Interacting with camera - ArcBall/Trackball metaphore

Other approach: ArcBall/Trackball behavior
- 3 dof: left/right, top/down, but also twist

assets/trackball_arrow.png

Idea: Use the 2D cursor position as "3D point on the trackball"
- Motion between 2 cursor positions = 3D Rotation applied to the ball
- K. Shoemake. A User Interface for Specifying Three-Dimensional Orientation Using a Mouse. Graphics Interface, 1992.

assets/arcball.png

Algorithm:
- Inputs \(p_1=(p_{1x},p_{1y})\), \(p_2=(p_{2x},p_{2y})\) in screen coord.
- \(q_{1/2}\) = ArcBallProjection\((p_{1/2})\)
- \(R\)= rotation between vectors \((q_1,q_2)\)

- ArcBallProjection(p)
- \(d=\)norm(p)
- if(d<\(1/\sqrt{2}\))
- - \(q=(p,\sqrt{1-d^2})\)
- else // hyperbola
- - \(q=(p,1/(2 d))\)
- return q

Note: the hyperbola smoothly extends the sphere in the entire screen.