`EMPTY` rect has suboptimal values

[alice-i-cecile]

The EMPTY rect should be one in which max is set to MIN and min is set to MAX. In other words, it's a rectangle of infinite negative size.

This is a common practice in many other geometry libraries. The reasoning is simple: an empty rectangle is often used when calculating the union of a series of rectangles (that is, the outer bounds of all of them.). The union of a finite rect A with a negative infinite rect B is just A. So we can start with an empty rect and successively union with each rectangle in turn, using a classic "reduce" or "fold" method.

Note that the EMPTY rect is not the same as a zero-size rect. The rect that is the result of too much negative inflation is not the same as EMPTY because it is still centered at the point of the original rect.

Originally posted by @viridia in #13452 (comment)

[viridia]

I want to point out that in three.js the initial values are +INFINITY and -INFINITY, not FLOAT_MAX and FLOAT_MIN. For integer rects, there's no infinity, so MAX/MIN are the correct values.

This works because min(value, INFINITY) == value for all finite numbers. The converse is true for max/-INFINITY.

In practice, of course, no one is going to actually use a rectangle of either infinite or max size in rendering. The only purpose for having this is as a starting point for geometrical calculations.

Both Box2 and Box3 (the 3D version of Box) in three.js use this construction.

[viridia]

One more comment: A classic use case here is finding a bounding box of a set of points. By setting the initial rectangle to negative infinite size, we can then call union_point(pt) for each point in the set, without needing to treat the first point in the list as a special case.

[Olle-Lukowski]

I could go ahead and change this, I assume it is just updating the implementation of rect and updating docs accordingly that is needed?