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	// rotation to the point on the object underneath the mouse.  That
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	// rotation to the point on the object underneath the mouse.  That
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	// point would then track the mouse as closely as possible.  This is a
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	// point would then track the mouse as closely as possible.  This is a
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	// simple example, though, so that is left as an exercise.
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	// simple example, though, so that is left as an exercise.
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	ballsize = 2.0f;
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	ballsize = 2.0f;
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	screen_centre = Vec2i(width/2, height/2);
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	screen_centre = Vec2i(width/2, height/2);
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	qrot = Quaternion(0.0, 0.0, 0.0, 1.0);
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	qrot = Quatf(0.0, 0.0, 0.0, 1.0);
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	qinc = Quaternion(0.0, 0.0, 0.0, 1.0);
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	qinc = Quatf(0.0, 0.0, 0.0, 1.0);
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	trans = Vec2f(0.0, 0.0);
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	trans = Vec2f(0.0, 0.0);
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    }
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    }
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    void QuatTrackBall::grab_ball(TrackBallAction act, const Vec2i& v)
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    void QuatTrackBall::grab_ball(TrackBallAction act, const Vec2i& v)
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    {
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    {
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    if(v[0] < 0 || v[0] >= static_cast<int>(width)
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       || v[1] < 0 || v[1] >= static_cast<int>(height))
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      return;
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	set_position(scalePoint(v));
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	set_position(scalePoint(v));
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	current_action = act;
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	current_action = act;
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    }
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    }
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    void QuatTrackBall::roll_ball(const Vec2i& v)
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    void QuatTrackBall::roll_ball(const Vec2i& v)
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    {
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    {
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    if(v[0] < 0 || v[0] >= static_cast<int>(width)
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       || v[1] < 0 || v[1] >= static_cast<int>(height))
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      return;
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	Vec2f w = scalePoint(v);
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	Vec2f w = scalePoint(v);
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	switch (current_action)
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	switch (current_action)
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	{
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	{
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			case ROTATE_ACTION:
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			case ROTATE_ACTION:
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    void QuatTrackBall::calcRotation(const Vec2f& new_pos)
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    void QuatTrackBall::calcRotation(const Vec2f& new_pos)
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    {
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    {
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	// Check for zero rotation
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	// Check for zero rotation
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	if (new_pos == last_pos)
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	if (new_pos == last_pos)
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	    qinc = Quaternion(0.0f, 0.0f, 0.0f, 1.0f);
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	    qinc = Quatf(0.0f, 0.0f, 0.0f, 1.0f);
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	else
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	else
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	{
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	{
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		// Form two vectors based on input points, find rotation axis
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		// Form two vectors based on input points, find rotation axis
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		Vec3f p1 = Vec3f(new_pos[0], new_pos[1], projectToSphere(new_pos));
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		Vec3f p1 = Vec3f(new_pos[0], new_pos[1], projectToSphere(new_pos));
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		Vec3f p2 = Vec3f(last_pos[0], last_pos[1], projectToSphere(last_pos));
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		Vec3f p2 = Vec3f(last_pos[0], last_pos[1], projectToSphere(last_pos));
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        qinc.make_rot(normalize(p1), normalize(p2));
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/*
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		Vec3f q = cross(p1, p2);		/* axis of rotation from p1 and p2 */
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		Vec3f q = cross(p1, p2);		// axis of rotation from p1 and p2
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		float L = sqrt(1.0f-dot(q,q) / (dot(p1,p1) * dot(p2,p2)));
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		float L = sqrt(1.0f-dot(q,q) / (dot(p1,p1) * dot(p2,p2)));
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		q.normalize();				/* q' = axis of rotation */
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		q.normalize();				// q' = axis of rotation
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		q *= sqrt((1 - L)/2);	/* q' = q' * sin(phi) */
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		q *= sqrt((1 - L)/2);	// q' = q' * sin(phi)
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		qinc.set(q[0],q[1],q[2],sqrt((1 + L)/2));
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		qinc.set(q[0],q[1],q[2],sqrt((1 + L)/2));
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*/
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	    }
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	}
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    }
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    }
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    // Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
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    // Project an x,y pair onto a sphere of radius r OR a hyperbolic sheet
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    // if we are away from the center of the sphere.
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    // if we are away from the center of the sphere.
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    float QuatTrackBall::projectToSphere(const Vec2f& v)
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    float QuatTrackBall::projectToSphere(const Vec2f& v)
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    {
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    {
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	float d, t, z;
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#ifndef M_SQRT_2
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	  const double M_SQRT_2 = 0.707106781187;
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#endif
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	d = v.length();
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      float d = v.length();
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      float t = ballsize*M_SQRT_2;
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      float z;
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141
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	// Inside sphere
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      // Inside sphere
129 
	if (d < ballsize * 0.70710678118654752440) {
143 
      if(d < ballsize)
130 
	    z = sqrt(ballsize*ballsize - d*d);
 144 
        z = sqrt(ballsize*ballsize - d*d);
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 145 
      else if(d < t)
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	}
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        z = 0.0;
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	// On hyperbola
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      // On hyperbola
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	else {
148 
      else
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	    t = ballsize / 1.41421356237309504880;
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	    z = t*t / d;
 149 
        z = t*t/d;
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	}
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150 
 
138 
	return z;
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      return z;
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    }
 152 
    }
140
153
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    // Scales integer point to the range [-1, 1]
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    // Scales integer point to the range [-1, 1]
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    Vec2f QuatTrackBall::scalePoint(const Vec2i& v) const
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    Vec2f QuatTrackBall::scalePoint(const Vec2i& v) const
143 
    {
 156 
    {
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	return w;
161 
	return w;
149 
    }
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    }
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    void QuatTrackBall::get_view_param(Vec3f& eye, Vec3f& _centre, Vec3f& up) const
 164 
    void QuatTrackBall::get_view_param(Vec3f& eye, Vec3f& _centre, Vec3f& up) const
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    {
 165 
    {
153 
	up  = qrot.apply(Vec3f(0,1,0));
 166 
	up  = qrot.apply_unit(Vec3f(0,1,0));
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	Vec3f right = qrot.apply(Vec3f(1,0,0));
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	Vec3f right = qrot.apply(Vec3f(1,0,0));
155 
	_centre = centre - up * trans[1] - right * trans[0];
168 
	_centre = centre - up * trans[1] - right * trans[0];
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	eye = qrot.apply(Vec3f(0,0,1)*eye_dist) + _centre;
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	eye = qrot.apply_unit(Vec3f(0,0,1)*eye_dist) + _centre;
157 
    }
 170 
    }
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    // Modify the current gl matrix by the trackball rotation and translation.
 173 
    // Modify the current gl matrix by the trackball rotation and translation.
161 
    void QuatTrackBall::set_gl_modelview() const
 174 
    void QuatTrackBall::set_gl_modelview() const
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		  up[0],up[1],up[2]);
 184 
		  up[0],up[1],up[2]);
172 
    }
 185 
    }
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186
174 
    bool QuatTrackBall::is_spinning() const
 187 
    bool QuatTrackBall::is_spinning() const
175 
    {
 188 
    {
176 
	static const Quaternion null_quat(0,0,0,1);
 189 
	static const Quatf null_quat(0,0,0,1);
177 
	if(!(qinc == null_quat))
 190 
	if(!(qinc == null_quat))
178 
	    return true;
 191 
	    return true;
179 
	return false;
 192 
	return false;
180 
    }
 193 
    }
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}
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}