(frame()));

  // Small hack:  attach a temporary frame to take advantage of lookAt without
  // modifying frame
  static ManipulatedCameraFrame *tempFrame = new ManipulatedCameraFrame();
  ManipulatedCameraFrame *const originalFrame = frame();
  tempFrame->setPosition(frame()->position());
  tempFrame->setOrientation(frame()->orientation());
  setFrame(tempFrame);
  showEntireScene();
  setFrame(originalFrame);

  interpolationKfi_->addKeyFrame(*(tempFrame));

  interpolationKfi_->startInterpolation();
}

/*! Smoothly interpolates the Camera on a KeyFrameInterpolator path so that it
  goes to \p fr.

  \p fr is expressed in world coordinates. \p duration tunes the interpolation
  speed (default is 1 second).

  See also interpolateToFitScene() and interpolateToZoomOnPixel(). */
CGAL_INLINE_FUNCTION
void Camera::interpolateTo(const Frame &fr, qreal duration) {
  if (interpolationKfi_->interpolationIsStarted())
    interpolationKfi_->stopInterpolation();

  interpolationKfi_->deletePath();
  interpolationKfi_->addKeyFrame(*(frame()));
  interpolationKfi_->addKeyFrame(fr, duration);

  interpolationKfi_->startInterpolation();
}

/*! Returns the coordinates of the 3D point located at pixel (x,y) on screen.

 Calls a \c glReadPixel to get the pixel depth and applies an
 unprojectedCoordinatesOf() to the result. \p found indicates whether a point
 was found or not (i.e. background pixel, result's depth is zFar() in that
 case).

 \p x and \p y are expressed in pixel units with an origin in the upper left
 corner. Use screenHeight() - y to convert to OpenGL standard.

 \attention This method assumes that a GL context is available, and that its
 content was drawn using the Camera (i.e. using its projection and modelview
 matrices). This method hence cannot be used for offscreen Camera computations.
 Use cameraCoordinatesOf() and worldCoordinatesOf() to perform similar
 operations in that case.

 \note The precision of the z-Buffer highly depends on how the zNear() and
 zFar() values are fitted to your scene. Loose boundaries will result in
 imprecision along the viewing direction. */
CGAL_INLINE_FUNCTION
Vec Camera::pointUnderPixel(const QPoint &pixel, bool &found) const {
  float depth = 2.0;
  // Qt uses upper corner for its origin while GL uses the lower corner.
  if(auto p = dynamic_cast<QOpenGLFunctions*>(parent()))
  {
    p->glReadPixels(pixel.x(), screenHeight() - 1 - pixel.y(), 1, 1,
                    GL_DEPTH_COMPONENT, GL_FLOAT, &depth);
  }
  found = depth < 1.0;
  Vec point(pixel.x(), pixel.y(), depth);
  point = unprojectedCoordinatesOf(point);
  return point;
}

/*! Moves the Camera so that the entire scene is visible.

 Calls fitSphere() on a sphere defined by sceneCenter() and
 sceneRadius(), and resets the default FOV.

 You will typically use this method in CGAL::QGLViewer::init() after you defined a new
 sceneRadius(). */
CGAL_INLINE_FUNCTION
void Camera::showEntireScene()
{
  setFieldOfView(CGAL_PI/4.0);
  fitSphere(sceneCenter(), sceneRadius());
}

/*! Moves the Camera so that its sceneCenter() is projected on the center of the
 window. The orientation() and fieldOfView() are unchanged.

 Simply projects the current position on a line passing through sceneCenter().
 See also showEntireScene().*/
CGAL_INLINE_FUNCTION
void Camera::centerScene() {
  frame()->projectOnLine(sceneCenter(), viewDirection());
}

/*! Sets the Camera orientation(), so that it looks at point \p target (defined
 in the world coordinate system).

 The Camera position() is not modified. Simply setViewDirection().

 See also setUpVector(), setOrientation(), showEntireScene(), fitSphere() and
 fitBoundingBox(). */
CGAL_INLINE_FUNCTION
void Camera::lookAt(const Vec &target) {
  setViewDirection(target - position());
}

/*! Moves the Camera so that the sphere defined by (\p center, \p radius) is
 visible and fits in the frustum.

 The Camera is simply translated to center the sphere in the screen and make it
 fit the frustum. Its orientation() and its fieldOfView() are unchanged.

 You should therefore orientate the Camera before you call this method. See
 lookAt(), setOrientation() and setUpVector(). */
CGAL_INLINE_FUNCTION
void Camera::fitSphere(const Vec &center, qreal radius) {
  qreal distance = 0.0;
  switch (type()) {
  case Camera::PERSPECTIVE: {
    const qreal yview = radius / sin(fieldOfView() / 2.0);
    const qreal xview = radius / sin(horizontalFieldOfView() / 2.0);
    distance = qMax(xview, yview);
    break;
  }
  case Camera::ORTHOGRAPHIC: {
    distance =
        ((center - pivotPoint()) * viewDirection()) + (radius / orthoCoef_);
    break;
  }
  }
  Vec newPos(center - distance * viewDirection());
  frame()->setPositionWithConstraint(newPos);
}

/*! Moves the Camera so that the (world axis aligned) bounding box (\p min, \p
  max) is entirely visible, using fitSphere(). */
CGAL_INLINE_FUNCTION
void Camera::fitBoundingBox(const Vec &min, const Vec &max) {
  qreal diameter = qMax(fabs(max[1] - min[1]), fabs(max[0] - min[0]));
  diameter = qMax(fabs(max[2] - min[2]), diameter);
  fitSphere(0.5 * (min + max), 0.5 * diameter);
}

/*! Moves the Camera so that the rectangular screen region defined by \p
  rectangle (pixel units, with origin in the upper left corner) fits the screen.

  The Camera is translated (its orientation() is unchanged) so that \p rectangle
  is entirely visible. Since the pixel coordinates only define a \e frustum in
  3D, it's the intersection of this frustum with a plane (orthogonal to the
  viewDirection() and passing through the sceneCenter()) that is used to define
  the 3D rectangle that is eventually fitted. */
CGAL_INLINE_FUNCTION
void Camera::fitScreenRegion(const QRect &rectangle) {
  const Vec vd = viewDirection();
  const qreal distToPlane = distanceToSceneCenter();
  const QPoint center = rectangle.center();

  Vec orig, dir;
  convertClickToLine(center, orig, dir);
  Vec newCenter = orig + distToPlane / (dir * vd) * dir;

  convertClickToLine(QPoint(rectangle.x(), center.y()), orig, dir);
  const Vec pointX = orig + distToPlane / (dir * vd) * dir;

  convertClickToLine(QPoint(center.x(), rectangle.y()), orig, dir);
  const Vec pointY = orig + distToPlane / (dir * vd) * dir;

  qreal distance = 0.0;
  switch (type()) {
  case Camera::PERSPECTIVE: {
    const qreal distX =
        (pointX - newCenter).norm() / sin(horizontalFieldOfView() / 2.0);
    const qreal distY = (pointY - newCenter).norm() / sin(fieldOfView() / 2.0);
    distance = qMax(distX, distY);
    break;
  }
  case Camera::ORTHOGRAPHIC: {
    const qreal dist = ((newCenter - pivotPoint()) * vd);
    //#CONNECTION# getOrthoWidthHeight
    const qreal distX = (pointX - newCenter).norm() / orthoCoef_ /
                        ((aspectRatio() < 1.0) ? 1.0 : aspectRatio());
    const qreal distY = (pointY - newCenter).norm() / orthoCoef_ /
                        ((aspectRatio() < 1.0) ? 1.0 / aspectRatio() : 1.0);
    distance = dist + qMax(distX, distY);
    break;
  }
  }

  Vec newPos(newCenter - distance * vd);
  frame()->setPositionWithConstraint(newPos);
}

/*! Rotates the Camera so that its upVector() becomes \p up (defined in the
 world coordinate system).

 The Camera is rotated around an axis orthogonal to \p up and to the current
 upVector() direction. Use this method in order to define the Camera horizontal
 plane.

 When \p noMove is set to \c false, the orientation modification is compensated
 by a translation, so that the pivotPoint() stays projected at the same position
 on screen. This is especially useful when the Camera is used as an observer of
 the scene (default mouse binding).

 When \p noMove is \c true (default), the Camera position() is left unchanged,
 which is an intuitive behavior when the Camera is in a walkthrough fly mode
 (see the CGAL::QGLViewer::MOVE_FORWARD and CGAL::QGLViewer::MOVE_BACKWARD
 CGAL::QGLViewer::MouseAction).

 The frame()'s ManipulatedCameraFrame::sceneUpVector() is set accordingly.

 See also setViewDirection(), lookAt() and setOrientation(). */
CGAL_INLINE_FUNCTION
void Camera::setUpVector(const Vec &up, bool noMove) {
  Quaternion q(Vec(0.0, 1.0, 0.0), frame()->transformOf(up));

  if (!noMove)
    frame()->setPosition(pivotPoint() -
                         (frame()->orientation() * q)
                             .rotate(frame()->coordinatesOf(pivotPoint())));

  frame()->rotate(q);

  // Useful in fly mode to keep the horizontal direction.
  frame()->updateSceneUpVector();
}

/*! Sets the orientation() of the Camera using polar coordinates.

 \p theta rotates the Camera around its Y axis, and \e then \p phi rotates it
 around its X axis. The polar coordinates are defined in the world coordinates
 system: \p theta = \p phi = 0 means that the Camera is directed towards the
 world Z axis. Both angles are expressed in radians.

 See also setUpVector(). The position() of the Camera is unchanged, you may want
 to call showEntireScene() after this method to move the Camera.

 This method can be useful to create Quicktime VR panoramic sequences, see the
 CGAL::QGLViewer::saveSnapshot() documentation for details. */
CGAL_INLINE_FUNCTION
void Camera::setOrientation(qreal theta, qreal phi) {
  Vec axis(0.0, 1.0, 0.0);
  const Quaternion rot1(axis, theta);
  axis = Vec(-cos(theta), 0.0, sin(theta));
  const Quaternion rot2(axis, phi);
  setOrientation(rot1 * rot2);
}

/*! Sets the Camera orientation(), defined in the world coordinate system. */
CGAL_INLINE_FUNCTION
void Camera::setOrientation(const Quaternion &q) {
  frame()->setOrientation(q);
  frame()->updateSceneUpVector();
}

/*! Rotates the Camera so that its viewDirection() is \p direction (defined in
 the world coordinate system).

 The Camera position() is not modified. The Camera is rotated so that the
 horizon (defined by its upVector()) is preserved. See also lookAt() and
 setUpVector(). */
CGAL_INLINE_FUNCTION
void Camera::setViewDirection(const Vec &direction) {
  if (direction.squaredNorm() < 1E-10)
    return;

  Vec xAxis = direction ^ upVector();
  if (xAxis.squaredNorm() < 1E-10) {
    // target is aligned with upVector, this means a rotation around X axis
    // X axis is then unchanged, let's keep it !
    xAxis = frame()->inverseTransformOf(Vec(1.0, 0.0, 0.0));
  }

  Quaternion q;
  q.setFromRotatedBasis(xAxis, xAxis ^ direction, -direction);
  frame()->setOrientationWithConstraint(q);
}

// Compute a 3 by 3 determinant.
static qreal det(qreal m00, qreal m01, qreal m02, qreal m10, qreal m11,
                 qreal m12, qreal m20, qreal m21, qreal m22) {
  return m00 * m11 * m22 + m01 * m12 * m20 + m02 * m10 * m21 - m20 * m11 * m02 -
         m10 * m01 * m22 - m00 * m21 * m12;
}

// Computes the index of element [i][j] in a \c qreal matrix[3][4].
static inline unsigned int ind(unsigned int i, unsigned int j) {
  return (i * 4 + j);
}

/*! Returns the Camera position (the eye), defined in the world coordinate
system.

Use setPosition() to set the Camera position. Other convenient methods are
showEntireScene() or fitSphere(). Actually returns \c frame()->position().

This position corresponds to the projection center of a Camera::PERSPECTIVE
Camera. It is not located in the image plane, which is at a zNear() distance
ahead. */
CGAL_INLINE_FUNCTION
Vec Camera::position() const { return frame()->position(); }

/*! Returns the normalized up vector of the Camera, defined in the world
coordinate system.

Set using setUpVector() or setOrientation(). It is orthogonal to viewDirection()
and to rightVector().

It corresponds to the Y axis of the associated frame() (actually returns
frame()->inverseTransformOf(Vec(0.0, 1.0, 0.0)) ). */
CGAL_INLINE_FUNCTION
Vec Camera::upVector() const {
  return frame()->inverseTransformOf(Vec(0.0, 1.0, 0.0));
}
/*! Returns the normalized view direction of the Camera, defined in the world
coordinate system.

Change this value using setViewDirection(), lookAt() or setOrientation(). It is
orthogonal to upVector() and to rightVector().

This corresponds to the negative Z axis of the frame() (
frame()->inverseTransformOf(Vec(0.0, 0.0, -1.0)) ). */
CGAL_INLINE_FUNCTION
Vec Camera::viewDirection() const {
  return frame()->inverseTransformOf(Vec(0.0, 0.0, -1.0));
}

/*! Returns the normalized right vector of the Camera, defined in the world
coordinate system.

This vector lies in the Camera horizontal plane, directed along the X axis
(orthogonal to upVector() and to viewDirection()). Set using setUpVector(),
lookAt() or setOrientation().

Simply returns frame()->inverseTransformOf(Vec(1.0, 0.0, 0.0)). */
CGAL_INLINE_FUNCTION
Vec Camera::rightVector() const {
  return frame()->inverseTransformOf(Vec(1.0, 0.0, 0.0));
}

/*! Returns the Camera orientation, defined in the world coordinate system.

Actually returns \c frame()->orientation(). Use setOrientation(), setUpVector()
or lookAt() to set the Camera orientation. */
CGAL_INLINE_FUNCTION
Quaternion Camera::orientation() const { return frame()->orientation(); }

/*! Sets the Camera position() (the eye), defined in the world coordinate
 * system. */
CGAL_INLINE_FUNCTION
void Camera::setPosition(const Vec &pos) { frame()->setPosition(pos); }

/*! Returns the Camera frame coordinates of a point \p src defined in world
coordinates.

worldCoordinatesOf() performs the inverse transformation.

Note that the point coordinates are simply converted in a different coordinate
system. They are not projected on screen. Use projectedCoordinatesOf() for that.
*/
CGAL_INLINE_FUNCTION
Vec Camera::cameraCoordinatesOf(const Vec &src) const {
  return frame()->coordinatesOf(src);
}

/*! Returns the world coordinates of the point whose position \p src is defined
in the Camera coordinate system.

cameraCoordinatesOf() performs the inverse transformation. */
CGAL_INLINE_FUNCTION
Vec Camera::worldCoordinatesOf(const Vec &src) const {
  return frame()->inverseCoordinatesOf(src);
}

/*! Returns the fly speed of the Camera.

Simply returns frame()->flySpeed(). See the ManipulatedCameraFrame::flySpeed()
documentation. This value is only meaningful when the MouseAction bindings is
CGAL::QGLViewer::MOVE_FORWARD or CGAL::QGLViewer::MOVE_BACKWARD.

Set to 1% of the sceneRadius() by setSceneRadius(). See also setFlySpeed(). */
CGAL_INLINE_FUNCTION
qreal Camera::flySpeed() const { return frame()->flySpeed(); }

/*! Sets the Camera flySpeed().

\attention This value is modified by setSceneRadius(). */
CGAL_INLINE_FUNCTION
void Camera::setFlySpeed(qreal speed) { frame()->setFlySpeed(speed); }

/*! The point the Camera pivots around with the CGAL::QGLViewer::ROTATE mouse binding.
Defined in world coordinate system.

Default value is the sceneCenter().

\attention setSceneCenter() changes this value. */
CGAL_INLINE_FUNCTION
Vec Camera::pivotPoint() const { return frame()->pivotPoint(); }

/*! Sets the Camera's position() and orientation() from an OpenGL ModelView
matrix.

This enables a Camera initialisation from an other OpenGL application. \p
modelView is a 16 GLdouble vector representing a valid OpenGL ModelView matrix,
such as one can get using: \code GLdouble mvm[16];
glGetDoublev(GL_MODELVIEW_MATRIX, mvm);
myCamera->setFromModelViewMatrix(mvm);
\endcode

After this method has been called, getModelViewMatrix() returns a matrix
equivalent to \p modelView.

Only the orientation() and position() of the Camera are modified.

\note If you defined your matrix as \c GLdouble \c mvm[4][4], pass \c
&(mvm[0][0]) as a parameter. */
CGAL_INLINE_FUNCTION
void Camera::setFromModelViewMatrix(const GLdouble *const modelViewMatrix) {
  // Get upper left (rotation) matrix
  qreal upperLeft[3][3];
  for (int i = 0; i < 3; ++i)
    for (int j = 0; j < 3; ++j)
      upperLeft[i][j] = modelViewMatrix[i * 4 + j];

  // Transform upperLeft into the associated Quaternion
  Quaternion q;
  q.setFromRotationMatrix(upperLeft);

  setOrientation(q);
  setPosition(-q.rotate(
      Vec(modelViewMatrix[12], modelViewMatrix[13], modelViewMatrix[14])));
}

/*! Defines the Camera position(), orientation() and fieldOfView() from a
 projection matrix.

 \p matrix has to be given in the format used by vision algorithm. It has 3
 lines and 4 columns. It transforms a point from the world homogeneous
 coordinate system (4 coordinates: \c sx, \c sy, \c sz and \c s) into a point in
 the screen homogeneous coordinate system (3 coordinates: \c sx, \c sy, and \c
 s, where \c x and \c y are the pixel coordinates on the screen).

 Its three lines correspond to the homogeneous coordinates of the normals to the
 planes x=0, y=0 and z=0, defined in the Camera coordinate system.

 The elements of the matrix are ordered in line major order: you can call \c
 setFromProjectionMatrix(&(matrix[0][0])) if you defined your matrix as a \c
 qreal \c matrix[3][4].

 \attention Passing the result of getProjectionMatrix() or getModelViewMatrix()
 to this method is not possible (purposefully incompatible matrix dimensions).
 \p matrix is more likely to be the product of these two matrices, without the
 last line.

 Use setFromModelViewMatrix() to set position() and orientation() from a \c
 GL_MODELVIEW matrix. fieldOfView() can also be retrieved from a \e perspective
 \c GL_PROJECTION matrix using 2.0 * atan(1.0/projectionMatrix[5]).

 This code was written by Sylvain Paris. */
CGAL_INLINE_FUNCTION
void Camera::setFromProjectionMatrix(const qreal matrix[12]) {
  // The 3 lines of the matrix are the normals to the planes x=0, y=0, z=0
  // in the camera CS. As we normalize them, we do not need the 4th coordinate.
  Vec line_0(matrix[ind(0, 0)], matrix[ind(0, 1)], matrix[ind(0, 2)]);
  Vec line_1(matrix[ind(1, 0)], matrix[ind(1, 1)], matrix[ind(1, 2)]);
  Vec line_2(matrix[ind(2, 0)], matrix[ind(2, 1)], matrix[ind(2, 2)]);

  line_0.normalize();
  line_1.normalize();
  line_2.normalize();

  // The camera position is at (0,0,0) in the camera CS so it is the
  // intersection of the 3 planes. It can be seen as the kernel
  // of the 3x4 projection matrix. We calculate it through 4 dimensional
  // vectorial product. We go directly into 3D that is to say we directly
  // divide the first 3 coordinates by the 4th one.

  // We derive the 4 dimensional vectorial product formula from the
  // computation of a 4x4 determinant that is developped according to
  // its 4th column. This implies some 3x3 determinants.
  const Vec cam_pos =
      Vec(det(matrix[ind(0, 1)], matrix[ind(0, 2)], matrix[ind(0, 3)],
              matrix[ind(1, 1)], matrix[ind(1, 2)], matrix[ind(1, 3)],
              matrix[ind(2, 1)], matrix[ind(2, 2)], matrix[ind(2, 3)]),

          -det(matrix[ind(0, 0)], matrix[ind(0, 2)], matrix[ind(0, 3)],
               matrix[ind(1, 0)], matrix[ind(1, 2)], matrix[ind(1, 3)],
               matrix[ind(2, 0)], matrix[ind(2, 2)], matrix[ind(2, 3)]),

          det(matrix[ind(0, 0)], matrix[ind(0, 1)], matrix[ind(0, 3)],
              matrix[ind(1, 0)], matrix[ind(1, 1)], matrix[ind(1, 3)],
              matrix[ind(2, 0)], matrix[ind(2, 1)], matrix[ind(2, 3)])) /

      (-det(matrix[ind(0, 0)], matrix[ind(0, 1)], matrix[ind(0, 2)],
            matrix[ind(1, 0)], matrix[ind(1, 1)], matrix[ind(1, 2)],
            matrix[ind(2, 0)], matrix[ind(2, 1)], matrix[ind(2, 2)]));

  // We compute the rotation matrix column by column.

  // GL Z axis is front facing.
  Vec column_2 = -line_2;

  // X-axis is almost like line_0 but should be orthogonal to the Z axis.
  Vec column_0 = ((column_2 ^ line_0) ^ column_2);
  column_0.normalize();

  // Y-axis is almost like line_1 but should be orthogonal to the Z axis.
  // Moreover line_1 is downward oriented as the screen CS.
  Vec column_1 = -((column_2 ^ line_1) ^ column_2);
  column_1.normalize();

  qreal rot[3][3];
  rot[0][0] = column_0[0];
  rot[1][0] = column_0[1];
  rot[2][0] = column_0[2];

  rot[0][1] = column_1[0];
  rot[1][1] = column_1[1];
  rot[2][1] = column_1[2];

  rot[0][2] = column_2[0];
  rot[1][2] = column_2[1];
  rot[2][2] = column_2[2];

  // We compute the field of view

  // line_1^column_0 -> vector of intersection line between
  // y_screen=0 and x_camera=0 plane.
  // column_2*(...)  -> cos of the angle between Z vector et y_screen=0 plane
  // * 2 -> field of view = 2 * half angle

  // We need some intermediate values.
  Vec dummy = line_1 ^ column_0;
  dummy.normalize();
  qreal fov = acos(column_2 * dummy) * 2.0;

  // We set the camera.
  Quaternion q;
  q.setFromRotationMatrix(rot);
  setOrientation(q);
  setPosition(cam_pos);
  setFieldOfView(fov);
}

/*
  // persp : projectionMatrix_[0]  = f/aspectRatio();
CGAL_INLINE_FUNCTION
void Camera::setFromProjectionMatrix(const GLdouble* projectionMatrix)
{
  QString message;
  if ((fabs(projectionMatrix[1]) > 1E-3) ||
    (fabs(projectionMatrix[2]) > 1E-3) ||
    (fabs(projectionMatrix[3]) > 1E-3) ||
    (fabs(projectionMatrix[4]) > 1E-3) ||
    (fabs(projectionMatrix[6]) > 1E-3) ||
    (fabs(projectionMatrix[7]) > 1E-3) ||
    (fabs(projectionMatrix[8]) > 1E-3) ||
    (fabs(projectionMatrix[9]) > 1E-3))
  message = "Non null coefficient in projection matrix - Aborting";
  else
  if ((fabs(projectionMatrix[11]+1.0) < 1E-5) && (fabs(projectionMatrix[15]) <
1E-5))
    {
  if (projectionMatrix[5] < 1E-4)
    message="Negative field of view in Camera::setFromProjectionMatrix";
  else
    setType(Camera::PERSPECTIVE);
    }
  else
    if ((fabs(projectionMatrix[11]) < 1E-5) && (fabs(projectionMatrix[15]-1.0) <
1E-5)) setType(Camera::ORTHOGRAPHIC); else message = "Unable to determine camera
type in setFromProjectionMatrix - Aborting";

  if (!message.isEmpty())
  {
    qWarning(message);
    return;
  }

  switch (type())
  {
  case Camera::PERSPECTIVE:
    {
  setFieldOfView(2.0 * atan(1.0/projectionMatrix[5]));
  const qreal far = projectionMatrix[14] / (2.0 * (1.0 + projectionMatrix[10]));
  const qreal near = (projectionMatrix[10]+1.0) / (projectionMatrix[10]-1.0) *
far; setSceneRadius((far-near)/2.0); setSceneCenter(position() + (near +
sceneRadius())*viewDirection()); break;
    }
  case Camera::ORTHOGRAPHIC:
    {
  GLdouble w, h;
  getOrthoWidthHeight(w,h);
  projectionMatrix_[0]  = 1.0/w;
  projectionMatrix_[5]  = 1.0/h;
  projectionMatrix_[10] = -2.0/(ZFar - ZNear);
  projectionMatrix_[11] = 0.0;
  projectionMatrix_[14] = -(ZFar + ZNear)/(ZFar - ZNear);
  projectionMatrix_[15] = 1.0;
  // same as glOrtho( -w, w, -h, h, zNear(), zFar() );
  break;
    }
  }
}
*/

///////////////////////// Camera to world transform ///////////////////////

/*! Same as cameraCoordinatesOf(), but with \c qreal[3] parameters (\p src and
 * \p res may be identical pointers). */
CGAL_INLINE_FUNCTION
void Camera::getCameraCoordinatesOf(const qreal src[3], qreal res[3]) const {
  Vec r = cameraCoordinatesOf(Vec(src));
  for (int i = 0; i < 3; ++i)
    res[i] = r[i];
}

/*! Same as worldCoordinatesOf(), but with \c qreal[3] parameters (\p src and \p
 * res may be identical pointers). */
CGAL_INLINE_FUNCTION
void Camera::getWorldCoordinatesOf(const qreal src[3], qreal res[3]) const {
  Vec r = worldCoordinatesOf(Vec(src));
  for (int i = 0; i < 3; ++i)
    res[i] = r[i];
}

/*! Fills \p viewport with the Camera OpenGL viewport.

This method is mainly used in conjunction with \c gluProject, which requires
such a viewport. Returned values are (0, screenHeight(), screenWidth(), -
screenHeight()), so that the origin is located in the \e upper left corner of
the window (Qt style coordinate system). */
CGAL_INLINE_FUNCTION
void Camera::getViewport(GLint viewport[4]) const {
  viewport[0] = 0;
  viewport[1] = screenHeight();
  viewport[2] = screenWidth();
  viewport[3] = -screenHeight();
}

//source code of GluProject and GluUnproject, imported here to avoid the dependency to Glu
CGAL_INLINE_FUNCTION
int project(qreal objx, qreal objy, qreal objz, GLdouble *modelview,
            GLdouble *projection, int *viewport, GLdouble*winX, GLdouble *winY,GLdouble *winZ)
  {
      //Transformation vectors
      GLdouble fTempo[8];
      //Modelview transform
      fTempo[0]=modelview[0]*objx+modelview[4]*objy+modelview[8]*objz+modelview[12];  //w is always 1
      fTempo[1]=modelview[1]*objx+modelview[5]*objy+modelview[9]*objz+modelview[13];
      fTempo[2]=modelview[2]*objx+modelview[6]*objy+modelview[10]*objz+modelview[14];
      fTempo[3]=modelview[3]*objx+modelview[7]*objy+modelview[11]*objz+modelview[15];
      fTempo[4]=projection[0]*fTempo[0]+projection[4]*fTempo[1]+projection[8]*fTempo[2]+projection[12]*fTempo[3];
      fTempo[5]=projection[1]*fTempo[0]+projection[5]*fTempo[1]+projection[9]*fTempo[2]+projection[13]*fTempo[3];
      fTempo[6]=projection[2]*fTempo[0]+projection[6]*fTempo[1]+projection[10]*fTempo[2]+projection[14]*fTempo[3];
      fTempo[7]=projection[3]*fTempo[0]+projection[7]*fTempo[1]+projection[11]*fTempo[2]+projection[15]*fTempo[3];
      //The result normalizes between -1 and 1
      if(fTempo[7]==0.0)        //The w value
         return 0;
      fTempo[7]=1.0/fTempo[7];
      //Perspective division
      fTempo[4]*=fTempo[7];
      fTempo[5]*=fTempo[7];
      fTempo[6]*=fTempo[7];
      //Window coordinates
      //Map x, y to range 0-1
      *winX=(fTempo[4]*0.5+0.5)*viewport[2]+viewport[0];
      *winY=(fTempo[5]*0.5+0.5)*viewport[3]+viewport[1];
      //This is only correct when glDepthRange(0.0, 1.0)
      *winZ=(1.0+fTempo[6])*0.5;        //Between 0 and 1
      return 1;
}

CGAL_INLINE_FUNCTION
void MultiplyMatrices4by4OpenGL_GLdouble(GLdouble *result, GLdouble *matrix1, GLdouble *matrix2)
 {
   result[0]=matrix1[0]*matrix2[0]+
     matrix1[4]*matrix2[1]+
     matrix1[8]*matrix2[2]+
     matrix1[12]*matrix2[3];
   result[4]=matrix1[0]*matrix2[4]+
     matrix1[4]*matrix2[5]+
     matrix1[8]*matrix2[6]+
     matrix1[12]*matrix2[7];
   result[8]=matrix1[0]*matrix2[8]+
     matrix1[4]*matrix2[9]+
     matrix1[8]*matrix2[10]+
     matrix1[12]*matrix2[11];
   result[12]=matrix1[0]*matrix2[12]+
     matrix1[4]*matrix2[13]+
     matrix1[8]*matrix2[14]+
     matrix1[12]*matrix2[15];
   result[1]=matrix1[1]*matrix2[0]+
     matrix1[5]*matrix2[1]+
     matrix1[9]*matrix2[2]+
     matrix1[13]*matrix2[3];
   result[5]=matrix1[1]*matrix2[4]+
     matrix1[5]*matrix2[5]+
     matrix1[9]*matrix2[6]+
     matrix1[13]*matrix2[7];
   result[9]=matrix1[1]*matrix2[8]+
     matrix1[5]*matrix2[9]+
     matrix1[9]*matrix2[10]+
     matrix1[13]*matrix2[11];
   result[13]=matrix1[1]*matrix2[12]+
     matrix1[5]*matrix2[13]+
     matrix1[9]*matrix2[14]+
     matrix1[13]*matrix2[15];
   result[2]=matrix1[2]*matrix2[0]+
     matrix1[6]*matrix2[1]+
     matrix1[10]*matrix2[2]+
     matrix1[14]*matrix2[3];
   result[6]=matrix1[2]*matrix2[4]+
     matrix1[6]*matrix2[5]+
     matrix1[10]*matrix2[6]+
     matrix1[14]*matrix2[7];
   result[10]=matrix1[2]*matrix2[8]+
     matrix1[6]*matrix2[9]+
     matrix1[10]*matrix2[10]+
     matrix1[14]*matrix2[11];
   result[14]=matrix1[2]*matrix2[12]+
     matrix1[6]*matrix2[13]+
     matrix1[10]*matrix2[14]+
     matrix1[14]*matrix2[15];
   result[3]=matrix1[3]*matrix2[0]+
     matrix1[7]*matrix2[1]+
     matrix1[11]*matrix2[2]+
     matrix1[15]*matrix2[3];
   result[7]=matrix1[3]*matrix2[4]+
     matrix1[7]*matrix2[5]+
     matrix1[11]*matrix2[6]+
     matrix1[15]*matrix2[7];
   result[11]=matrix1[3]*matrix2[8]+
     matrix1[7]*matrix2[9]+
     matrix1[11]*matrix2[10]+
     matrix1[15]*matrix2[11];
   result[15]=matrix1[3]*matrix2[12]+
     matrix1[7]*matrix2[13]+
     matrix1[11]*matrix2[14]+
     matrix1[15]*matrix2[15];
 }

CGAL_INLINE_FUNCTION
 void MultiplyMatrixByVector4by4OpenGL_GLdouble(GLdouble *resultvector, const GLdouble *matrix, const GLdouble *pvector)
 {
   resultvector[0]=matrix[0]*pvector[0]+matrix[4]*pvector[1]+matrix[8]*pvector[2]+matrix[12]*pvector[3];
   resultvector[1]=matrix[1]*pvector[0]+matrix[5]*pvector[1]+matrix[9]*pvector[2]+matrix[13]*pvector[3];
   resultvector[2]=matrix[2]*pvector[0]+matrix[6]*pvector[1]+matrix[10]*pvector[2]+matrix[14]*pvector[3];
   resultvector[3]=matrix[3]*pvector[0]+matrix[7]*pvector[1]+matrix[11]*pvector[2]+matrix[15]*pvector[3];
 }

   #define SWAP_ROWS_DOUBLE(a, b) { double *_tmp = a; (a)=(b); (b)=_tmp; }
   #define SWAP_ROWS_GLdouble(a, b) { GLdouble *_tmp = a; (a)=(b); (b)=_tmp; }
   #define MAT(m,r,c) (m)[(c)*4+(r)]
   //This code comes directly from GLU except that it is for GLdouble
 CGAL_INLINE_FUNCTION
 int glhInvertMatrixf2(GLdouble *m, GLdouble *out)
  {
   GLdouble wtmp[4][8];
   GLdouble m0, m1, m2, m3, s;
   GLdouble *r0, *r1, *r2, *r3;
   r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
   r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1),
      r0[2] = MAT(m, 0, 2), r0[3] = MAT(m, 0, 3),
      r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
      r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1),
      r1[2] = MAT(m, 1, 2), r1[3] = MAT(m, 1, 3),
      r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
      r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1),
      r2[2] = MAT(m, 2, 2), r2[3] = MAT(m, 2, 3),
      r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
      r3[0] = MAT(m, 3, 0), r3[1] = MAT(m, 3, 1),
      r3[2] = MAT(m, 3, 2), r3[3] = MAT(m, 3, 3),
      r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
   /* choose pivot - or die */
   if (fabs(r3[0]) > fabs(r2[0]))
      SWAP_ROWS_GLdouble(r3, r2);
   if (fabs(r2[0]) > fabs(r1[0]))
      SWAP_ROWS_GLdouble(r2, r1);
   if (fabs(r1[0]) > fabs(r0[0]))
      SWAP_ROWS_GLdouble(r1, r0);
   if (0.0 == r0[0])
      return 0;
   /* eliminate first variable     */
   m1 = r1[0] / r0[0];
   m2 = r2[0] / r0[0];
   m3 = r3[0] / r0[0];
   s = r0[1];
   r1[1] -= m1 * s;
   r2[1] -= m2 * s;
   r3[1] -= m3 * s;
   s = r0[2];
   r1[2] -= m1 * s;
   r2[2] -= m2 * s;
   r3[2] -= m3 * s;
   s = r0[3];
   r1[3] -= m1 * s;
   r2[3] -= m2 * s;
   r3[3] -= m3 * s;
   s = r0[4];
   if (s != 0.0) {
      r1[4] -= m1 * s;
      r2[4] -= m2 * s;
      r3[4] -= m3 * s;
   }
   s = r0[5];
   if (s != 0.0) {
      r1[5] -= m1 * s;
      r2[5] -= m2 * s;
      r3[5] -= m3 * s;
   }
   s = r0[6];
   if (s != 0.0) {
      r1[6] -= m1 * s;
      r2[6] -= m2 * s;
      r3[6] -= m3 * s;
   }
   s = r0[7];
   if (s != 0.0) {
      r1[7] -= m1 * s;
      r2[7] -= m2 * s;
      r3[7] -= m3 * s;
   }
   /* choose pivot - or die */
   if (fabs(r3[1]) > fabs(r2[1]))
      SWAP_ROWS_GLdouble(r3, r2);
   if (fabs(r2[1]) > fabs(r1[1]))
      SWAP_ROWS_GLdouble(r2, r1);
   if (0.0 == r1[1])
      return 0;
   /* eliminate second variable */
   m2 = r2[1] / r1[1];
   m3 = r3[1] / r1[1];
   r2[2] -= m2 * r1[2];
   r3[2] -= m3 * r1[2];
   r2[3] -= m2 * r1[3];
   r3[3] -= m3 * r1[3];
   s = r1[4];
   if (0.0 != s) {
      r2[4] -= m2 * s;
      r3[4] -= m3 * s;
   }
   s = r1[5];
   if (0.0 != s) {
      r2[5] -= m2 * s;
      r3[5] -= m3 * s;
   }
   s = r1[6];
   if (0.0 != s) {
      r2[6] -= m2 * s;
      r3[6] -= m3 * s;
   }
   s = r1[7];
   if (0.0 != s) {
      r2[7] -= m2 * s;
      r3[7] -= m3 * s;
   }
   /* choose pivot - or die */
   if (fabs(r3[2]) > fabs(r2[2]))
      SWAP_ROWS_GLdouble(r3, r2);
   if (0.0 == r2[2])
      return 0;
   /* eliminate third variable */
   m3 = r3[2] / r2[2];
   r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
      r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7];
   /* last check */
   if (0.0 == r3[3])
      return 0;
   s = 1.0 / r3[3];                /* now back substitute row 3 */
   r3[4] *= s;
   r3[5] *= s;
   r3[6] *= s;
   r3[7] *= s;
   m2 = r2[3];                        /* now back substitute row 2 */
   s = 1.0 / r2[2];
   r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
      r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
   m1 = r1[3];
   r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
      r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
   m0 = r0[3];
   r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
      r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
   m1 = r1[2];                        /* now back substitute row 1 */
   s = 1.0 / r1[1];
   r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
      r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
   m0 = r0[2];
   r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
      r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
   m0 = r0[1];                        /* now back substitute row 0 */
   s = 1.0 / r0[0];
   r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
      r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
   MAT(out, 0, 0) = r0[4];
   MAT(out, 0, 1) = r0[5], MAT(out, 0, 2) = r0[6];
   MAT(out, 0, 3) = r0[7], MAT(out, 1, 0) = r1[4];
   MAT(out, 1, 1) = r1[5], MAT(out, 1, 2) = r1[6];
   MAT(out, 1, 3) = r1[7], MAT(out, 2, 0) = r2[4];
   MAT(out, 2, 1) = r2[5], MAT(out, 2, 2) = r2[6];
   MAT(out, 2, 3) = r2[7], MAT(out, 3, 0) = r3[4];
   MAT(out, 3, 1) = r3[5], MAT(out, 3, 2) = r3[6];
   MAT(out, 3, 3) = r3[7];
   return 1;
  }

#undef MAT
#undef SWAP_ROWS_GLdouble
#undef SWAP_ROWS_DOUBLE

CGAL_INLINE_FUNCTION
int unProject(GLdouble winx, GLdouble winy, GLdouble winz, GLdouble *modelview, GLdouble *projection, int *viewport,
              GLdouble *objX,GLdouble *objY,GLdouble *objZ)
 {
     //Transformation matrices
     GLdouble m[16], A[16];
     GLdouble in[4], out[4];
     //Calculation for inverting a matrix, compute projection x modelview
     //and store in A[16]
     MultiplyMatrices4by4OpenGL_GLdouble(A, projection, modelview);
     //Now compute the inverse of matrix A
     if(glhInvertMatrixf2(A, m)==0)
        return 0;
     //Transformation of normalized coordinates between -1 and 1
     in[0]=(winx-(GLdouble)viewport[0])/(GLdouble)viewport[2]*2.0-1.0;
     in[1]=(winy-(GLdouble)viewport[1])/(GLdouble)viewport[3]*2.0-1.0;
     in[2]=2.0*winz-1.0;
     in[3]=1.0;
     //Objects coordinates
     MultiplyMatrixByVector4by4OpenGL_GLdouble(out, m, in);
     if(out[3]==0.0)
        return 0;
     out[3]=1.0/out[3];
     *objX=out[0]*out[3];
     *objY=out[1]*out[3];
     *objZ=out[2]*out[3];
     return 1;
 }

/*! Returns the screen projected coordinates of a point \p src defined in the \p frame coordinate
 system.
 When \p frame in \c nullptr (default), \p src is expressed in the world coordinate system.
 The x and y coordinates of the returned Vec are expressed in pixel, (0,0) being the \e upper left
 corner of the window. The z coordinate ranges between 0.0 (near plane) and 1.0 (excluded, far
 plane). See the \c gluProject man page for details.
 unprojectedCoordinatesOf() performs the inverse transformation.
 See the <a href="../examples/screenCoordSystem.html">screenCoordSystem example</a>.
 This method only uses the intrinsic Camera parameters (see getModelViewMatrix(),
 getProjectionMatrix() and getViewport()) and is completely independent of the OpenGL \c
 GL_MODELVIEW, \c GL_PROJECTION and viewport matrices. You can hence define a virtual Camera and use
 this method to compute projections out of a classical rendering context.
 \attention However, if your Camera is not attached to a CGAL::QGLViewer (used for offscreen computations
 for instance), make sure the Camera matrices are updated before calling this method. Call
 computeModelViewMatrix() and computeProjectionMatrix() to do so.
 If you call this method several times with no change in the matrices, consider precomputing the
 projection times modelview matrix to save computation time if required (\c P x \c M in the \c
 gluProject man page).
 Here is the code corresponding to what this method does (kindly submitted by Robert W. Kuhn) :
 \code
 Vec project(Vec point)
 {
    GLint    Viewport[4];
    GLdouble Projection[16], Modelview[16];
    GLdouble matrix[16];
    // Precomputation begin
    glGetIntegerv(GL_VIEWPORT         , Viewport);
    glGetDoublev (GL_MODELVIEW_MATRIX , Modelview);
    glGetDoublev (GL_PROJECTION_MATRIX, Projection);
    for (unsigned short m=0; m<4; ++m)
    {
        for (unsigned short l=0; l<4; ++l)
        {
            qreal sum = 0.0;
            for (unsigned short k=0; k<4; ++k)
                sum += Projection[l+4*k]*Modelview[k+4*m];
            matrix[l+4*m] = sum;
        }
    }
    // Precomputation end
    GLdouble v[4], vs[4];
    v[0]=point[0]; v[1]=point[1]; v[2]=point[2]; v[3]=1.0;
    vs[0]=matrix[0 ]*v[0] + matrix[4 ]*v[1] + matrix[8 ]*v[2] + matrix[12 ]*v[3];
    vs[1]=matrix[1 ]*v[0] + matrix[5 ]*v[1] + matrix[9 ]*v[2] + matrix[13 ]*v[3];
    vs[2]=matrix[2 ]*v[0] + matrix[6 ]*v[1] + matrix[10]*v[2] + matrix[14 ]*v[3];
    vs[3]=matrix[3 ]*v[0] + matrix[7 ]*v[1] + matrix[11]*v[2] + matrix[15 ]*v[3];
    vs[0] /= vs[3];
    vs[1] /= vs[3];
    vs[2] /= vs[3];
    vs[0] = vs[0] * 0.5 + 0.5;
    vs[1] = vs[1] * 0.5 + 0.5;
    vs[2] = vs[2] * 0.5 + 0.5;
    vs[0] = vs[0] * Viewport[2] + Viewport[0];
    vs[1] = vs[1] * Viewport[3] + Viewport[1];
    return Vec(vs[0], Viewport[3]-vs[1], vs[2]);
  }
 \endcode
 */
CGAL_INLINE_FUNCTION
Vec Camera::projectedCoordinatesOf(const Vec& src, const Frame* frame) const
{
    GLdouble x = 0.f, y = 0.f, z = 0.f;
    static GLint viewport[4];
    getViewport(viewport);

    if (frame)
    {
        const Vec tmp = frame->inverseCoordinatesOf(src);
        project(tmp.x,tmp.y,tmp.z, modelViewMatrix_, projectionMatrix_, viewport,  &x,&y,&z);
    }
    else
        project(src.x,src.y,src.z, modelViewMatrix_, projectionMatrix_, viewport,  &x,&y,&z);

    return Vec(x,y,z);
}

/*! Returns the world unprojected coordinates of a point \p src defined in the screen coordinate
 system.
 The \p src.x and \p src.y input values are expressed in pixels, (0,0) being the \e upper left corner
 of the window. \p src.z is a depth value ranging in [0..1[ (respectively corresponding to the near
 and far planes). Note that src.z is \e not a linear interpolation between zNear and zFar.
 /code
 src.z = zFar() / (zFar() - zNear()) * (1.0 - zNear() / z);
 /endcode
 Where z is the distance from the point you project to the camera, along the viewDirection().
 See the \c gluUnProject man page for details.
 The result is expressed in the \p frame coordinate system. When \p frame is \c nullptr (default), the
 result is expressed in the world coordinates system. The possible \p frame Frame::referenceFrame()
 are taken into account.
 projectedCoordinatesOf() performs the inverse transformation.
 This method only uses the intrinsic Camera parameters (see getModelViewMatrix(),
 getProjectionMatrix() and getViewport()) and is completely independent of the OpenGL \c
 GL_MODELVIEW, \c GL_PROJECTION and viewport matrices. You can hence define a virtual Camera and use
 this method to compute un-projections out of a classical rendering context.
 \attention However, if your Camera is not attached to a CGAL::QGLViewer (used for offscreen computations
 for instance), make sure the Camera matrices are updated before calling this method (use
 computeModelViewMatrix(), computeProjectionMatrix()). See also setScreenWidthAndHeight().
 This method is not computationally optimized. If you call it several times with no change in the
 matrices, you should buffer the entire inverse projection matrix (modelview, projection and then
 viewport) to speed-up the queries. See the \c gluUnProject man page for details. */
CGAL_INLINE_FUNCTION
Vec Camera::unprojectedCoordinatesOf(const Vec& src, const Frame* frame) const
{
    GLdouble x = 0.f, y = 0.f, z = 0.f;
    static GLint viewport[4];
    getViewport(viewport);
    unProject(src.x,src.y,src.z, modelViewMatrix_,  projectionMatrix_,  viewport,  &x,&y,&z);
    if (frame)
        return frame->coordinatesOf(Vec(x,y,z));
    else
        return Vec(x,y,z);
}

/*! Same as projectedCoordinatesOf(), but with \c qreal parameters (\p src and
 * \p res can be identical pointers). */
CGAL_INLINE_FUNCTION
void Camera::getProjectedCoordinatesOf(const qreal src[3], qreal res[3],
                                       const Frame *frame) const {
  Vec r = projectedCoordinatesOf(Vec(src), frame);
  for (int i = 0; i < 3; ++i)
    res[i] = r[i];
}

/*! Same as unprojectedCoordinatesOf(), but with \c qreal parameters (\p src and
 * \p res can be identical pointers). */
CGAL_INLINE_FUNCTION
void Camera::getUnprojectedCoordinatesOf(const qreal src[3], qreal res[3],
                                         const Frame *frame) const {
  Vec r = unprojectedCoordinatesOf(Vec(src), frame);
  for (int i = 0; i < 3; ++i)
    res[i] = r[i];
}

/////////////////////////////////////  KFI
////////////////////////////////////////////

/*! Returns the KeyFrameInterpolator that defines the Camera path number \p i.

If path \p i is not defined for this index, the method returns a \c nullptr
pointer. */
CGAL_INLINE_FUNCTION
KeyFrameInterpolator *Camera::keyFrameInterpolator(unsigned int i) const {
  if (kfi_.contains(i))
    return kfi_[i];
  else
    return nullptr;
}

/*! Sets the KeyFrameInterpolator that defines the Camera path of index \p i.

 The previous keyFrameInterpolator() is lost and should be deleted by the
 calling method if needed.

 The KeyFrameInterpolator::interpolated() signal of \p kfi probably needs to be
 connected to the Camera's associated CGAL::QGLViewer::update() slot, so that when the
 Camera position is interpolated using \p kfi, every interpolation step updates
 the display: \code myViewer.camera()->deletePath(3);
 myViewer.camera()->setKeyFrameInterpolator(3, myKeyFrameInterpolator);
 connect(myKeyFrameInterpolator, SIGNAL(interpolated()), myViewer,
 SLOT(update()); \endcode

 \note These connections are done automatically when a Camera is attached to a
 CGAL::QGLViewer, or when a new KeyFrameInterpolator is defined using the
 CGAL::QGLViewer::addKeyFrameKeyboardModifiers() and CGAL::QGLViewer::pathKey() (default is
 Alt+F[1-12]). See the <a href="../keyboard.html">keyboard page</a> for details.
 */
CGAL_INLINE_FUNCTION
void Camera::setKeyFrameInterpolator(unsigned int i,
                                     KeyFrameInterpolator *const kfi) {
  if (kfi)
    kfi_[i] = kfi;
  else
    kfi_.remove(i);
}

/*! Adds the current Camera position() and orientation() as a keyFrame to the
path number \p i.

This method can also be used if you simply want to save a Camera point of view
(a path made of a single keyFrame). Use playPath() to make the Camera play the
keyFrame path (resp. restore the point of view). Use deletePath() to clear the
path.

The default keyboard shortcut for this method is Alt+F[1-12]. Set
CGAL::QGLViewer::pathKey() and CGAL::QGLViewer::addKeyFrameKeyboardModifiers().

If you use directly this method and the keyFrameInterpolator(i) does not exist,
a new one is created. Its KeyFrameInterpolator::interpolated() signal should
then be connected to the CGAL::QGLViewer::update() slot (see
setKeyFrameInterpolator()). */
CGAL_INLINE_FUNCTION
void Camera::addKeyFrameToPath(unsigned int i) {
  if (!kfi_.contains(i))
    setKeyFrameInterpolator(i, new KeyFrameInterpolator(frame()));

  kfi_[i]->addKeyFrame(*(frame()));
}

/*! Makes the Camera follow the path of keyFrameInterpolator() number \p i.

 If the interpolation is started, it stops it instead.

 This method silently ignores undefined (empty) paths (see
 keyFrameInterpolator()).

 The default keyboard shortcut for this method is F[1-12]. Set
 CGAL::QGLViewer::pathKey() and CGAL::QGLViewer::playPathKeyboardModifiers(). */
CGAL_INLINE_FUNCTION
void Camera::playPath(unsigned int i) {
  if (kfi_.contains(i)) {
    if (kfi_[i]->interpolationIsStarted())
      kfi_[i]->stopInterpolation();
    else
      kfi_[i]->startInterpolation();
  }
}

/*! Resets the path of the keyFrameInterpolator() number \p i.

If this path is \e not being played (see playPath() and
KeyFrameInterpolator::interpolationIsStarted()), resets it to its starting
position (see KeyFrameInterpolator::resetInterpolation()). If the path is
played, simply stops interpolation. */
CGAL_INLINE_FUNCTION
void Camera::resetPath(unsigned int i) {
  if (kfi_.contains(i)) {
    if ((kfi_[i]->interpolationIsStarted()))
      kfi_[i]->stopInterpolation();
    else {
      kfi_[i]->resetInterpolation();
      kfi_[i]->interpolateAtTime(kfi_[i]->interpolationTime());
    }
  }
}

/*! Deletes the keyFrameInterpolator() of index \p i.

Disconnect the keyFrameInterpolator() KeyFrameInterpolator::interpolated()
signal before deleting the keyFrameInterpolator() if needed: \code
disconnect(camera()->keyFrameInterpolator(i), SIGNAL(interpolated()), this,
SLOT(update())); camera()->deletePath(i); \endcode */
CGAL_INLINE_FUNCTION
void Camera::deletePath(unsigned int i) {
  if (kfi_.contains(i)) {
    kfi_[i]->stopInterpolation();
    delete kfi_[i];
    kfi_.remove(i);
  }
}


////////////////////////////////////////////////////////////////////////////////

/*! Gives the coefficients of a 3D half-line passing through the Camera eye and
 pixel (x,y).

 The origin of the half line (eye position) is stored in \p orig, while \p dir
 contains the properly oriented and normalized direction of the half line.

 \p x and \p y are expressed in Qt format (origin in the upper left corner). Use
 screenHeight() - y to convert to OpenGL units.

 This method is useful for analytical intersection in a selection method.

 See the <a href="../examples/select.html">select example</a> for an
 illustration. */
CGAL_INLINE_FUNCTION
void Camera::convertClickToLine(const QPoint &pixel, Vec &orig,
                                Vec &dir) const {
  switch (type()) {
  case Camera::PERSPECTIVE:
    orig = position();
    dir = Vec(((2.0 * pixel.x() / screenWidth()) - 1.0) *
                  tan(fieldOfView() / 2.0) * aspectRatio(),
              ((2.0 * (screenHeight() - pixel.y()) / screenHeight()) - 1.0) *
                  tan(fieldOfView() / 2.0),
              -1.0);
    dir = worldCoordinatesOf(dir) - orig;
    dir.normalize();
    break;

  case Camera::ORTHOGRAPHIC: {
    GLdouble w, h;
    getOrthoWidthHeight(w, h);
    orig = Vec((2.0 * pixel.x() / screenWidth() - 1.0) * w,
               -(2.0 * pixel.y() / screenHeight() - 1.0) * h, 0.0);
    orig = worldCoordinatesOf(orig);
    dir = viewDirection();
    break;
  }
  }
}


/*! Returns the 6 plane equations of the Camera frustum.

The six 4-component vectors of \p coef respectively correspond to the left,
right, near, far, top and bottom Camera frustum planes. Each vector holds a
plane equation of the form: \code a*x + b*y + c*z + d = 0 \endcode where \c a,
\c b, \c c and \c d are the 4 components of each vector, in that order.

See the <a href="../examples/frustumCulling.html">frustumCulling example</a> for
an application.

This format is compatible with the \c glClipPlane() function. One camera frustum
plane can hence be applied in an other viewer to visualize the culling results:
\code
 // Retrieve plane equations
 GLdouble coef[6][4];
 mainViewer->camera()->getFrustumPlanesCoefficients(coef);

 // These two additional clipping planes (which must have been enabled)
 // will reproduce the mainViewer's near and far clipping.
 glClipPlane(GL_CLIP_PLANE0, coef[2]);
 glClipPlane(GL_CLIP_PLANE1, coef[3]);
\endcode */
CGAL_INLINE_FUNCTION
void Camera::getFrustumPlanesCoefficients(GLdouble coef[6][4]) const {
  // Computed once and for all
  const Vec pos = position();
  const Vec viewDir = viewDirection();
  const Vec up = upVector();
  const Vec right = rightVector();
  const qreal posViewDir = pos * viewDir;

  static Vec normal[6];
  static GLdouble dist[6];

  switch (type()) {
  case Camera::PERSPECTIVE: {
    const qreal hhfov = horizontalFieldOfView() / 2.0;
    const qreal chhfov = cos(hhfov);
    const qreal shhfov = sin(hhfov);
    normal[0] = -shhfov * viewDir;
    normal[1] = normal[0] + chhfov * right;
    normal[0] = normal[0] - chhfov * right;

    normal[2] = -viewDir;
    normal[3] = viewDir;

    const qreal hfov = fieldOfView() / 2.0;
    const qreal chfov = cos(hfov);
    const qreal shfov = sin(hfov);
    normal[4] = -shfov * viewDir;
    normal[5] = normal[4] - chfov * up;
    normal[4] = normal[4] + chfov * up;

    for (int i = 0; i < 2; ++i)
      dist[i] = pos * normal[i];
    for (int j = 4; j < 6; ++j)
      dist[j] = pos * normal[j];

    // Natural equations are:
    // dist[0,1,4,5] = pos * normal[0,1,4,5];
    // dist[2] = (pos + zNear() * viewDir) * normal[2];
    // dist[3] = (pos + zFar()  * viewDir) * normal[3];

    // 2 times less computations using expanded/merged equations. Dir vectors
    // are normalized.
    const qreal posRightCosHH = chhfov * pos * right;
    dist[0] = -shhfov * posViewDir;
    dist[1] = dist[0] + posRightCosHH;
    dist[0] = dist[0] - posRightCosHH;
    const qreal posUpCosH = chfov * pos * up;
    dist[4] = -shfov * posViewDir;
    dist[5] = dist[4] - posUpCosH;
    dist[4] = dist[4] + posUpCosH;

    break;
  }
  case Camera::ORTHOGRAPHIC:
    normal[0] = -right;
    normal[1] = right;
    normal[4] = up;
    normal[5] = -up;

    GLdouble hw, hh;
    getOrthoWidthHeight(hw, hh);
    dist[0] = (pos - hw * right) * normal[0];
    dist[1] = (pos + hw * right) * normal[1];
    dist[4] = (pos + hh * up) * normal[4];
    dist[5] = (pos - hh * up) * normal[5];
    break;
  }

  // Front and far planes are identical for both camera types.
  normal[2] = -viewDir;
  normal[3] = viewDir;
  dist[2] = -posViewDir - zNear();
  dist[3] = posViewDir + zFar();

  for (int i = 0; i < 6; ++i) {
    coef[i][0] = GLdouble(normal[i].x);
    coef[i][1] = GLdouble(normal[i].y);
    coef[i][2] = GLdouble(normal[i].z);
    coef[i][3] = dist[i];
  }
}

CGAL_INLINE_FUNCTION
void Camera::onFrameModified() {
  projectionMatrixIsUpToDate_ = false;
  modelViewMatrixIsUpToDate_ = false;
}

CGAL_INLINE_FUNCTION
void Camera::setHorizontalFieldOfView(qreal hfov) {
  setFieldOfView(2.0 * atan(tan(hfov / 2.0) / aspectRatio()));
}

CGAL_INLINE_FUNCTION
qreal Camera::horizontalFieldOfView() const {
  return 2.0 * atan(tan(fieldOfView() / 2.0) * aspectRatio());
}



CGAL_INLINE_FUNCTION
void Camera::setFrustum(double frustum[6])
{
  double l(frustum[0]),r(frustum[1]),t(frustum[2]),
      b(frustum[3]),n(frustum[4]),f(frustum[5]);
  if(type() == PERSPECTIVE)
  {
    double A = 2*n/(r-l);
    double B = (r+l)/(r-l);
    double C = 2*n/(t-b);
    double D = (t+b)/(t-b);
    double E = -(f+n)/(f-n);
    double F = -2*(f*n)/(f-n);
    projectionMatrix_[0] = A; projectionMatrix_[4] = 0; projectionMatrix_[8] = B ; projectionMatrix_[12] = 0;
    projectionMatrix_[1] = 0; projectionMatrix_[5] = C; projectionMatrix_[9] = D ; projectionMatrix_[13] = 0;
    projectionMatrix_[2] = 0; projectionMatrix_[6] = 0; projectionMatrix_[10] = E ; projectionMatrix_[14] = F;
    projectionMatrix_[3] =0; projectionMatrix_[7] =0; projectionMatrix_[11] =-1; projectionMatrix_[15] =0;
  }
  else
  {
    double A = 2/(r-l);
    double B = -(r+l)/(r-l);
    double C = 2/(t-b);
    double D = -(t+b)/(t-b);
    double E = -(f+n)/(f-n);
    double F = -2/(f-n);
    projectionMatrix_[0] = A; projectionMatrix_[1] = 0; projectionMatrix_[2] = 0 ; projectionMatrix_[3] = 0;
    projectionMatrix_[4] = 0; projectionMatrix_[5] = C; projectionMatrix_[6] = 0 ; projectionMatrix_[7] = 0;
    projectionMatrix_[8] = 0; projectionMatrix_[9] = 0; projectionMatrix_[10] = F ; projectionMatrix_[11] = 0;
    projectionMatrix_[12] = B; projectionMatrix_[13] = D; projectionMatrix_[14] = E; projectionMatrix_[15] = 1;
  }
  projectionMatrixIsUpToDate_ = true;
}

CGAL_INLINE_FUNCTION
void Camera::getFrustum(double frustum[6])
{
  double l,r,t,b,n,f;
  if(type() == PERSPECTIVE)
  {
  n = projectionMatrix_[14]/2*((projectionMatrix_[10]+1)/(projectionMatrix_[10]-1)-1);
  f = n*(projectionMatrix_[10]-1)/(projectionMatrix_[10]+1);
  l = ((2*n/projectionMatrix_[0])*(projectionMatrix_[8]-1)/(projectionMatrix_[8]+1))/(1-(projectionMatrix_[8]-1)/(projectionMatrix_[8]+1));
  r = 2*n/projectionMatrix_[0]+l;
  b=(-2*n/projectionMatrix_[5]*(1-projectionMatrix_[9])/(1+projectionMatrix_[9]))/(1+(1-projectionMatrix_[9])/(1+projectionMatrix_[9]));
  t = 2*n/projectionMatrix_[5]+b;
  }
  else
  {
    double A(projectionMatrix_[0]),B(projectionMatrix_[12]),
        C(projectionMatrix_[5]),D(projectionMatrix_[13]),
        E(projectionMatrix_[14]),F(projectionMatrix_[10]);
    double B1 = (B+1)/(1-B), D1 = (1-D)/(D+1),
        E1=(E+1)/(1-E);

    l = -2*B1/(1+B1*A);
    r = 2+A*l;
    t = 2*D1/(C*(1+D1));
    b =t -2/C;
    n = -2/(F*(1+E1));
    f=n-2/F;

  }
  frustum[0] = l;
  frustum[1] = r;
  frustum[2] = t;
  frustum[3] = b;
  frustum[4] = n;
  frustum[5] = f;
}
}}//end of namespace