Creates an outline to a lineString similar to the outline stroke feature in illustrator

input.geojson

lineStringOutline.js

// Example Result (e.g. paste into http://geojson.io)
// {"type":"Feature","properties":{},"geometry":{"type":"Polygon","coordinates":[[[7.162147402259639,51.95323664248935],[9.397525357884254,52.01990267103883],[10.276573430855475,52.73102957225263],[11.384078028489244,52.73187278993396],[12.440828207929341,52.53150641982873],[12.432220352373731,52.51430530461843],[11.379594760127718,52.71409821694048],[10.28983037386654,52.714941107317614],[9.41106598137281,52.0039700143863],[7.16402409736249,51.93529310810906],[7.162147402259639,51.95323664248935]]]}}

var turf = require('turf');

var ls = {
    "type": "Feature",
    "properties": {},
    "geometry": {
        "type": "LineString",
        "coordinates": [
            [
                7.163085937499999,
                51.944264879028765
            ],
            [
                9.404296875,
                52.01193653675363
            ],
            [
                10.283203125,
                52.72298552457069
            ],
            [
                11.3818359375,
                52.72298552457069
            ],
            [
                12.436523437499998,
                52.522905940278065
            ]
        ]
    }
}

console.log();
console.log('Input');
console.log(JSON.stringify(ls));
console.log();
console.log('Output');
console.log(JSON.stringify(computeOutline(ls, 2)));

function computeOutline(lineString, thickness) {
    // thickness in km

    // Start
    var uppers = [];
    var lowers = [];
    var newCoordinates = [];
    var r = thickness / 2;
    var coordinates = lineString.geometry.coordinates;
    var initialBearing = turf.bearing(turf.point(coordinates[0]), turf.point(coordinates[1]));
    var firstUpper = turf.destination(turf.point(coordinates[0]), r, initialBearing - 90);
    var firstLower = turf.destination(turf.point(coordinates[0]), r, initialBearing + 90);

    newCoordinates.push(firstUpper.geometry.coordinates);

    // Mid
    for (var i = 1; i < coordinates.length - 1; i++) {
        var prev = coordinates[i - 1];
        var curr = coordinates[i];
        var next = coordinates[i + 1];
        var bearingFromPrev = turf.bearing(turf.point(curr), turf.point(prev));
        var bearingToNext = turf.bearing(turf.point(curr), turf.point(next));
        var bearingMid = (bearingFromPrev + bearingToNext) / 2;
        var upper = turf.destination(turf.point(curr), r, bearingMid);
        var lower = turf.destination(turf.point(curr), r, bearingMid + 180);
        newCoordinates.push(upper.geometry.coordinates);
        lowers.push(lower.geometry.coordinates);
    }

    lowers.reverse()

    // End
    var lastBearing = turf.bearing(turf.point(coordinates[coordinates.length - 2]), turf.point(coordinates[coordinates.length - 1]));
    var lastUpper = turf.destination(turf.point(coordinates[coordinates.length - 1]), r, lastBearing - 90);
    var midLower = turf.destination(turf.point(coordinates[coordinates.length - 1]), r, lastBearing + 90);

    newCoordinates.push(lastUpper.geometry.coordinates);
    newCoordinates.push(midLower.geometry.coordinates);
    newCoordinates = newCoordinates.concat( lowers );
    newCoordinates.push(firstLower.geometry.coordinates);
    newCoordinates.push(newCoordinates[0]);
    return turf.polygon([newCoordinates]);
}

output.geojson