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TrackBall Class (with no Gimbal Lock)

August 1st, 2009 Leave a comment Go to comments

To download:

1	bzr branch http://bazaar.enseed.com/lib/Generic/ look under Geometry/TrackBall.h

A trackball is useful when you display 3D objects and want to let the user change the position of the camera around an object by click-and-dragging the mouse. A trackball simulates a 3D ball in the scene, and rotates as though the user was dragging a point on the surface of sphere.

Here is how to trackball computes the rotation:

find the line between the click point and the current point
find the position of these points on the virtual sphere
find the axis of rotation (it is perpendicular to the two points’ line)
estimate the angle of rotation based on the distance of the two points on the sphere
represend that rotation using a quaternion. This quaternion can then be used to extract a rotation matrix.

It’s quite trivial to use. Say you have a 640×480 window. You would create a TrackBall with radius 240 and a center at (320, 240):

1 2	// create the trackball TrackBall trackball(240, Point2f(320.0f, 240.0f));

When you get a “mouse down” event, you’d tell the trackball to begin tracking:

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// we had a mouse down
void MouseDown(Point2f mousePos)
{
trackball.beginTracking(mousePos);
}

Finally, when the mouse is dragged, you update the trackball and extract the rotation

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// we had a mouse drag event
void MouseDrag(Point2f mousePos)
{
Quatf q = trackball.track(mousePos);
Matrix4x4 rotMatrix;
q.to4x4Matrix(&rotMatrix);

// rotMatrix now holds a rotation matrix for our view or object
}

If you are doing OpenGL, you can use this matrix to change your view:

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glMatrixMode(GL_PROJECTION);
glLoadIdentity();
// setup your view here
// ...

// multiply with our rotation matrix. We have
// to transpose since OpenGL uses column vector matrices
// while we use row vector matrices...
glMultMatrix(rotMatrix.transposed().ptr());