text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
  //
  // This Source Code Form is subject to the terms of the Mozilla
  // Public License v. 2.0. If a copy of the MPL was not distributed
  // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  
  #include <iostream>
  #include "trackball.h"
  #include "camera.h"
  
  using namespace Eigen;
  
  void Trackball::track(const Vector2i& point2D)
  {
    if (mpCamera==0)
      return;
    Vector3f newPoint3D;
    bool newPointOk = mapToSphere(point2D, newPoint3D);
  
    if (mLastPointOk && newPointOk)
    {
      Vector3f axis = mLastPoint3D.cross(newPoint3D).normalized();
      float cos_angle = mLastPoint3D.dot(newPoint3D);
      if ( std::abs(cos_angle) < 1.0 )
      {
        float angle = 2. * acos(cos_angle);
        if (mMode==Around)
          mpCamera->rotateAroundTarget(Quaternionf(AngleAxisf(angle, axis)));
        else
          mpCamera->localRotate(Quaternionf(AngleAxisf(-angle, axis)));
      }
    }
  
    mLastPoint3D = newPoint3D;
    mLastPointOk = newPointOk;
  }
  
  bool Trackball::mapToSphere(const Vector2i& p2, Vector3f& v3)
  {
    if ((p2.x() >= 0) && (p2.x() <= int(mpCamera->vpWidth())) &&
        (p2.y() >= 0) && (p2.y() <= int(mpCamera->vpHeight())) )
    {
      double x  = (double)(p2.x() - 0.5*mpCamera->vpWidth())  / (double)mpCamera->vpWidth();
      double y  = (double)(0.5*mpCamera->vpHeight() - p2.y()) / (double)mpCamera->vpHeight();
      double sinx         = sin(M_PI * x * 0.5);
      double siny         = sin(M_PI * y * 0.5);
      double sinx2siny2   = sinx * sinx + siny * siny;
  
      v3.x() = sinx;
      v3.y() = siny;
      v3.z() = sinx2siny2 < 1.0 ? sqrt(1.0 - sinx2siny2) : 0.0;
  
      return true;
    }
    else
      return false;
  }
  