rhombic & deltoidal

README.md

@@ -96,7 +96,19 @@ The cubic projection.
 
 [<img src="https://raw.githubusercontent.com/d3/d3-geo-polygon/main/test/snapshots/dodecahedral.png" width="480" height="250">](https://observablehq.com/@fil/dodecahedral-projection)
 
-The dodecahedral projection.
+The pentagonal dodecahedral projection.
+
+<a href="#geoRhombic" name="geoRhombic">#</a> d3.<b>geoRhombic</b>() · [Source](https://github.com/d3/d3-geo-polygon/blob/main/src/polyhedral/rhombic.js), [Examples](https://observablehq.com/d/881a8431e638b408)
+
+[<img src="https://raw.githubusercontent.com/d3/d3-geo-polygon/main/test/snapshots/rhombic.png" width="480" height="250">](https://observablehq.com/d/881a8431e638b408)
+
+The rhombic dodecahedral projection.
+
+<a href="#geoDeltoidal" name="geoDeltoidal">#</a> d3.<b>geoDeltoidal</b>() · [Source](https://github.com/d3/d3-geo-polygon/blob/main/src/polyhedral/deltoidal.js), [Examples](https://observablehq.com/d/881a8431e638b408)
+
+[<img src="https://raw.githubusercontent.com/d3/d3-geo-polygon/main/test/snapshots/deltoidal.png" width="480" height="250">](https://observablehq.com/d/881a8431e638b408)
+
+The deltoidal hexecontahedral projection.
 
 <a href="#geoIcosahedral" name="geoIcosahedral">#</a> d3.<b>geoIcosahedral</b>() · [Source](https://github.com/d3/d3-geo-polygon/blob/main/src/icosahedral.js), [Examples](https://observablehq.com/@fil/icosahedral-projections)
 

package.json

@@ -27,6 +27,14 @@
     {
       "name": "Philippe Rivière",
       "url": "https://visionscarto.net"
+    },
+    {
+      "name": "Enrico Spinielli",
+      "url": "https://enrico.spinielli.net/"
+    },
+    {
+      "name": "Ronnie Bathoorn",
+      "url": "https://github.com/bathoorn"
     }
   ],
   "type": "module",

src/polyhedral/butterfly.js → src/butterfly.js

@@ -1,7 +1,7 @@
 import {geoCentroid as centroid, geoGnomonic as gnomonic} from "d3-geo";
-import {pi} from "../math.js";
-import polyhedral from "./index.js";
-import octahedron from "./octahedron.js";
+import {pi} from "./math.js";
+import polyhedral from "./polyhedral/index.js";
+import octahedron from "./polyhedral/octahedron.js";
 
 export default function(faceProjection = ((face) => {
   const c = centroid({type: "MultiPoint", coordinates: face});

src/cartesian.js

@@ -35,10 +35,9 @@ export function cartesianScale(vector, k) {
   return [vector[0] * k, vector[1] * k, vector[2] * k];
 }
 
-// TODO return d
-export function cartesianNormalizeInPlace(d) {
+export function cartesianNormalize(d) {
   const l = hypot(d[0], d[1], d[2]);
-  d[0] /= l, d[1] /= l, d[2] /= l;
+  return [d[0] / l, d[1] / l, d[2] / l];
 }
 
 export function cartesianEqual(a, b) {

src/clip/polygon.js

@@ -160,7 +160,7 @@ function clipLine(segments, pointVisible) {
       point: (lambda, phi, close) => {
         if (cos(lambda) == -1) lambda -= sign(sin(lambda)) * 1e-5; // move away from -180/180 https://github.com/d3/d3-geo/pull/108#issuecomment-323798937
         if (close) (lambda = lambda00), (phi = phi00);
-        let point = cartesian([lambda, phi]);
+        let point = cartesian([lambda * 0.9999999999, phi + 1e-14]);
         let v = v0;
         if (point0) {
           const intersections = [];
@@ -178,7 +178,7 @@ function clipLine(segments, pointVisible) {
               ) {
                 const t = 1e-4;
                 lambda = ((lambda + 3 * pi + randsign(i, j) * t) % (2 * pi)) - pi;
-                phi = min(pi / 2 - 1e-4, max(1e-4 - pi / 2, phi + randsign(i, j) * t));
+                phi = min(pi / 2 - t, max(t - pi / 2, phi + randsign(i, j) * t));
                 segment = new intersectSegment(point0, (point = cartesian([lambda, phi])));
                 (i = -1), --j;
                 intersections.length = 0;
@@ -188,9 +188,9 @@ function clipLine(segments, pointVisible) {
               intersection.distance = clipPolygonDistance(point0, intersection);
               intersection.index = i;
               intersection.t = clipPolygonDistance(s.from, intersection);
-              (intersection[0] = sph[0]),
-                (intersection[1] = sph[1]),
-                intersection.pop();
+              intersection[0] = sph[0];
+              intersection[1] = sph[1];
+              delete intersection[2];
               intersections.push(intersection);
             }
           }
@@ -237,7 +237,8 @@ function clipLine(segments, pointVisible) {
           v00 = v = pointVisible((lambda00 = lambda), (phi00 = phi));
           if (v) line = [], line.push([lambda, phi]);
         }
-        (point0 = point), (v0 = v);
+        point0 = point;
+        v0 = v;
       },
       // Rejoin first and last segments if there were intersections and the first
       // and last points were visible.

src/collignon.js

@@ -1,6 +1,9 @@
-// code duplicated from d3-geo-projection
+import {geoCentroid as centroid, geoProjection as projection} from "d3-geo";
 import {asin, pi, sin, sqrt, sqrtPi} from "./math.js";
+import polyhedral from "./polyhedral/index.js";
+import octahedron from "./polyhedral/octahedron.js";
 
+// code duplicated from d3-geo-projection
 export function collignonRaw(lambda, phi) {
   const alpha = sqrt(1 - sin(phi));
   return [(2 / sqrtPi) * lambda * alpha, sqrtPi * (1 - alpha)];
@@ -10,3 +13,35 @@ collignonRaw.invert = function(x, y) {
   const lambda = (y / sqrtPi - 1);
   return [lambda ? x * sqrt(pi) / lambda / 2 : 0, asin(1 - lambda ** 2)];
 };
+
+
+const kx = 2 / sqrt(3);
+
+function collignonK(a, b) {
+  const p = collignonRaw(a, b);
+  return [p[0] * kx, p[1]];
+}
+
+collignonK.invert = (x,y) => collignonRaw.invert(x / kx, y);
+
+export default function(faceProjection = (face) => {
+  const c = centroid({type: "MultiPoint", coordinates: face});
+  return projection(collignonK).translate([0, 0]).scale(1).rotate(c[1] > 0 ? [-c[0], 0] : [180 - c[0], 180]);
+}) {
+  const faces = octahedron.map((face) => ({face, project: faceProjection(face)}));
+
+  [-1, 0, 0, 1, 0, 1, 4, 5].forEach((d, i) => {
+    const node = faces[d];
+    node && (node.children || (node.children = [])).push(faces[i]);
+  });
+
+  return polyhedral(
+    faces[0],
+    (lambda, phi) => faces[lambda < -pi / 2 ? phi < 0 ? 6 : 4
+            : lambda < 0 ? phi < 0 ? 2 : 0
+            : lambda < pi / 2 ? phi < 0 ? 3 : 1
+            : phi < 0 ? 7 : 5])
+    .angle(-30)
+    .scale(121.906)
+    .center([0, 48.5904]);
+}

src/cubic.js

@@ -5,7 +5,21 @@
  *
  */
 import voronoi from "./polyhedral/voronoi.js";
-import { default as cube } from "./polyhedral/cube.js";
+import {atan, degrees, sqrt1_2} from "./math.js";
+
+const phi1 = atan(sqrt1_2) * degrees;
+const cube1 = [
+  [0, phi1], [90, phi1], [180, phi1], [-90, phi1],
+  [0, -phi1], [90, -phi1], [180, -phi1], [-90, -phi1]
+];
+const cube = [
+  [0, 3, 2, 1], // N
+  [0, 1, 5, 4],
+  [1, 2, 6, 5],
+  [2, 3, 7, 6],
+  [3, 0, 4, 7],
+  [4, 5, 6, 7] // S
+].map((face) => face.map((i) => cube1[i]));
 
 export default function() {
   const polygons = {

src/deltoidal.js

@@ -0,0 +1,149 @@
+/*
+ * 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";
+import { geoCentroid, geoInterpolate } from "d3-geo";
+
+export default function () {
+  const theta = atan(0.5) * degrees;
+
+  // construction inspired by
+  // https://en.wikipedia.org/wiki/Regular_icosahedron#Spherical_coordinates
+  const vertices = [[0, 90], [0, -90]].concat(
+    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9].map((i) => [
+      ((i * 36 + 180) % 360) - 180,
+      i & 1 ? theta : -theta
+    ])
+  );
+
+  // icosahedron
+  const 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((face) => {
+    const t = face.map((i) => vertices[i]);
+    // create 3 polygons from these using centroid and midpoints
+    const a0 = geoInterpolate(t[1], t[2])(0.5);
+    const a1 = geoInterpolate(t[0], t[2])(0.5);
+    const a2 = geoInterpolate(t[0], t[1])(0.5);
+    const c = geoCentroid({ type: "MultiPoint", coordinates: t });
+    return [
+      [t[0], a2, c, a1],
+      [t[1], a0, c, a2],
+      [t[2], a1, c, a0]
+    ];
+  });
+
+  const polygons = {
+    type: "FeatureCollection",
+    features: polyhedron.flat().map((face) => ({
+      type: "Feature",
+      properties: {
+        sitecoordinates: geoCentroid({
+          type: "MultiPoint",
+          coordinates: face,
+        }),
+      },
+      geometry: {
+        type: "Polygon",
+        coordinates: [[...face, face[0]]],
+      },
+    }))
+  };
+
+  const 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)
+    .polygons(polygons)
+    .angle(3)
+    .rotate([108, 0])
+    .translate([72, 252])
+    .scale(136.67);
+}

src/polyhedral/dodecahedral.js → src/dodecahedral.js

@@ -1,5 +1,5 @@
-import {acos, asin, degrees, sqrt} from "../math.js";
-import voronoi from "./voronoi.js";
+import {acos, asin, degrees, sqrt} from "./math.js";
+import voronoi from "./polyhedral/voronoi.js";
 
 export default function() {
   const A0 = asin(1/sqrt(3)) * degrees;

src/index.js

@@ -1,17 +1,19 @@
 export {default as geoClipPolygon} from "./clip/polygon.js";
 export {default as geoIntersectArc} from "./intersect.js";
 export {default as geoPolyhedral} from "./polyhedral/index.js";
-export {default as geoPolyhedralButterfly} from "./polyhedral/butterfly.js";
-export {default as geoPolyhedralCollignon} from "./polyhedral/collignon.js";
-export {default as geoPolyhedralWaterman} from "./polyhedral/waterman.js";
+export {default as geoPolyhedralButterfly} from "./butterfly.js";
+export {default as geoPolyhedralCollignon} from "./collignon.js";
+export {default as geoPolyhedralWaterman} from "./waterman.js";
 export {default as geoPolyhedralVoronoi} from "./polyhedral/voronoi.js";
-export {default as geoDodecahedral} from "./polyhedral/dodecahedral.js";
+export {default as geoDodecahedral} from "./dodecahedral.js";
 export {default as geoCox, coxRaw as geoCoxRaw} from "./cox.js";
 export {default as geoTetrahedralLee, leeRaw as geoLeeRaw} from "./tetrahedralLee.js";
 export {default as geoGrayFullerRaw} from "./grayfuller.js";
 export {default as geoAirocean} from "./airocean.js";
 export {default as geoIcosahedral} from "./icosahedral.js";
 export {default as geoImago, imagoBlock as geoImagoBlock, imagoRaw as geoImagoRaw} from "./imago.js";
 export {default as geoCubic} from "./cubic.js";
+export {default as geoRhombic} from "./rhombic.js";
+export {default as geoDeltoidal} from "./deltoidal.js";
 export {default as geoCahillKeyes, cahillKeyesRaw as geoCahillKeyesRaw} from "./cahillKeyes.js";
 export {default as geoComplexLog, complexLogRaw as geoComplexLogRaw} from "./complexLog.js";