I am currently working with data points that define the boundaries of a constellation.
let boundaries = [
{
ra: 344.46530375,
dec: 35.1682358
},
{
ra: 344.34285125,
dec: 53.1680298
},
{
ra: 351.45289375,
dec: 53.1870041
},
...
]
Although these values have been obtained from IAU quoted sources, my task is to calculate the "great circle distance" or orthodromic distance between each pair of consecutive points i and i+1. This involves interpolating between point i and point i+1 at a specified precision x.
To achieve this, I have developed a function specifically designed for this interpolation operation in Equatorial Coordinates. The function is written in Typescript ES6 as follows:
/**
* getInterpolatedEquatorialCoordinates()
*
* @description This function takes in a start and end
* @param start EquatorialCoordinate
* @param end EquatorialCoordinate
* @param precision number
* @output returns the interpolated array of []EquatorialCoordinate points:
*/
export const getInterpolatedEquatorialCoordinates = (
start: EquatorialCoordinate,
end: EquatorialCoordinate,
precision: number
): Array<EquatorialCoordinate> => {
// The interpolated points array to return:
const points: Array<EquatorialCoordinate> = []
// Obtain the difference between the end coordinate's Right Ascension, RA, and the start coordinate's RA:
let nra = ((end.ra - start.ra)) % 360
if (nra > 180) nra = nra - 360
if (nra < -180) nra = nra + 360
// Calculate the rate of change of RA:
const dra: number = nra / precision
// Obtain the difference between the end coordinate's Declination, dec, and the start coordinate's dec:
const ndec = ((end.dec - start.dec))
// Calculate the rate of change of dec:
const ddec: number = ndec / precision
// Interpolated calculation for each step:
let i = 0
while (i < precision) {
i++
points.push({
ra: start.ra + (dra * i),
dec: start.dec + (ddec * i)
})
}
return points
}
In order to validate the mathematical accuracy of this function, I conducted tests using the first two points from the 'boundaries' array:
test('getInterpolatedEquatorialCoordinates', function () {
const start = {
ra: 344.46530375,
dec: 35.1682358
}
const end = {
ra: 344.34285125,
dec: 53.1680298
}
const minRA = Math.min(start.ra, end.ra)
const minDec = Math.min(start.dec, end.dec)
const maxRA = Math.max(start.ra, end.ra)
const maxDec = Math.max(start.ra, end.ra)
const precision = 10
const points = getInterpolatedEquatorialCoordinates(start, end, precision)
// Assertions for validation
})
The resulting interpolated points are detailed below:
[
{ ra: 344.4530585, dec: 36.968215199999996 },
{ ra: 344.44081324999996, dec: 38.7681946 },
...
]
Question:
My next objective is to apply the interpolation process to all points in the 'boundaries' array, combining them into one cohesive array. What method would be best suited for achieving this? Although I attempted to utilize the Array.prototype.map method, I encountered difficulties...
The desired output format should resemble the following structure based on the initial 'boundaries' array:
let boundaries = [
{
ra: 344.46530375,
dec: 35.1682358
},
...
]
let desiredOutput = [
{
ra: 344.46530375,
dec: 35.1682358
},
// Intermediate interpolated values
{
ra: ...,
dec: ...
},
...
]