add rhombic and deltoidal projections

d3 · Jun 10, 2024 · 7a91eda · 7a91eda
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diff --git a/src/deltoidal.js b/src/deltoidal.js
@@ -0,0 +1,168 @@
+/*
+ * Deltoidal Hexecontahedron map
+ *
+ * Implemented for D3.js by Ronnie Bathoorn (2024),
+ * based on Icosahedron map by Jason Davies (2013)
+ * Enrico Spinielli (2017) and Philippe Rivière (2017, 2018)
+ *
+ */
+import { atan, degrees } from "./math.js";
+import voronoi from "./polyhedral/voronoi.js";
+
+
+export default function() {
+  var theta = atan(0.5) * degrees;
+
+  // construction inspired by
+  // https://en.wikipedia.org/wiki/Regular_icosahedron#Spherical_coordinates
+  var vertices = [[0, 90], [0, -90]].concat(
+    [0,1,2,3,4,5,6,7,8,9].map(function(i) {
+      var phi = (i * 36 + 180) % 360 - 180;
+      return [phi, i & 1 ? theta : -theta];
+    })
+  );
+
+  // icosahedron
+  var polyhedron = [
+    [0, 3, 11],
+    [0, 5, 3],
+    [0, 7, 5],
+    [0, 9, 7],
+    [0, 11, 9], // North
+    [2, 11, 3],
+    [3, 4, 2],
+    [4, 3, 5],
+    [5, 6, 4],
+    [6, 5, 7],
+    [7, 8, 6],
+    [8, 7, 9],
+    [9, 10, 8],
+    [10, 9, 11],
+    [11, 2, 10], // Equator
+    [1, 2, 4],
+    [1, 4, 6],
+    [1, 6, 8],
+    [1, 8, 10],
+    [1, 10, 2] // South
+  ].map(function(face) {
+    var t = face.map(function(i) {
+      return vertices[i];
+    });
+    // create 3 polygons from these using centroid and midpoints
+    var f1 = [
+      t[0], 
+      d3.geoInterpolate(t[0],t[1])(0.5), 
+      d3.geoCentroid({type:"MultiPoint", coordinates:t}), 
+      d3.geoInterpolate(t[0],t[2])(0.5)
+    ];
+    var f2 = [
+      t[1], 
+      d3.geoInterpolate(t[1],t[2])(0.5), 
+      d3.geoCentroid({type:"MultiPoint", coordinates:t}), 
+      d3.geoInterpolate(t[1],t[0])(0.5)
+    ];
+    var f3 = [
+      t[2], 
+      d3.geoInterpolate(t[2],t[0])(0.5), 
+      d3.geoCentroid({type:"MultiPoint", coordinates:t}), 
+      d3.geoInterpolate(t[2],t[1])(0.5)
+    ];
+    return [f1, f2, f3];
+  });
+
+  var polygons = {
+    type: "FeatureCollection",
+    features: polyhedron.flat().map(function(face) {
+      face.push(face[0]);
+      return {
+        properties: { sitecoordinates: d3.geoCentroid({type:"MultiPoint", coordinates: face}) },
+        geometry: {
+          type: "Polygon",
+          coordinates: [ face ]
+        }
+      };
+    })
+  };
+
+  var parents = [
+      -1, // 0
+      2, // 1
+      0, // 2
+      5, // 3
+      5, // 4
+      22, // 5
+      8, // 6
+      8, // 7
+      28, // 8
+      11, // 9
+      11, // 10
+      34, // 11
+      14, // 12
+      14, // 13
+      40, // 14
+      16, // 15
+      2, // 16
+      16, // 17
+      17, // 18
+      18, // 19
+      18, // 20
+      19, // 21
+      21, // 22
+      21, // 23
+      23, // 24
+      24, // 25
+      24, // 26
+      25, // 27
+      27, // 28
+      27, // 29
+      29, // 30
+      30, // 31
+      30, // 32
+      31, // 33
+      33, // 34
+      33, // 35
+      35, // 36
+      36, // 37
+      36, // 38
+      37, // 39
+      39, // 40
+      39, // 41
+      41, // 42
+      42, // 43
+      42, // 44
+      46, // 45
+      20, // 46
+      46, // 47
+      49, // 48
+      26, // 49
+      49, // 50
+      52, // 51
+      32, // 52
+      52, // 53
+      55, // 54
+      38, // 55
+      55, // 56
+      58, // 57
+      44, // 58
+      58, // 59
+    ];
+
+  //return polygons;
+  return voronoi()
+  .parents(parents)
+  .angle(0)
+  .polygons(polygons)
+  .rotate([108,0])
+  .scale(131.777)
+  .center([162, 0]);
+  }
+
+
+/*
+    // Jarke J. van Wijk, "Unfolding the Earth: Myriahedral Projections",
+    // The Cartographic Journal Vol. 45 No. 1 pp. 32–42 February 2008, fig. 8
+    // https://bl.ocks.org/espinielli/475f5fde42a5513ab7eba3f53033ea9e
+    d3.geoIcosahedral().parents([-1,0,1,11,3,0,7,1,7,8,9,10,11,12,13,6,8,10,19,15])
+   .angle(-60)
+   .rotate([-83.65929, 25.44458, -87.45184])
+*/
diff --git a/src/rhombic.js b/src/rhombic.js
@@ -0,0 +1,87 @@
+/*
+ * Rhombic Dodecahedron map
+ *
+ * Implemented for D3.js by Ronnie Bathoorn (2024)
+ * based on Cubic map by Enrico Spinielli (2017) and Philippe Rivière (2017, 2018)
+ *
+ */
+import { atan, degrees } from "./math.js";
+import voronoi from "./polyhedral/voronoi.js";
+
+export default function() {
+  var phi1 = atan(Math.SQRT1_2) * degrees;
+  var vertices = [
+    [0, 90],      // 0
+    [0, phi1],    // 1
+    [90, phi1],   // 2
+    [180, phi1],  // 3
+    [-90, phi1],  // 4
+    [45, 0],      // 5
+    [135, 0],     // 6
+    [-135, 0],     // 7
+    [-45, 0],     // 8
+    [0, -phi1],   // 9
+    [90, -phi1],  // 10
+    [180, -phi1], // 11
+    [-90, -phi1], // 12
+    [0, -90]      // 13
+  ];
+
+  // rhombic dodecahedron
+  var polyhedron = [
+    [0, 1, 8, 4],
+    [0, 2, 5, 1],
+    [0, 3, 6, 2],
+    [0, 4, 7, 3],
+
+    [1, 5, 9, 8],
+    [2, 6, 10, 5],
+    [3, 7, 11, 6],
+    [4, 8, 12, 7],
+
+    [8, 9, 13, 12],
+    [5, 10, 13, 9],
+    [6, 11, 13, 10],
+    [7, 12, 13, 11]
+  ].map(function(face) {
+          return face.map(function(i) {
+            return vertices[i];
+          });
+  });
+
+  var polygons = {
+    type: "FeatureCollection",
+    features: polyhedron.map(function(face) {
+      return {
+        properties: { sitecoordinates: d3.geoCentroid({type:"MultiPoint", coordinates: face}) },
+        geometry: {
+          type: "Polygon",
+          coordinates: [[...face, face[0]]]
+        }
+      };
+    })
+  };
+
+  var parents = [
+      -1, // 0
+      0, // 1
+      6, // 2
+      2, // 3
+      1, // 4
+      9, // 5
+      11, // 6
+      3, // 7
+      4, // 8
+      8, // 9
+      5, // 10
+      10, // 11
+    ];
+
+
+  return voronoi()
+    .polygons(polygons)
+    .parents(parents)
+    .angle(20)
+    .rotate([-76.5, 27, -84]);
+}
+