Improve isless definition (#1144)

Author: juliohm

src/Meshes.jl

@@ -14,20 +14,20 @@ using Random
 
 using Bessels: gamma
 using Unitful: AbstractQuantity, numtype
-using StatsBase: AbstractWeights, Weights, quantile
+using CoordRefSystems: Basic, Geographic, Projected
 using Distances: PreMetric, Euclidean, Mahalanobis
 using Distances: Haversine, SphericalAngle
 using Distances: evaluate, result_type
 using Rotations: Rotation, QuatRotation, Angle2d
 using Rotations: rotation_between
-using TiledIteration: TileIterator
-using CoordRefSystems: Basic, Projected, Geographic
 using NearestNeighbors: KDTree, BallTree
 using NearestNeighbors: knn, inrange
 using DelaunayTriangulation: triangulate, voronoi
 using DelaunayTriangulation: each_solid_triangle
 using DelaunayTriangulation: get_polygons
 using DelaunayTriangulation: get_polygon_points
+using StatsBase: AbstractWeights, Weights, quantile
+using TiledIteration: TileIterator
 using ScopedValues: ScopedValue
 using Base.Cartesian: @nloops, @nref, @ntuple
 using Base: @propagate_inbounds
@@ -36,7 +36,6 @@ import Random
 import Base: sort
 import Base: ==, !
 import Base: +, -, *
-import Base: <, >, ≤, ≥
 import StatsBase: sample
 import Distances: evaluate
 import NearestNeighbors: MinkowskiMetric

src/geometries/primitives/point.jl

@@ -68,6 +68,11 @@ function ==(A::Point{🌐,<:LatLon}, B::Point{🌐,<:LatLon})
   lat₁ == lat₂ && lon₁ == lon₂ || (abs(lon₁) == 180u"°" && lon₁ == -lon₂)
 end
 
+function Base.isless(A::Point, B::Point)
+  A′, B′ = promote(A, B)
+  isless(to(A′), to(B′))
+end
+
 function Base.isapprox(A::Point, B::Point; atol=atol(lentype(A)), kwargs...)
   A′, B′ = promote(A, B)
   isapprox(to(A′), to(B′); atol, kwargs...)

src/predicates/ordering.jl

@@ -2,58 +2,6 @@
 # Licensed under the MIT License. See LICENSE in the project root.
 # ------------------------------------------------------------------
 
-# ----------------------
-# LEXICOGRAPHICAL ORDER
-# ----------------------
-
-"""
-    <(A::Point, B::Point)
-
-The lexicographical order of points `A` and `B` (`<`).
-
-`A < B` if the tuples of coordinates satisfy `(a₁, a₂, ...) < (b₁, b₂, ...)`.
-
-See <https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets>
-"""
-<(A::Point, B::Point) = CoordRefSystems.values(coords(A)) < CoordRefSystems.values(coords(B))
-
-"""
-    >(A::Point, B::Point)
-
-The lexicographical order of points `A` and `B` (`>`).
-
-`A > B` if the tuples of coordinates satisfy `(a₁, a₂, ...) > (b₁, b₂, ...)`.
-
-See <https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets>
-"""
->(A::Point, B::Point) = CoordRefSystems.values(coords(A)) > CoordRefSystems.values(coords(B))
-
-"""
-    ≤(A::Point, B::Point)
-
-The lexicographical order of points `A` and `B` (`\\le`).
-
-`A ≤ B` if the tuples of coordinates satisfy `(a₁, a₂, ...) ≤ (b₁, b₂, ...)`.
-
-See <https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets>
-"""
-≤(A::Point, B::Point) = CoordRefSystems.values(coords(A)) ≤ CoordRefSystems.values(coords(B))
-
-"""
-    ≥(A::Point, B::Point)
-
-The lexicographical order of points `A` and `B` (`\\ge`).
-
-`A ≥ B` if the tuples of coordinates satisfy `(a₁, a₂, ...) ≥ (b₁, b₂, ...)`.
-
-See <https://en.wikipedia.org/wiki/Partially_ordered_set#Orders_on_the_Cartesian_product_of_partially_ordered_sets>
-"""
-≥(A::Point, B::Point) = CoordRefSystems.values(coords(A)) ≥ CoordRefSystems.values(coords(B))
-
-# --------------
-# PRODUCT ORDER
-# --------------
-
 """
     ≺(A::Point, B::Point)