System Modelling
6-DOF Visual Positioning
It is possible to position and orientate an object relative to a camera, given only three of its points (e.g. LEDs) in image-space. In fact, this is the minimal visual positioning system. It infers depth from the object’s size, rather than using a stereo camera system. It also infers the object’s 3-DOF orientation (with a [...]
6-DOF Rigid Body Dynamics
If you throw an arbitrarily-shaped rigid object into the air with some random rotational motion, the motion can proceed semi-chaotically, unless it happens to be spinning purely around one of its “principle axes”. (You could try your mobile phone, for example – give most spin around its tall axis for interesting results.) General rigid body [...]
Expressing 3-DOF Rotation
The pose of a rigid body is a 6-DOF quantity, consisting of translational position (3-DOF) and rotational position, or orientation (3-DOF). Translational position is straightforwardly expressed by a triplet (x, y, z). Rotational position, or orientation, is not so simple. Rotation Vector Rotations, like translations, can be represented by a 3D vector. The rotation vector’s [...]