However, let me give an analogy. Aeroplanes live in X-dimensional phase space. Three space coordinates, three attitude coordinates (pitch/roll/yaw), three velocity coordinates (usually, but not always, aligned with the attitude) at a given time. Thus we need to deal with a map from one dimension - time - to nine dimensions. If we simplify some things, then look also at the other rates of change, we get a complex representation of non-independent variables (velocity is just rateof change of position, for example), but in the complexity of the representation, some of the behavior becomes simplified.
Now take clusters of these measurements and try to identify from among them which ones all correspond to the same object. Another analogy - not what I do - is to take lots of position measurements widely spaced in time of planes in an acrobatic airshow, and try to identify the trajectories of individual 'planes.
Now do it all in a noisy environment with instrument error, and if you've arranged it just right, finding equal sized cuts of convex or near convex bodies can correspond to separating the plots of different objects.
Actually, I can get a function that lifts, supports and separates convex bodies. I called it the "Playtex Function", but because of the work I do I couldn't publish.
All that is obscure, I know, but it gives some sense of what I do. Sorry I can't be clearer.
However, let me give an analogy. Aeroplanes live in X-dimensional phase space. Three space coordinates, three attitude coordinates (pitch/roll/yaw), three velocity coordinates (usually, but not always, aligned with the attitude) at a given time. Thus we need to deal with a map from one dimension - time - to nine dimensions. If we simplify some things, then look also at the other rates of change, we get a complex representation of non-independent variables (velocity is just rateof change of position, for example), but in the complexity of the representation, some of the behavior becomes simplified.
Now take clusters of these measurements and try to identify from among them which ones all correspond to the same object. Another analogy - not what I do - is to take lots of position measurements widely spaced in time of planes in an acrobatic airshow, and try to identify the trajectories of individual 'planes.
Now do it all in a noisy environment with instrument error, and if you've arranged it just right, finding equal sized cuts of convex or near convex bodies can correspond to separating the plots of different objects.
Actually, I can get a function that lifts, supports and separates convex bodies. I called it the "Playtex Function", but because of the work I do I couldn't publish.
All that is obscure, I know, but it gives some sense of what I do. Sorry I can't be clearer.