Illustrator Scripting: transfer real life longitude & latitude on Illustrator Map - help needed(!)

Hallo Nils, 

hast du eventuell auch die deinen Dokumentengrenzen entsprechenden Geo-Koordinaten? Denn dann könnte man doch normalerweise die City-Koordinaten durch Dreisatz-Berechnung ermitteln.

Oder habe ich die Aufgabenstellung nicht richtig verstanden?

Hi @Nils M. Barner, Edit: I have updated my code below (and thanks to the solveMatrix function from ChatGPT!) and I hope it will work this time! 🙂

The idea is you call the "getTransform" function, giving it your example transformation pairs [ [lat,long], [x, y] ] and it returns a function that you can use thereafter for transforming your coordinates. Let me know if it works in practice!

- Mark

/**
 * @file Transform Latitude Longitude.js
 * Demo of transforming lat,long coordinates
 * into Illustrator coordinates.
 *
 * Notes:
 * - This is a quick, simple method and hardly tested,
 *   so be careful to check the results.
 * - It knows nothing about actual cartography or
 *   map projections!
 * - It works using the supplied example transformations.
 *
 * @author m1b, chatGPT
 * @discussion https://community.adobe.com/t5/illustrator-discussions/illustrator-scripting-transfer-real-life-longitude-amp-latitude-on-illustrator-map-help-needed/m-p/14716499
 */
(function () {

    const mm = 2.834645;

    // these examples are necessary to calibrate the transformer
    var city1 = [48.7491239657, 9.17012929916],
        city2 = [47.6264900005, 7.65646999127],
        city3 = [49.4682342, 8.5611973];

    var city1_pts = [116.60 * mm, 82.97 * mm],
        city2_pts = [39.83 * mm, 168.54 * mm],
        city3_pts = [83.67 * mm, 29.33 * mm];

    // generate a transform function using some examples
    var transform = getTransform([
        [city1, city1_pts],
        [city2, city2_pts],
        [city3, city3_pts],
    ]);

    // calculate position of a new city
    var city4 = [48.123456, 8.654321],
        city4_pts = transform(city4);

    $.writeln('city4_pts = ' + city4_pts);

})();

/**
 * Returns a transform function that transforms
 * [latitude, longitude] into Illustrator [x, y],
 * given an array of example `pairs`.
 * @author m1b and chatGPT
 * @version 2024-07-03
 * @param {Array<Array>} pairs - array of [lat_lon, pts] pairs.
 * @returns {Function}
 */
function getTransform(pairs) {

    var A = [],
        B = [];

    for (var i = 0; i < pairs.length; i++) {
        A.push([pairs[i][0][0], pairs[i][0][1], 1, 0, 0, 0]);
        A.push([0, 0, 0, pairs[i][0][0], pairs[i][0][1], 1]);
        B.push(pairs[i][1][0], pairs[i][1][1]);
    }

    // Solve for the affine transformation matrix using matrix algebra (A * X = B)
    var X = solveMatrix(A, B);

    var m = [
        [X[0], X[1], X[2]],
        [X[3], X[4], X[5]],
    ];

    // Transform function to apply the affine transformation
    return (

        function transform(latLon) {
            return [
                m[0][0] * latLon[0] + m[0][1] * latLon[1] + m[0][2],
                m[1][0] * latLon[0] + m[1][1] * latLon[1] + m[1][2],
            ];
        }

    );


};

/**
 * Solves a system of linear equations using Gaussian elimination.
 * 
 * This function solves the system of equations represented by the augmented matrix [A|B],
 * where A is an n x n matrix and B is an n x 1 vector.
 * 
 * @author chatGPT
 * @version 2024-07-03
 * @param {Array<Array<Number>>} A - The coefficient an n x n matrix of the system of equations.
 * @param {Array<Number>} B - The constant terms vector of the system of equations.
 * @returns {Array<Number>} - The solution vector X such that A * X = B.
 */
function solveMatrix(A, B) {

    var n = A.length;

    for (var i = 0; i < n; i++)
        A[i].push(B[i]);

    for (var i = 0; i < n; i++) {

        var maxRow = i;

        for (var k = i + 1; k < n; k++)
            if (Math.abs(A[k][i]) > Math.abs(A[maxRow][i]))
                maxRow = k;

        var tmp = A[maxRow];
        A[maxRow] = A[i];
        A[i] = tmp;

        for (var k = i + 1, c; k < n; k++) {

            c = -A[k][i] / A[i][i];

            for (var j = i; j < n + 1; j++) {
                if (i === j)
                    A[k][j] = 0;
                else
                    A[k][j] += c * A[i][j];
            }

        }

    }

    var X = new Array(n);

    for (var i = n - 1; i >= 0; i--) {

        X[i] = A[i][n] / A[i][i];

        for (var k = i - 1; k >= 0; k--)
            A[k][n] -= A[k][i] * X[i];
    }

    return X;

};