Implement a parametrization function for Wedge (#1162)

* Add draft parametrization function

* Improve parametrization of Wedge

* Change naming

* Fix test

* Use API instead of direct struct access

* Add a test_throws for out-of-bounds coord, add T converts

* Update error type

* Change parametrization to use Quadrangles instead of Triangles

* Simplify code

---------

Co-authored-by: Júlio Hoffimann <julio.hoffimann@gmail.com>

src/geometries/polytopes/wedge.jl

@@ -15,3 +15,14 @@ nvertices(::Type{<:Wedge}) = 6
 
 Base.isapprox(t₁::Wedge, t₂::Wedge; atol=atol(lentype(t₁)), kwargs...) =
   all(isapprox(v₁, v₂; atol, kwargs...) for (v₁, v₂) in zip(t₁.vertices, t₂.vertices))
+
+function (wedge::Wedge)(u, v, w)
+  if (u < 0 || u > 1) || (v < 0 || v > 1) || (w < 0 || w > 1)
+    throw(DomainError((u, v, w), "wedge(u, v, w) is not defined for u, v, w outside [0, 1]³."))
+  end
+  a₁, a₂, a₃, b₁, b₂, b₃ = vertices(wedge)
+  q₁ = Quadrangle(a₁, b₁, b₂, a₂)
+  q₂ = Quadrangle(a₁, b₁, b₃, a₃)
+  s = Segment(q₁(u, v), q₂(u, v))
+  s(w)
+end

test/polytopes.jl

@@ -978,6 +978,8 @@ end
   @test crs(w) <: Cartesian{NoDatum}
   @test Meshes.lentype(w) == ℳ
   @test volume(w) ≈ T(1 / 2) * u"m^3"
+  @test w(T(1), T(1), T(1)) == vertices(w)[6]
+  @test_throws DomainError w(T(0), T(0), T(1.5))
   m = boundary(w)
   @test m isa Mesh
   @test nelements(m) == 5