How do I implement a quaternion based camera?

Question

UPDATE The error here was a pretty simple one. I have missed a radian to degrees conversion. No need to read the whole thing if you have some other problem.

I looked at several tutorials about this and when I thought I understood I tried to implement a quaternion based camera. The problem is it doesn't work correctly, after rotating for approx. 10 degrees it jumps back to -10 degrees. I have no idea what's wrong. I'm using openTK and it already has a quaternion class. I'm a noob at opengl, I'm doing this just for fun, and don't really understand quaternions, so probably I'm doing something stupid here. Here is some code: (Actually almost all the code except the methods that load and draw a vbo (it is taken from an OpenTK sample that demonstrates vbo-s))

I load a cube into a vbo and initialize the quaternion for the camera

protected override void OnLoad(EventArgs e) {
    base.OnLoad(e);

    cameraPos = new Vector3(0, 0, 7);
    cameraRot = Quaternion.FromAxisAngle(new Vector3(0,0,-1), 0);

    GL.ClearColor(System.Drawing.Color.MidnightBlue);
    GL.Enable(EnableCap.DepthTest);

    vbo = LoadVBO(CubeVertices, CubeElements);
}

I load a perspective projection here. This is loaded at the beginning and every time I resize the window.

protected override void OnResize(EventArgs e) {
    base.OnResize(e);

    GL.Viewport(0, 0, Width, Height);

    float aspect_ratio = Width / (float)Height;

    Matrix4 perpective = Matrix4.CreatePerspectiveFieldOfView(MathHelper.PiOver4, aspect_ratio, 1, 64);
    GL.MatrixMode(MatrixMode.Projection);
    GL.LoadMatrix(ref perpective);
}

Here I get the last rotation value and create a new quaternion that represents only the last rotation and multiply it with the camera quaternion. After this I transform this into axis-angle so that opengl can use it. (This is how I understood it from several online quaternion tutorials)

protected override void OnRenderFrame(FrameEventArgs e) {
    base.OnRenderFrame(e);

    GL.Clear(ClearBufferMask.ColorBufferBit | ClearBufferMask.DepthBufferBit);

    double speed = 1;
    double rx = 0, ry = 0;

    if (Keyboard[Key.A]) {
        ry = -speed * e.Time;
    }

    if (Keyboard[Key.D]) {
        ry = +speed * e.Time;
    }

    if (Keyboard[Key.W]) {
        rx = +speed * e.Time;
    }

    if (Keyboard[Key.S]) {
        rx = -speed * e.Time;
    }

    Quaternion tmpQuat = Quaternion.FromAxisAngle(new Vector3(0,1,0), (float)ry);
    cameraRot = tmpQuat * cameraRot;
    cameraRot.Normalize();

    GL.MatrixMode(MatrixMode.Modelview);
    GL.LoadIdentity();

    Vector3 axis;
    float angle;

    cameraRot.ToAxisAngle(out axis, out angle);
    //////////////////////////////////////////////////////////////////////
    // THIS IS WHAT I DID WRONG: I NEED TO CONVERT FROM RADIANS TO DEGREES
    //////////////////////////////////////////////////////////////////////
    //BEFORE
    //GL.Rotate(angle, axis);
    //AFTER
    GL.Rotate(angle * (float)180.0/(float)Math.PI, axis);
    GL.Translate(-cameraPos);

    Draw(vbo);
    SwapBuffers();
}

Here are 2 images to explain better: I rotate a while and from this:

it jumps into this

Any help is appreciated.

Update1: I add these to a streamwriter that writes into a file:

    sw.WriteLine("camerarot: X:{0} Y:{1} Z:{2} W:{3} L:{4}", cameraRot.X, cameraRot.Y, cameraRot.Z, cameraRot.W, cameraRot.Length);
    sw.WriteLine("ry: {0}", ry);

The log is available here: http://www.pasteall.org/26133/text. At line 770 the cube jumps from right to left, when camerarot.Y changes signs. I don't know if this is normal.

Update2 Here is the complete project.

Answer 1

While you haven't shown the necessary code to verify my assumption here, I can almost guarantee that your problem is actually that this line:

cameraRot.ToAxisAngle(out axis, out angle);

is returning an angle value expressed in radians, while

GL.Rotate(angle, axis);

wants angle to be provided in degrees.

To fix it, you need to convert the angle value when passing it to GL.Rotate(), like this:

GL.Rotate(angle * 180.0/3.141593, axis);

Answer 2

Don't. It may seem that it would be less work to have a camera that can be manipulated like other scene objects, but in the long run it is better to have a camera where you can define a position, eye direction and up vector. Especially when you start programming motion models it is really a pain to work with quaternions.

Answer 3

Don't know much about OpenTK internals. In my experience I did not see math library with proper implementation of quat that keeps needed precision (machine), because all of them affects e^2-e^3 errors. So the effect you see: the precision (and epsilon value) is about 10^-5, and it 'jumps' near zero. This is my guess :)