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

[Nils M. Barner]

Hi community,

this one is a really hard one!

Going back and forth for a couple of days now my brain got completely stucked... so please give me some input or maybe someone can work out a functional script in this case:

A bunch of coordinates (longitude & latitude values) must be transfered onto an Illustrator map to set a dot for each location... I'm stuggeling with creating the right formular to set them right... I'm pretty sure it's just a mathematical logical issue thing...

// the locations in latitude & longitude as vars:
    var lat1 = 48.7491239657; //city_1
    var lon1 = 9.17012929916; //city_1

    var lat2 = 47.6264900005; //city_2
    var lon2 = 7.65646999127; //city_2

    var lat3 = 49.4682342; //city_3
    var lon3 = 8.5611973; //city_3


// the locations manually set on the Illustrator-Map as vars:
    var my_x1 = mm(116.60); //city_1
    var my_y1 = mm(82.97); //city_1

    var my_x2 = mm(39.83); //city_2
    var my_y2 = mm(168.54); //city_2

    var my_x3 = mm(83.67); //city_3
    var my_y3 = mm(29.33); //city_3

//mm to point converter
function mm(n) {
    return n * 2.83464567;
}

PS. and as always – only scripting solutions appreceated! 😉

[m1b]

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;

};

[Nils M. Barner]

@mark: is this the fixed version now? or should I still ignore?

[m1b]

Please take it for a test drive!

[m1b]

Sorry about posting my faulty code before. I've updated it now, thanks to some help from ChatGPT!, and tested a bit more and it gives the expected results now. - Mark

[Nils M. Barner]

@m1b: Hi Mark,

I tried your Script but coords are still far off...

Just tried to figure out why but I got even more confused now...

Please find a simplified demo .ai file attached (please rename the .pdf > .ai) so you can try on your own...

My thoughts on the case:

Something might be twisted (lang/long, x/y, ...) so values get mixed up... 

Here's my script so far (just added some more functions and vars to it):

/**
 * @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
 */

#target illustrator

////// first things first and basic checks

    var docRef = app.activeDocument;
    var artboardRef = docRef.artboards;
    var scriptRef = new File($.fileName).path;
    var separator = '\\';
    var lineBreak = '\r';
    var CSVref = '';
    var GoodToGo = false;

    var thisX;
    var thisY;
    var xStartPos = 0; //// just in case to move
    var yStartPos = 0; //// just in case to move

    var hsdDiameter = mm(1.65); //// size of hotspot dot
    var hsdStrokeWidth = 0.5;  //// stroke weight of hotspot dot
    var hsdColor = makeCMYKColor(10,100,90,0);
    var hsdStrokeColor = makeCMYKColor(100,0,0,0);

(function () {

    const mm = 2.834645;

    // these examples are necessary to calibrate the transformer
    var city1 = [48.7491239657, 9.17012929916], //// this ist Stuttgart //_latitude (north/south > Y) then _longitude (west/east > X)
        city2 = [47.6264900005, 7.65646999127], //// this is Lörrach
        city3 = [49.4682342, 8.5611973]; //// this is Mannheim
//     var city4 = [48.7493055, 8.2197765], //// this is Baden-Baden
//     var city5 = [48.984742, 8.403163], //// this is Karlsruhe
//     var city6 = [48.2315269, 9.8833368], //// this is Ulm (might be a bit off)
//     var city7 = [49.5985400069, 9.69389004153], //// this is Tauberbischofsheim


    var city1_pts = [152,887 * mm, 99,701 * mm], //// this is Stuttgart //_x then _y
        city2_pts = [76,123 * mm, 185,265 * mm], //// this is Lörrach
        city3_pts = [119,954 * mm, 46,053 * mm]; //// this is Mannheim

    // 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 = [48.7491239657, 9.17012929916], // this is Baden-Baden
        city4_pts = transform(city4);
    var city5 = [48.984742, 8.403163], //// this is Karlsruhe
        city5_pts = transform(city5);
     var city7 = [49.5985400069, 9.69389004153], //// this is Tauberbischofsheim
         city7_pts = transform(city7);

    $.writeln('city4_pts = ' + city4_pts);
alert(city4_pts);
    var thisX = city4_pts[0] + xStartPos;
    var thisY = city4_pts[1] + yStartPos;
    createHotSpot(thisX,thisY,hsdDiameter);
    
alert(city5_pts);
    var thisX = city5_pts[0] + xStartPos;
    var thisY = city5_pts[1] + yStartPos;
    createHotSpot(thisX,thisY,hsdDiameter);
        
alert(city7_pts);
    var thisX = city7_pts[0] + xStartPos;
    var thisY = city7_pts[1] + yStartPos;
    createHotSpot(thisX,thisY,hsdDiameter);

})();


// create hotspot
function createHotSpot(xHS, yHS, diaHS) {

    var myX = xHS + diaHS/2; //for center point
    var myY = yHS - diaHS/2; //for center point
    
    var thisHotSpot = docRef.activeLayer.pathItems.ellipse(myX, myY, diaHS, diaHS);

    thisHotSpot.fillColor = hsdColor;
    thisHotSpot.stroked = true;
    thisHotSpot.strokeWidth = hsdStrokeWidth;
    thisHotSpot.strokeColor = hsdStrokeColor;

    return thisHotSpot; // Return the created thisHotSpot
}


/**
 * 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;

};

function mm(n) {
    return n * 2.83464567;
}

function makeCMYKColor(c,m,y,k){
    var ink = new CMYKColor();
    ink.cyan   = c;
    ink.magenta = m;
    ink.yellow  = y;
    ink.black  = k;
    return ink;
}

  Thanks

Nils

[m1b]

Hi @Nils M. Barner, thanks for the map—that helped. Actually, my script seemed to work fine. This is what I did...

First, I entered three cities from your map: Lörrach, Mannheim and Ulm, both lat/long and map coordinates (taken as the centre of the circle on your map. These are to calibrate the transform function. Here is the data I added to the script (replacing all the city1, city2, ... stuff):

// these examples are necessary to calibrate the transformer
const lörrach = [47.6168, 7.6691],
    mannheim = [49.4875, 8.4660],
    ulm = [48.4011, 9.9876];

const lörrach_pts = [76.123 * mm, 185.265 * mm],
    mannheim_pts = [119.954 * mm, 46.053 * mm],
    ulm_pts = [191.809 * mm, 127.151 * mm];

// generate a transform function using some examples
var transform = getTransform([
    [lörrach, lörrach_pts],
    [mannheim, mannheim_pts],
    [ulm, ulm_pts],
]);

// calculate position of a new city
var stuttgart = [48.7758, 9.1829],
    heilbronn = [49.1427, 9.2109];

// now transform into map coordinates
var stuttgart_pts = transform(stuttgart),
    heilbronn_pts = transform(heilbronn);

$.writeln('stuttgart_pts = ' + stuttgart_pts);
$.writeln('heilbronn_pts = ' + heilbronn_pts);

Then I entered two new cities—Stuttgart and Heilbronn—lat/long and used the transform function to give me the coordinates in pts. Console output:

stuttgart_pts = 434.552869517851,281.040327929184
heilbronn_pts = 441.087488743414,203.598201369798

Then I just positioned a green circle at those two points on your map. This is what I got:

So not too bad at all. Does it work for you?

- Mark

[Nils M. Barner]

Hi Mark,

thank you so much!

This worked quite well with the original small region. Now I want to scale it to another map displaying whole Germany...

Calibrating with the new values, the city points are almost 80pt off their position now 🤷🏼‍

I fixed this by adding a simple offset var.

But there still seems to be a small destortion (especially to the north east = Berlin) within the calculation which I was not able to fix.

I also tried different locations for the basic calculation... but still no propper locations espacially at the edges...

this is the script so far (with a bunch of test locations in it) + the new ai file containing the whole map...

(rename .pdf to .ai)

/**
 *  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.
 *
 *  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
 */

#target illustrator

////// first things first and basic checks

    var docRef = app.activeDocument;
    var artboardRef = docRef.artboards;
    var scriptRef = new File($.fileName).path;
    var separator = '\\';
    var lineBreak = '\r';
    var CSVref = '';
    var GoodToGo = false;

    var thisX;
    var thisY;
    var xOffSet = conToMM(27.5); //// just in case to move 27.5
    var yOffSet = conToMM(28); //// just in case to move 28.0

    var hsdDiameter = conToMM(1.65); //// size of hotspot dot
    var hsdStrokeWidth = 0.5;  //// stroke weight of hotspot dot
    var hsdColor = makeCMYKColor(10,100,90,0);
    var hsdStrokeColor = makeCMYKColor(100,0,0,0);

(function () {

    const mm = 2.834645;
    
// these examples are necessary to calibrate the transformer (lat | lon)
const cal_aachen = [50.775292484480595, 6.083758910795308],
    cal_BadenBaden = [48.792237421096345, 8.19137173572452],
    cal_berlin = [52.51744623129174, 13.377098108197393],
    cal_dresden = [51.0505950198469, 13.738968779495721],
    cal_hamburg = [53.55024351363441, 9.99009185640509],
    cal_Heilbronn = [49.14245226211572, 9.218827568671607],
    cal_kiel = [54.32251390152231, 10.138055041116033],
    cal_loerrach = [47.6124273593957, 7.661110268609717],
    cal_mannheim = [49.48861640147493, 8.46917463343792],
    cal_passau = [48.57235422464215, 13.452475539919073],
    cal_ulm = [48.3995976891002, 9.989646869297806];

// (x|y)
const cal_aachen_pts = [8.4 * mm, 195.644 * mm],
    cal_BadenBaden_pts = [67.575 * mm, 289.449 * mm],
    cal_berlin_pts = [212.919 * mm, 116.749 * mm],
    cal_dresden_pts = [226.287 * mm, 183.441 * mm],
    cal_hamburg_pts = [119.91 * mm, 73.268 * mm],
    cal_Heilbronn_pts = [97.376 * mm, 272.929 * mm],
    cal_kiel_pts = [123.076 * mm, 38.199 * mm],
    cal_loerrach_pts = [49.006 * mm, 341.152 * mm],
    cal_mannheim_pts = [74.99 * mm, 256.732 * mm],
    cal_passau_pts = [222.885 * mm, 295.375 * mm],
    cal_ulm_pts = [120.077 * mm, 306.536 * mm];

// generate a transform function using some examples
var transform = getTransform([
    //[cal_BadenBaden, cal_BadenBaden_pts],
    //[cal_berlin, cal_berlin_pts],
    //[cal_dresden, cal_dresden_pts],
    [cal_hamburg, cal_hamburg_pts],
    //[cal_Heilbronn, cal_Heilbronn_pts],
    //[cal_kiel, cal_kiel_pts],
    [cal_loerrach, cal_loerrach_pts],
    //[cal_mannheim, cal_mannheim_pts],
    [cal_passau, cal_passau_pts],
    //[cal_ulm, cal_ulm_pts],
]);

// calculate position of a new city
var aachen = [50.775292484480595, 6.083758910795308],
    BadenBaden = [48.7493055, 8.2197765],
    berlin = [52.51744623129174, 13.377098108197393],
    dresden = [51.0505950198469, 13.738968779495721],
    hamburg = [53.55024351363441, 9.99009185640509],
    heilbronn = [49.1427, 9.2109],
    karlsruhe = [48.984742, 8.403163],
    kiel = [54.32251390152231, 10.138055041116033],
    loerrach = [47.6124273593957, 7.661110268609717],
    mannheim = [49.48861640147493, 8.46917463343792],
    passau = [48.57235422464215, 13.452475539919073],
    stuttgart = [48.7758, 9.1829],
    ulm = [48.3995976891002, 9.989646869297806];

// now transform into map coordinates
var aachen_pts = transform(aachen),
    BadenBaden_pts = transform(BadenBaden),
    berlin_pts = transform(berlin),
    dresden_pts = transform(dresden),
    hamburg_pts = transform(hamburg),
    heilbronn_pts = transform(heilbronn),
    karlsruhe_pts = transform(karlsruhe),
    kiel_pts = transform(kiel),
    loerrach = transform(loerrach),
    mannheim_pts = transform(mannheim),
    passau_pts = transform(passau),
    stuttgart_pts = transform(stuttgart),
    ulm_pts = transform(ulm);
    
    var thisX = aachen_pts[0] + xOffSet;
    var thisY = aachen_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);

    var thisX = BadenBaden_pts[0] + xOffSet;
    var thisY = BadenBaden_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);

    var thisX = berlin_pts[0] + xOffSet;
    var thisY = berlin_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,10);
    
    var thisX = dresden_pts[0] + xOffSet;
    var thisY = dresden_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);

    var thisX = hamburg_pts[0] + xOffSet;
    var thisY = hamburg_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);

    var thisX = heilbronn_pts[0] + xOffSet;
    var thisY = heilbronn_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);

    var thisX = karlsruhe_pts[0] + xOffSet;
    var thisY = karlsruhe_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);
    
    var thisX = kiel_pts[0] + xOffSet;
    var thisY = kiel_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);

    var thisX = loerrach[0] + xOffSet;
    var thisY = loerrach[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);

    var thisX = mannheim_pts[0] + xOffSet;
    var thisY = mannheim_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);

    var thisX = passau_pts[0] + xOffSet;
    var thisY = passau_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);
    
    var thisX = stuttgart_pts[0] + xOffSet;
    var thisY = stuttgart_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);
    
    var thisX = ulm_pts[0] + xOffSet;
    var thisY = ulm_pts[1] + yOffSet;
    createHotSpot(thisX,thisY,hsdDiameter);

    $.writeln('stuttgart_pts = ' + stuttgart_pts);
    $.writeln('heilbronn_pts = ' + heilbronn_pts);

})();


// create hotspot
function createHotSpot(xHS, yHS, diaHS) {

    var myX = xHS - (diaHS/2); //for center point
    var myY = (yHS - (diaHS/2))*(-1); //for center point
    
    var thisHotSpot = docRef.activeLayer.pathItems.ellipse(myY, myX, diaHS, diaHS);

    thisHotSpot.fillColor = hsdColor;
    thisHotSpot.stroked = true;
    thisHotSpot.strokeWidth = hsdStrokeWidth;
    thisHotSpot.strokeColor = hsdStrokeColor;

    return thisHotSpot; // Return the created thisHotSpot
}


/**
 * Returns a transform function that transforms
 * [latitude, longitude] into Illustrator [x, y],
 * given an array of example `pairs`.
 *  m1b and chatGPT
 *  2024-07-03
 *  {Array<Array>} pairs - array of [lat_lon, pts] pairs.
 *  {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.
 * 
 *  chatGPT
 *  2024-07-03
 *  {Array<Array<Number>>} A - The coefficient an n x n matrix of the system of equations.
 *  {Array<Number>} B - The constant terms vector of the system of equations.
 *  {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;

};


function conToMM(n) {
    return n * 2.83464567;
}


function makeCMYKColor(c,m,y,k){
    var ink = new CMYKColor();
    ink.cyan   = c;
    ink.magenta = m;
    ink.yellow  = y;
    ink.black  = k;
    return ink;
}

[pixxxelschubser]

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?

[Nils M. Barner]

Hi pixxxelschubser 😉

I was thinking of setting up a x/y start coordinate to give all points a fixed reference...

Wie meinst du genau mit der Dreisatzberechnung?

[pixxxelschubser]

Hallo Nils,

sofern du die entsprechenden Start und Endkoordinaten passend zu deiner Dokumentengröße verfügbar hast, ist es "simpler Dreisatz".

 

gegeben ist:

ein Dokument in der Größe 200 mm × 297 mm

ein Kartenausschnitt von 9,0° Ost bis 10,0° Ost und 49,0° Nord bis 48,0° Nord

die X-Koordinate von Stuttgart Bad Cannstatt ist fast exakt 9,2° Ost

Berechnung:

also pos X = (X-Koordinate Stuttgart Bad Cannstatt - KarteGeoCoorLinks) * Dokument Rechts / (KarteGeoCoorRechts - KarteGeoCoorLinks)

in mm
pos X = (9,2 - 9) * 200 / (10 - 9)

pos X = (0,2) * 200 / (1)

pos X = 40

bzw in pt

pos X = (9,2 - 9) * 566.929 / (10 - 9)

pos X = (0,2) * 566.929 / (1)

pos X = 113.385826771653

[pixxxelschubser]

Hallo Nils, 

die Variante mit den Start- und Endkoordinaten kommt für dich nicht in Frage?