Clean up Rect set operations (union, intersect, diff, overlaps)

[ffreyer]

This is something I will probably need for optimizing an SDF volume plots in Makie. Doesn't need to be merged/tagged until I get that near completion

Changes:

• added volumetric kwarg to isempty to switch between "any" and "all" widths <= 0 checks
• exclude all-empty rects from union (probably to avoid Rect() including Inf in unions)
• add bbox_diffto calculate the bounding box of the pieces left after cutting one rect out of another (without explicitly calculating the pieces)
• return empty rect in intersect if rects have no overlap (+ type promotion)
• all one rect being fully inside the other in overlaps
• move rect tests into their own file, categorize tests, add tests for
  • add tests for bbox_diff
  • add tests for isempty
  • extend tests for in (using explicit rects to go through specific situations rather than results from splt)
  • extend tests for overlaps to cover edge cases
  • add numeric tests for union (not just isa Rect)
  • add numeric tests for intersect (not just isa Rect)
  • add numeric tests for update (not just isa Rect)

TODO:

• consider removing Allen's Interval Algebra functions for general Rects, see below

[ffreyer]

https://en.wikipedia.org/wiki/Allen%27s_interval_algebra

GeometryBasics.jl/src/primitives/rectangles.jl

Lines 441 to 486 in 9918b18

	# http://en.wikipedia.org/wiki/Allen%27s_interval_algebra
	function before(b1::Rect{N}, b2::Rect{N}) where {N}
	for i in 1:N
	maximum(b1)[i] < minimum(b2)[i] || return false
	end
	return true
	end
	meets(b1::Rect{N}, b2::Rect{N}) where {N} = maximum(b1) == minimum(b2)
	function overlaps(b1::Rect{N}, b2::Rect{N}) where {N}
	for i in 1:N
	maximum(b2)[i] > maximum(b1)[i] > minimum(b2)[i] &&
	minimum(b1)[i] < minimum(b2)[i] || return false
	end
	return true
	end
	function starts(b1::Rect{N}, b2::Rect{N}) where {N}
	return if minimum(b1) == minimum(b2)
	for i in 1:N
	maximum(b1)[i] < maximum(b2)[i] || return false
	end
	return true
	else
	return false
	end
	end
	function during(b1::Rect{N}, b2::Rect{N}) where {N}
	for i in 1:N
	maximum(b1)[i] < maximum(b2)[i] && minimum(b1)[i] > minimum(b2)[i] || return false
	end
	return true
	end
	function finishes(b1::Rect{N}, b2::Rect{N}) where {N}
	return if maximum(b1) == maximum(b2)
	for i in 1:N
	minimum(b1)[i] > minimum(b2)[i] || return false
	end
	return true
	else
	return false
	end
	end

This stuff makes sense for intervals but I fail to see how this should generalize to rectangles. For examples saying one interval is before another is clear, but for 2D rects it could mean being outside towards -x, or -y or -(x, y) (current), or any of those. meets(a, b) could be:

--.--
a | b
--'--

or

| b |
|---|
| a |

or (current)

  | b
--+---
a |

or other rotations. Also, for the edge versions, do widths need to match for the dimension that doesn't meet?

This doesn't seem clear enough to have. It's been there since the dawn of GeometryTypes 11 years ago

[SimonDanisch]

since this is a base overload and not really self explanatory, i think this should be a kwarg.