feat(autoware_universe_utils): reduce dependence on Boost.Geometry

[mitukou1109]

Description

This PR adds the following functions to reduce dependence on Boost.Geometry.

Boost.Geometry (boost::geometry)	alternative (autoware::universe_utils)	supported types
area()	area()	polygon
convex_hull()	convex_hull()	point list
correct()	correct()	polygon
covered_by()	covered_by()	point & polygon
disjoint()	disjoint()	polygon & polygon
distance()	distance()	point & segment (2 edge points) / point & polygon
equals()	equals()	point & point / polygon & polygon
intersects()	intersects()	segment & segment / polygon & polygon
touches()	touches()	point & polygon
within()	within()	point & polygon / polygon & polygon

Notes:

• It is assumed that polygons are convex and do not have holes.
• Polygons do not have closing points (i.e. the last vertex in the array does not match the first, as any polygon given is considered to be closed).
• correct() sorts outer points in clockwise order with respect to the first point AND removes duplicate points.

Related links

Parent Issue:

• Reduce dependence on Boost.Geometry #8128

How was this PR tested?

colcon test --packages-select autoware_universe_utils

Benchmark result with 500 randomly generated polygons with 9 vertices:

function	Boost	self-impl.	task
area()	0.03ms	0.03ms	calculate the area of 500 polygons
convex_hull()	0.38ms	0.32ms	calculate the convex hull of vertices of 500 polygons
covered_by()	309.93ms	307.29ms	check if each vertex of 500 polygons is covered by (= inside or on border of) another 500 polygons
disjoint()	198.91ms	77.51ms	check if 500 polygons are disjoint (runs totally 250,000 times)
intersects()	199.10ms	58.56ms	check if 500 polygons intersect (runs totally 250,000 times)
touches()	296.44ms	310.73ms	check if each vertex of 500 polygons touches (= on border of) another 500 polygons
within()	1058.86ms	55.80ms	check if each of 500 polygons is within 500 polygons

Notes for reviewers

None.

Interface changes

None.

Effects on system behavior

None.

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[maxime-clem]

I did not check all the code in details yet but I think there are a few issues to fix because the PR can be merged.

• the alternative intersects only works for convex polygons (whereas the boost implementation also works for non-convex polygons).
• the random test only use convex polygons.
• GJK is already implemented so we should see which implementation to keep.

[maxime-clem]

(minor) I think the new code could be added to a separate file as the current one is becoming too big.
This can be done in a future PR.

[maxime-clem]

GJK is already implemented (https://github.com/autowarefoundation/autoware.universe/blob/main/common/autoware_universe_utils/src/geometry/gjk_2d.cpp) but it only works for convex polygon.
If your goal is to provide an alternative to the boost::geometry::intersects function, then you need to use a more general algorithm that also works for concave planners.

[mitukou1109]

I agree, but I already named the class for representing polygons ConvexPolygon2d and thus I do not expect the input to be concave (at least for now).

[maxime-clem]

This test should include non-convex polygons.

[maxime-clem]

This test (and probably the other random tests as well) should also use random non-convex polygons.
@mraditya01 is working on random polygon generation so maybe you can coordinate with him.

[maxime-clem]

From what I read (e.g., here or here), using std::numeric_limits<double>::epsilon() directly is not a good way to check for precision when comparing two numbers.
I think it would make more sense to define an epsilon based on the accuracy we want to reach (e.g., 1e-3 for mm accuracy).

[codecov]

Codecov Report

Attention: Patch coverage is 75.82846% with 124 lines in your changes missing coverage. Please review.

Project coverage is 30.50%. Comparing base (3d849e9) to head (c95aaaf).
Report is 969 commits behind head on main.

Files	Patch %	Lines
...universe_utils/test/src/geometry/test_geometry.cpp	69.73%	10 Missing and 92 partials ⚠️
.../autoware_universe_utils/src/geometry/geometry.cpp	89.93%	9 Missing and 7 partials ⚠️
...lude/autoware/universe_utils/geometry/geometry.hpp	64.70%	3 Missing and 3 partials ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main    #7778       +/-   ##
===========================================
+ Coverage   15.09%   30.50%   +15.41%     
===========================================
  Files        1967     1352      -615     
  Lines      135941   105603    -30338     
  Branches    42122    47098     +4976     
===========================================
+ Hits        20520    32217    +11697     
+ Misses      92700    64835    -27865     
+ Partials    22721     8551    -14170     

Flag	Coverage Δ
differential	30.50% <75.82%> (?)
total	?

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