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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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	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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	Vec2f w = scalePoint(v); 
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	Vec2f w = scalePoint(v); 
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	if(v[0] < 0 || v[0] >= static_cast<int>(width))
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	  w[0] = last_pos[0];
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	if(v[1] < 0 || v[1] >= static_cast<int>(height))
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	  w[1] = last_pos[1];
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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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	    rotate(w);
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	    rotate(w);
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	    break;
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	    break;
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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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		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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		q.normalize();				/* q' = axis of rotation */
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		qinc.make_rot(normalize(p1), normalize(p2));
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		q *= sqrt((1 - L)/2);	/* q' = q' * sin(phi) */
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	}
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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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    // 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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	return w; 
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	return w; 
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    }
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    }
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    void QuatTrackBall::get_view_param(Vec3f& eye, Vec3f& _centre, Vec3f& up) const
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    void QuatTrackBall::get_view_param(Vec3f& eye, Vec3f& _centre, Vec3f& up) const
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    {
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    {
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	up  = qrot.apply(Vec3f(0,1,0));
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	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));
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	_centre = centre - up * trans[1] - right * trans[0]; 
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	_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;
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    }
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    }
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    // Modify the current gl matrix by the trackball rotation and translation.
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    // Modify the current gl matrix by the trackball rotation and translation.
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    void QuatTrackBall::set_gl_modelview() const
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    void QuatTrackBall::set_gl_modelview() const
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		  up[0],up[1],up[2]);
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		  up[0],up[1],up[2]);
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    }
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    }
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    bool QuatTrackBall::is_spinning() const
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    bool QuatTrackBall::is_spinning() const
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    {
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    {
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	static const Quaternion null_quat(0,0,0,1);
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	static const Quatf null_quat(0,0,0,1);
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	if(!(qinc == null_quat))
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	if(qinc != null_quat)
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	    return true;
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	    return true;
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	return false;
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	return false;
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    }
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    }
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}
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}