Add MaxLengthDiscretization for Geometry (#1075)

* Add 'MaxLengthDiscretization' for 'Polygon'

* Use 'TriSubdivision'

* Apply suggestions

* Add tests

* Update method

* Update method

* Add more tests

* Apply suggestions

Author: eliascarv

src/discretization/maxlength.jl

@@ -27,10 +27,23 @@ end
 discretize(chain::Chain, method::MaxLengthDiscretization) =
   mapreduce(s -> discretize(s, method), merge, segments(chain))
 
+discretize(multi::Multi, method::MaxLengthDiscretization) = _iterativerefinement(multi, method)
+
+discretize(geometry::Geometry, method::MaxLengthDiscretization) = _iterativerefinement(geometry, method)
+
 # -----------------
 # HELPER FUNCTIONS
 # -----------------
 
+function _iterativerefinement(geometry, method)
+  iscoarse(e) = perimeter(e) > method.length * nvertices(e)
+  mesh = simplexify(geometry)
+  while any(iscoarse, mesh)
+    mesh = refine(mesh, TriSubdivision())
+  end
+  mesh
+end
+
 _sides(box::Box{<:𝔼}) = sides(box)
 
 function _sides(box::Box{<:🌐})

test/discretization.jl

@@ -467,6 +467,29 @@ end
   @test nelements(mesh) == 404
   @test eltype(mesh) <: Segment
   @test nvertices.(mesh) ⊆ [2]
+
+  tri = Triangle(cart(0, 0), cart(10, 0), cart(0, 10))
+  mesh = discretize(tri, MaxLengthDiscretization(T(3)))
+  @test nvertices(mesh) == 15
+  @test nelements(mesh) == 16
+  @test eltype(mesh) <: Triangle
+  @test nvertices.(mesh) ⊆ [3]
+
+  quad = Quadrangle(latlon(0, 0), latlon(0, 45), latlon(45, 45), latlon(45, 0))
+  mesh = discretize(quad, MaxLengthDiscretization(T(1e6)))
+  @test nvertices(mesh) == 81
+  @test nelements(mesh) == 128
+  @test eltype(mesh) <: Triangle
+  @test nvertices.(mesh) ⊆ [3]
+
+  quad1 = Quadrangle(latlon(0, 0), latlon(0, 45), latlon(45, 45), latlon(45, 0))
+  quad2 = Quadrangle(latlon(0, 0), latlon(-45, 0), latlon(-45, 45), latlon(0, 45))
+  multi = Multi([quad1, quad2])
+  mesh = discretize(multi, MaxLengthDiscretization(T(1e6)))
+  @test nvertices(mesh) == 162
+  @test nelements(mesh) == 256
+  @test eltype(mesh) <: Triangle
+  @test nvertices.(mesh) ⊆ [3]
 end
 
 @testitem "Discretize" setup = [Setup] begin