An 'inverted' Chebyshev distance measure, based on the *minimum* of the absolute distances across all dimensions. This is, strictly speaking, only a semi metric.

A 'next event' search when the quadtree is used to store spans (intervals). It assumes that a span or interval is represented by a point whose x coordinate corresponds to the span's start and whose y coordinate corresponds to the span's stop. Furthermore, it allows for spans to be unbounded: A span which does not have a defined start, should use quad.left as the x coordinate, and a span which does not have a defined stop, should use quad.right as the y coordinate. A span denoting the special value 'void' (no extent) can be encoded by giving it quad.right as x coordinate.

The measure searches for the next 'event' beginning from the query point which is supposed to have x == y == query-time point. It finds the closest span start _or_ span stop which is greater than or equal to the query-time point, i.e. the nearest neighbor satisfying qx >= x || qy >= y (given the special treatment of unbounded coordinates).

A 'previous event' search when the quadtree is used to store spans (intervals). It assumes that a span or interval is represented by a point whose x coordinate corresponds to the span's start and whose y coordinate corresponds to the span's stop. Furthermore, it allows for spans to be unbounded: A span which does not have a defined start, should use quad.left as the x coordinate, and a span which does not have a defined stop, should use quad.right as the y coordinate. A span denoting the special value 'void' (no extent) can be encoded by giving it quad.right as x coordinate.

The measure searches for the previous 'event' beginning from the query point which is supposed to have x == y == query-time point. It finds the closest span start _or_ span stop which is smaller than or equal to the query-time point, i.e. the nearest neighbor satisfying qx <= x || qy <= y (given the special treatment of unbounded coordinates).