J2000 = [
[-0.054876, -0.873437, -0.483835],
[0.494109, -0.444830, 0.746982],
[-0.867666, -0.198076, 0.455984]
]
j2000_e = EulerAnglesFromRotationMatrix(J2000) // equatorial to galactic
j2000_ei = EulerAnglesFromRotationMatrix(d3.transpose(J2000)) // galactic to equatorial
J1950 = [
[-0.066989, -0.872756, -0.483539],
[0.492728, -0.450347, 0.744585],
[-0.867601, -0.188375, 0.460200]
]
j1950_e = EulerAnglesFromRotationMatrix(J1950)
j1950_ei = EulerAnglesFromRotationMatrix(d3.transpose(J1950))
// https://www.astro.rug.nl/software/kapteyn-beta/celestialbackground.html
galactic2super = [
[-7.357425748044e-01, 6.772612964139e-01, -6.085819597056e-17],
[-7.455377836523e-02, -8.099147130698e-02, 9.939225903998e-01],
[6.731453021092e-01, 7.312711658170e-01, 1.100812622248e-01]
]
supergalactic = matrix_multiply(galactic2super,J2000)
supergalactic_ei = EulerAnglesFromRotationMatrix(
// mlMatrix.inverse(supergalactic)
// the inverse of a rotation matrix is its transpose
// (transpose is faster and more accurate)
d3.transpose(supergalactic)
)
// https://www.gregslabaugh.net/publications/euler.pdf
function EulerAnglesFromRotationMatrix(R) {
const theta = asin(R[2][0]),
ooct = 1 / cos(theta),
psi = atan2(R[2][1] * ooct, R[2][2] * ooct),
phi = atan2(R[1][0] * ooct, R[0][0] * ooct);
return [phi, theta, psi].map(d => -d * (180 / Math.PI));
}
d3.geoRotation(j2000_ei).invert([0, 90]) // 12 days 49 minutes RA, Dec = 27°24′ = [192.25, 27.4] // [-167.75, 27.4]
// Axis-angle representation of a rotation given as Euler angles
// https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation#Recovering_the_axis-angle_representation
// https://www.astro.rug.nl/software/kapteyn-beta/_downloads/attitude.pdf
function AxisAngleFromEulerAngles(rotate) {
// the vector part of the quaternion (q1:3) should give the cartesian coordinates of the pole
const q = versor(rotate),
h0 = Math.hypot(q[1], q[2], q[3]),
r0 = 1 / h0;
// see [z, -y, x] https://github.com/Fil/versor/blob/master/src/index.js#L14
const axis = spherical([q[3], -q[2], q[1]].map(d => d * r0)).map(
d => d * degrees
);
const angle = 2 * atan2(h0, q[0]) * degrees;
return { axis, angle };
}
AxisAngleFromEulerAngles([360.1, 0, 0]) // [0, 90] // lambda
AxisAngleFromEulerAngles([0, 1, 0]) // [-90, 0] // phi
AxisAngleFromEulerAngles([0, 0, 1]) // [0, 0] // gamma
AxisAngleFromEulerAngles([0, 90, 0])
AxisAngleFromEulerAngles([0, 90, 0])
AxisAngleFromEulerAngles(j2000_ei)
(12 + 49 / 60) * (360 / 24)
27 + 24 / 60
versor = require("versor@0.1")
import { spherical } from "@fil/cartesian"
import { asin, atan2, cos, degrees } from "@fil/math"
matrix_multiply = (A, B) => {
function dot(v, w) {
return v.map((a, i) => a * w[i]).reduce((a, b) => a + b, 0);
}
const M = Array(A.length),
Bt = d3.transpose(B);
for (let i = 0; i < A.length; i++) {
const line = Array(Bt.length);
for (let j = 0; j < Bt.length; j++) {
line[j] = dot(A[i], Bt[j]);
}
M[i] = line;
}
return M;
}
matrix_multiply(J1950, d3.transpose(J2000))
d3 = require("d3@5")
versor([181, 0, 0])
attitude = require("attitude")
One platform to build and deploy the best data apps
Experiment and prototype by building visualizations in live JavaScript notebooks. Collaborate with your team and decide which concepts to build out.
Use Observable Framework to build data apps locally. Use data loaders to build in any language or library, including Python, SQL, and R.
Seamlessly deploy to Observable. Test before you ship, use automatic deploy-on-commit, and ensure your projects are always up-to-date.