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Spherical Ellipses
C0 = [90, 90 - colat]
C1 = [-90, 90 - colat]
ellipse = geoEllipse(C0, C1, radius)
projection = d3
.geoOrthographic()
.rotate([20, -65])
.precision(0.1)
function geoEllipse(p0, p1, radius) {
const precision = 6; // see geoCircle
const i = d3.geoInterpolate(p0, p1),
alpha = i.distance / 2,
theta = radius * radians,
A = tan(alpha),
A2 = A * A,
D = tan(theta),
D2 = D * D,
R = 1 / sqrt(1 + D2),
Z = R * D,
Y = R * sqrt(D2 - A2);
if (alpha > pi / 2 || theta < alpha) return null;
if (theta >= pi - alpha) return { type: "Sphere" };
// calculate an ellipse centered on [0,0] and aligned on the equator
let ring = [];
for (let i = 0; i < 360; i += precision) {
const t = i * radians,
c = cos(t),
s = sin(t);
const y = s * Z,
z = c * Y,
x = sqrt(1 - y * y - z * z) * Math.sign(D);
ring.push(spherical([x, y, z]).map(d => d * degrees));
}
ring.push(ring[0]);
if (D < 0) ring.reverse();
// rotate to align it with the actual points
const o = i(0.5),
a = d3.geoRotation([-o[0], -o[1]])(p0),
b = i.distance / 2,
y = -asin(sin(a[1] * radians) / sin(b)),
r = [-o[0], -o[1], -(a[0] > 0 ? pi - y : y) * degrees];
return {
type: "Polygon",
coordinates: [ring.map(d3.geoRotation(r).invert)]
};
}
d3 = require("d3@6", "d3-geo-projection@3", "d3-geo-polygon@1")
height = 550
import { asin, cos, degrees, pi, radians, sin, sqrt, tan } from "@fil/math"
import { spherical } from "@fil/cartesian"
import { zoom } from "@d3/versor-zooming"
import { slider } from "@jashkenas/inputs"
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