Polar coordinate grid

Hi there. I've found some maps for Antarctica here: https://nga.maps.arcgis.com/home/webmap/viewer.html and my question is: How can I show polar coordinate grid for it? I've got the grid source code in grid_wgs.js (I use OpenSeaMap in my software that is based on OpenStreetMap), so I guess I just need to change some mathematical formulas there, but I've got no idea how to do that / what to change etc. Here's the grid_wgs.js code below. I appreciate any ideas and suggestions. Thanks.

//--------------------------------------------------------------------------------
// $Id: grid_wgs.js,v 1.6 2011/02/02 20:37:31 wolf Exp wolf $
//--------------------------------------------------------------------------------
// Erklärung: http://www.netzwolf.info/kartografie/openlayers/wgsgrid
//--------------------------------------------------------------------------------
// Fragen, Wuensche, Bedenken, Anregungen?
// <openlayers(%40)netzwolf.info>
//--------------------------------------------------------------------------------

OpenLayers.Layer.GridWGS = OpenLayers.Class (OpenLayers.Layer.Vector, {

    initialize: function (name, options){
        OpenLayers.Layer.Vector.prototype.initialize.apply(this, [name, options]);
    },

    gridSizeText: null,

    gridSizeDiv: null,

    zoomUnits: null,

    //---------------------------------------------------------
    // Find matching grid unit (minutes) or return null
    //---------------------------------------------------------

    getGridUnit: function (distance) {

        if (this.zoomUnits) return this.zoomUnits[this.map.zoom];

        for (var i=0; i<this.gridUnits.length; i++) {
            if (distance<this.gridUnits[i])
                return this.gridUnits[i];
        }
        return null;
    },

    // in Winkelsekunden
    gridUnits: [
        //3,        // 0.05'
        6, 12, 30,  // 0.1'  0.2'  0.5'
        1*60, 2*60, 3*60, 5*60, 10*60, 20*60, 30*60,
        1*3600, 2*3600, 3*3600, 4*3600, 6*3600, 10*3600, 15*3600, 30*3600, 45*3600],

    gridPixelDistance: 100,

    //---------------------------------------------------------
    // Format gridsize
    //---------------------------------------------------------

    dd: function (n) {
        return parseInt(n)>=10 ? n : '0'+n;
    },

    formatGridSize: function (s) {
        var h = Math.floor(s/3600);
        var m = s%3600/60;
        return (h?h+"°":"")+(m?m+"'":"");
    },

    formatDegrees: function (s, unit) {
        return Math.floor(s/3600) + "°"
            + (unit%3600?this.dd(s%3600/60)+"'":"")
    },

    //---------------------------------------------------------
    // Draw grid on move or zoom
    //---------------------------------------------------------

    moveTo: function (bounds, zoomChanged, dragging) {

        //---------------------------------------------------------
        // but not while dragging
        //---------------------------------------------------------

        if (dragging) return;

        //---------------------------------------------------------
        // Remove old grid
        //---------------------------------------------------------

        this.destroyFeatures();

        //---------------------------------------------------------

        //---------------------------------------------------------

        var mapBounds = bounds.clone().
            transform(this.map.getProjectionObject(), this.map.displayProjection);

        //---------------------------------------------------------
        // Grid unit
        //---------------------------------------------------------

        var seconds = 3600 * (mapBounds.top-mapBounds.bottom);

        var unit = this.getGridUnit (seconds / this.map.getSize().h * this.gridPixelDistance);

        //---------------------------------------------------------
        // Grid size display object
        // (TODO: create a OpenLayers.Control-Object)
        //---------------------------------------------------------

        if (this.gridSizeText && !this.gridSizeDiv) {
            this.gridSizeDiv=OpenLayers.Util.createDiv(this.id);
            this.gridSizeDiv.className='olControlGridWGS';
            this.gridSizeDiv.style.zIndex=map.Z_INDEX_BASE['Control']+ map.controls.length;
            this.gridSizeDiv.setAttribute("unselectable","on");
            this.map.viewPortDiv.appendChild (this.gridSizeDiv);
        }

        //---------------------------------------------------------
        // Hide grid size (if configured)
        //---------------------------------------------------------

        if (this.gridSizeDiv) this.gridSizeDiv.style.display='none';

        //---------------------------------------------------------
        // Create new grid
        //---------------------------------------------------------

        if (unit) {

            //---------------------------------------------------------
            // Compute grid
            //---------------------------------------------------------

            var x1 = Math.max (-180.0*3600, Math.ceil  (3600 * mapBounds.left  / unit) * unit);
            var x2 = Math.min (+180.0*3600, Math.floor (3600 * mapBounds.right / unit) * unit);
            var y1 = Math.max ( -90.0*3600, Math.ceil  (3600 * mapBounds.bottom/ unit) * unit);
            var y2 = Math.min ( +90.0*3600, Math.floor (3600 * mapBounds.top   / unit) * unit);

            var features = [];

            //---------------------------------------------------------
            // Vertical lines
            //---------------------------------------------------------

            for (var x=x1; x<=x2; x+= unit) {
                var p1 = new OpenLayers.LonLat (x/3600, Math.min(+85, mapBounds.top))
                    .transform(map.displayProjection, map.getProjectionObject());
                var p2 = new OpenLayers.LonLat (x/3600, Math.max(-85, mapBounds.bottom))
                    .transform(map.displayProjection, map.getProjectionObject());
                v1 = new OpenLayers.Feature.Vector ( new OpenLayers.Geometry.LineString( [
                    new OpenLayers.Geometry.Point (p1.lon, p1.lat),
                    new OpenLayers.Geometry.Point (p2.lon, p2.lat)
                ]));
                v1.style={
                    label: this.formatDegrees (Math.abs(x), unit),
                    labelAlign: "lt",
                    strokeColor: "#666666",
                    strokeWidth: 1,
                    strokeOpacity: 0.8
                };
                features.push (v1);
            }

            //---------------------------------------------------------
            // Horizontal lines
            //---------------------------------------------------------

            for (var y=y1; y<=y2; y+=unit) {
                var p1 = new OpenLayers.LonLat (Math.max(-180, mapBounds.left), y/3600)
                    .transform(map.displayProjection, map.getProjectionObject());
                var p2 = new OpenLayers.LonLat (Math.min(+180, mapBounds.right), y/3600)
                    .transform(map.displayProjection, map.getProjectionObject());
                v1 = new OpenLayers.Feature.Vector ( new OpenLayers.Geometry.LineString( [
                    new OpenLayers.Geometry.Point (p1.lon, p1.lat),
                    new OpenLayers.Geometry.Point (p2.lon, p2.lat)
                ]));
                v1.style={
                    label: this.formatDegrees (Math.abs(y), unit),
                    labelAlign: "lb",
                    strokeColor: "#666666",
                    strokeWidth: 1,
                    strokeOpacity: 0.8
                };
                features.push (v1);
            }

            //---------------------------------------------------------
            // Add grid lines to vector layer
            //---------------------------------------------------------

            this.addFeatures(features);

            //---------------------------------------------------------
            // Display grid size
            //---------------------------------------------------------

            if (this.gridSizeDiv) {
                this.gridSizeDiv.innerHTML = OpenLayers.String.format(this.gridSizeText,
                    {grid: this.formatGridSize(unit)});
                this.gridSizeDiv.style.display=null;
            }
        }

        //---------------------------------------------------------
        // Superclass
        //---------------------------------------------------------

        OpenLayers.Layer.Vector.prototype.moveTo.apply(this,arguments);
    },

    CLASS_NAME: "OpenLayers.Layer.GridWGS"
});

//--------------------------------------------------------------------------------
// $Id: grid_wgs.js,v 1.6 2011/02/02 20:37:31 wolf Exp wolf $
//--------------------------------------------------------------------------------