A Chebychev distance measure, based on the maximum of the absolute distances across all dimensions.
A measure that uses the euclidean squared distance which is faster than the euclidean distance as the square root does not need to be taken.
A 'next event' search when the quadtree is used to store spans (intervals).
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).
the tree's root square which is used to deduce the special values for representing unbounded spans
the measure instance
A 'previous event' search when the quadtree is used to store spans (intervals).
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).
the tree's root square which is used to deduce the special values for representing unbounded spans
the measure instance
An 'inverted' Chebychev distance measure, based on the *minimum* of the absolute distances across all dimensions.
An 'inverted' Chebychev distance measure, based on the *minimum* of the absolute distances across all dimensions. This is, strictly speaking, only a semi metric.