More general dual methods

src/main/scala/io/github/scala_tessella/tessella/Tiling.scala

@@ -206,7 +206,11 @@ class Tiling private(edges: List[Edge]) extends Graph(edges) with Ordered[Tiling
   /** Unit length of the perimeter */
   val perimeterLength: Int =
     perimeter.toRingNodes.size
-
+
+  /** Edges inside of the perimeter */
+  def nonPerimeterEdges: List[Edge] =
+    graphEdges.diff(perimeter.toRingEdges.toList)
+
   /** All [[PolygonPath]], those touching the perimeter and those that don't */
   private lazy val (perimeterPolygons, innerPolygons) : (List[PolygonPath], List[PolygonPath]) =
     orientedPolygons.partition(_.hasSharedNodesWith(perimeter.toRingNodes))
@@ -598,6 +602,26 @@ class Tiling private(edges: List[Edge]) extends Graph(edges) with Ordered[Tiling
     def compare(a: Edge, b: Edge): Int =
       MinAngleEdgeNodeOrdering.orElse(MaxAngleEdgeNodeOrdering).compare(a, b)
 
+  /** Extracts data from the dual of the tiling
+   *
+   * @param f   map polygons to an element U
+   * @param g   transforms couples of U into target
+   * @tparam T  target
+   * @tparam U  element associated to a polygon
+   */
+  def dualTransform[T, U](f: List[PolygonPath] => Map[List[Edge], U], g: (U, U) => T): List[T] =
+    nonPerimeterEdges
+      .map(edge => f(orientedPolygons).filter((edges, _) => edges.contains(edge)).values)
+      .map(_.toList.toCouple)
+      .map(g(_, _))
+
+  /** Dual graph obtained by connecting each adjacent polygon */
+  def dual: Graph =
+    Graph(dualTransform(
+      _.map(_.toPolygonEdges).zipWithIndex.map((edges, i) => (edges, Node(i + 1))).toMap,
+      Edge(_, _)
+    ))
+
 /** Companion object for [[Tiling]] */
 object Tiling extends UniTriangle with UniHex with Uni4Hex with Uni5Hex with Layered with Quadratic:
 

src/main/scala/io/github/scala_tessella/tessella/conversion/SVG.scala

@@ -323,27 +323,18 @@ object SVG extends ConverterSVG:
       else
         None
 
-    private def polygonsCentreCoords: Map[List[Edge], Point] =
-      tiling.orientedPolygons.map(path =>
-        path.toPolygonEdges -> RegularPolygon2D(path.toPolygonPathNodes.map(tiling.coords).toList).center()
-      ).toMap
-
-    private def innerEdges: List[Edge] =
-      tiling.graphEdges.diff(tiling.perimeter.toRingEdges.toList)
-
-    private def dualSegments: List[LineSegment] =
-      innerEdges
-        .map(edge => polygonsCentreCoords.filter((edges, _) => edges.contains(edge)).values)
-        .map(_.toList.toCouple)
-        .map(LineSegment(_, _))
-
     private def dualSVG(showDual: Boolean): Option[Elem] =
       if showDual then
         Option(
           group(
             Option(Title("Dual")),
             Option(Description("Dual tessellation by joining the centres of each two polygons sharing an edge")),
-            dualSegments.map(line)*
+            tiling.dualTransform(
+              _.map(path =>
+                path.toPolygonEdges -> RegularPolygon2D(path.toPolygonPathNodes.map(tiling.coords).toList).center()
+              ).toMap,
+              LineSegment(_, _)
+            ).map(line)*
           ).withStyle(dualStyle)
         )
       else

src/test/scala/io/github/scala_tessella/tessella/TilingSpec.scala

@@ -457,5 +457,23 @@ class TilingSpec extends AnyFlatSpec with Accuracy with should.Matchers {
       .forall({ case ((a, b), (c, d)) => a == c && b.~=(d) }) shouldBe
       true
   }
+
+  "A tiling" can "have an empty dual graph" in {
+    triangle.dual.graphEdges.isEmpty shouldBe
+      true
+  }
+
+  it can "have a dual graph that is a valid tiling" in {
+    sqr4x4Reticulate.dual.toMaybeTiling.isRight shouldBe
+      true
+  }
+
+  it can "have a dual graph" in {
+    tri4x4Reticulate.dual.graphEdges shouldBe
+      List(
+        6--8, 9--10, 14--15, 3--4, 2--7, 11--12, 4--5, 2--8, 10--11,
+        13--15, 5--6, 8--9, 10--14, 15--16, 1--4, 2--3, 7--11, 12--13
+      )
+  }
 
 }