Add parametric function for Chain

src/geometries/polytopes.jl

@@ -8,7 +8,7 @@
 We say that a geometry is a K-polytope when it is a collection of "flat" sides
 that constitute a `K`-dimensional subspace. They are called chain, polygon and
 polyhedron respectively for 1D (`K=1`), 2D (`K=2`) and 3D (`K=3`) subspaces.
-The parameter `K` is also known as the rank or parametric dimension 
+The parameter `K` is also known as the rank or parametric dimension
 of the polytope (<https://en.wikipedia.org/wiki/Abstract_polytope>).
 
 The term polytope expresses a particular combinatorial structure. A polyhedron,
@@ -156,6 +156,16 @@ function angles(c::Chain)
   map(i -> ∠(vs[i - 1], vs[i], vs[i + 1]), i1:i2)
 end
 
+function (c::Chain)(t)
+  if t < 0 || t > 1
+    throw(DomainError(t, "c(t) is not defined for t outside [0, 1]."))
+  end
+  n = nvertices(c) - !isclosed(c)
+  k = max(1, ceil(Int, n * t))
+  s, _ = iterate(segments(c), k)
+  s(n * t - k + 1)
+end
+
 # implementations of Chain
 include("polytopes/segment.jl")
 include("polytopes/rope.jl")

test/polytopes.jl

@@ -264,6 +264,21 @@ end
   r = Ring(merc.([(0, 0), (1, 0), (1, 1), (0, 1)]))
   @test crs(centroid(r)) === crs(r)
 
+  # parameterization
+  ri = Ring(latlon(45, 0), latlon(45, 90), latlon(90, 90))
+  @test ri(T(0)) == latlon(45, 0)
+  @test ri(T(0.25)) == latlon(45, 67.5)
+  @test ri(T(0.5)) == latlon(67.5, 90)
+  @test ri(T(0.75)) == latlon(78.75, 67.5)
+  @test ri(T(1)) == latlon(45, 0)
+
+  ro = Rope(latlon(45, 0), latlon(45, 90), latlon(90, 90))
+  @test ro(T(0)) == latlon(45, 0)
+  @test ro(T(0.25)) == latlon(45, 45)
+  @test ro(T(0.5)) == latlon(45, 90)
+  @test ro(T(0.75)) == latlon(67.5, 90)
+  @test ro(T(1)) == latlon(90, 90)
+
   ri = Ring(cart.([(1, 1), (2, 2), (3, 3)]))
   ro = Rope(cart.([(1, 1), (2, 2), (3, 3)]))
   @test sprint(show, ri) == "Ring((x: 1.0 m, y: 1.0 m), (x: 2.0 m, y: 2.0 m), (x: 3.0 m, y: 3.0 m))"