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Edited
Aug 21, 2024
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36 stars
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The Gray-Fuller spatial grid
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Voronoi
g = grid(N)
points = g
.map(d3.geoRotation([36, 0, 0]))
.map(d3.geoRotation(d3.geoAirocean().rotate()).invert)
coords = (radius) => (row, col) => [
(col - row / 2) * radius * Math.sqrt(3),
row * radius * (3 / 2)
]
function* triangleInner(N) {
const c = coords(radius(N));
for (let row = 1; row < N; row++)
for (let col = 1; col < row; col++) yield c(row, col);
}
function* triangleEdges(N) {
for (let row = 1; row <= N; row++) {
let start = 0,
end = row,
step = row;
if (row === N) {
start = 1;
end = N - 1;
step = 1;
}
for (let col = start; col <= end; col += step) yield coords(row, col);
}
}
function* triangleVertices(N) {
for (let [col, row] of [[0, 0], [0, N], [N, N]]) yield coords(row, col);
}
theta = atan(0.5) * degrees
// One of the icosahedron’s 20 equilateral triangles
triangle = ({
type: "Polygon",
coordinates: [[[0, theta], [36, -theta], [-36, -theta], [0, theta]]]
})
c = d3.geoCentroid(triangle)
tprojection = d3
.geoProjection(d3.geoGrayFullerRaw()) // d3.geoGnomonicRaw
.rotate([-c[0], -c[1]])
.center([0, triangle.coordinates[0][0][1] - c[1]])
.scale(1)
.translate([0, 0])
path = d3.geoPath(tprojection)
vertices = [[0, 90], [0, -90]].concat(
Array.from({ length: 10 }, function(_, i) {
var phi = ((i * 36 + 180) % 360) - 180;
return [phi, i & 1 ? -theta : theta];
})
)
bounds = path.bounds(triangle)
radius = (N) => (bounds[1][1] - bounds[0][1]) / N / 1.5
function grid(N) {
const _i = [],
_e = [],
_v = [];
const theta = atan(0.5) * degrees;
for (let h of triangleInner(N)) {
h = tprojection.invert(h);
for (let i = 0; i < 10; i++)
_i.push([h[0] + i * 36, (i % 2 ? -1 : 1) * h[1]]);
h = d3.geoRotation([0, 90 - theta, 180])(h);
for (let i = 0; i < 5; i++) _i.push([h[0] + i * 72, h[1]]);
for (let i = 0; i < 5; i++) _i.push([36 - h[0] + i * 72, -h[1]]);
}
for (let i = 0; i < vertices.length; i++) {
const h = vertices[i];
_v.push(h);
for (let j = i + 1; j < vertices.length; j++) {
const k = vertices[j];
// this test is a shortcut for listing the edges.
if (Math.abs(d3.geoDistance(h, k) - 1.1) < 0.01) {
const i = d3.geoInterpolate(h, k);
for (let n = 1; n < N; n++) _e.push(i(n / N));
}
}
}
return [_v, _e, _i].flat();
}
world = d3.json(
"https://unpkg.com/visionscarto-world-atlas@0.0.6/world/110m_land.geojson"
)
height = 520
import { atan, degrees } from "@fil/math"
d3 = require("d3@7", "d3-geo-projection@4", "d3-geo-polygon@1.8", "d3-geo-voronoi@2")
import { checkbox, select, slider } from "@jashkenas/inputs"
import { drag } from "@d3/versor-dragging"
// https://www.colourlovers.com/palette/932683
palette = d3.scaleOrdinal([0, 1, 2], ["#FF9E9D", "#3FB8AF", "#DAD8A7"])
projection = ({
Airocean: d3
.geoAirocean()
.rotate([-83.65929 + 1e-9, 25.44458, -87.45184]) // +1e-9 avoids a tiny bug
.fitExtent([[2, 2], [width - 2, height - 2]], { type: "Sphere" }),
"Gnomonic icosahedral": d3
.geoIcosahedral()
.faceProjection(face => {
const c = face.site.map(d => -d);
c[2] = Math.abs(c[1] - 52.62) < 1 || Math.abs(c[1] + 10.81) < 1 ? 60 : 0;
return d3
.geoProjection(d3.geoGnomonicRaw)
.rotate(c)
.translate([0, 0]);
})
.rotate([-83.65929, 25.44458, -87.45184])
.angle(60)
.fitExtent([[2, 2], [width - 2, height - 2]], { type: "Sphere" }),
"Gray-Fuller icosahedral": d3
.geoIcosahedral()
.faceProjection(face => {
var c = face.site.map(d => -d);
c[2] = Math.abs(c[1] - 52.62) < 1 || Math.abs(c[1] + 10.81) < 1 ? 60 : 0;
return d3
.geoProjection(d3.geoGrayFullerRaw())
.rotate(c)
.translate([0, 0]);
})
.rotate([-83.65929, 25.44458, -87.45184])
.angle(60)
.fitExtent([[2, 2], [width - 2, height - 2]], { type: "Sphere" }),
Orthographic: d3
.geoOrthographic()
.rotate([-110, -35])
.fitExtent([[2, 2], [width - 2, height - 2]], { type: "Sphere" }),
"Azimuthal equal-area": d3
.geoAzimuthalEqualArea()
.rotate([-110, -35])
.clipAngle(54)
.fitExtent([[2, 2], [width - 2, height - 2]], { type: "Sphere" }),
Mercator: d3
.geoMercator()
.fitExtent([[2, 2], [width - 2, height - 2]], { type: "Sphere" })
}[projname])
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