查找多边形中多段线段的总距离

我有一个地图，它将由多个"区域"组成，每个区域都创建为多边形覆盖。我还允许用户定义路线，并使用DirectionsService将路线渲染为同一地图上的多段线https://i.stack.imgur.com/DDZI1.png.你可以看到两个区域，一个是绿色，另一个是蓝色，路线是红色。在最终版本中，最多可以定义30个区域。

我需要做的是计算多段线（管线）在每个分区中花费的距离。根据道路的曲折程度，路线可能多次进出一个区域，也有可能完全存在于一个区域内，而不与区域边界相交。

我该怎么办？

这是我目前拥有的代码，它只需在地图上添加两个区域并绘制线。我还添加了"包含"方法，该方法允许我确定坐标是否位于多边形内，我使用该多边形在地图上为位于区域"a"的线段绘制新的多段线（黑色）。然而，这还不够具体，无法知道它第一次进入区域的时间，这可能发生在顶点之间。

// Functions ===============
// =========================
var calcRoute = function (start, end) {
var request = {
    origin: start,
    destination: end,
    travelMode: google.maps.TravelMode.DRIVING,
    provideRouteAlternatives: false,
    avoidHighways: false,
    avoidTolls: false,
    optimizeWaypoints: false
};
// Load directions
directions.service.route(request, function (result, status) {
    if (status == google.maps.DirectionsStatus.OK) {
        // Iterate through each route, adding it to th map
        $(result.routes).each(function onEach(index, route) {
            // Create a new Polyline, set its path to the route path
            var line = new google.maps.Polyline({
                path: route.overview_path,
                strokeColor: "#FF0000",
                strokeOpacity: 1,
                strokeWeight: 2
            });
            // Add line to the map
            line.setMap(map);
            // Find individual line segments
            var inside = [];
            var vertices = line.getPath();
            for (var i = 0; i < vertices.length; i++) {
                var vertix = vertices.getAt(i);
                // Check to see if the vertix exists within a specified Polygon
                if (zones.a.polygon.contains(vertix)) {
                    inside.push(vertix);
                }
            }
            // Add another Polyline for the segments inside the polygon
            var line = new google.maps.Polyline({
                path: inside,
                strokeColor: "#000000",
                strokeOpacity: 1,
                strokeWeight: 4
            });
            // Add line to the map
            line.setMap(map);
        });
    }
});
}
// ray casting alogrithm http://rosettacode.org/wiki/Ray-casting_algorithm
google.maps.Polygon.prototype.contains = function(point) {
var crossings = 0,
    path = this.getPath();
// for each edge
for (var i=0; i < path.getLength(); i++) {
    var a = path.getAt(i),
        j = i + 1;
    if (j >= path.getLength()) {
        j = 0;
    }
    var b = path.getAt(j);
    if (rayCrossesSegment(point, a, b)) {
        crossings++;
    }
}
// odd number of crossings?
return (crossings % 2 == 1);
function rayCrossesSegment(point, a, b) {
    var px = point.lng(),
        py = point.lat(),
        ax = a.lng(),
        ay = a.lat(),
        bx = b.lng(),
        by = b.lat();
    if (ay > by) {
        ax = b.lng();
        ay = b.lat();
        bx = a.lng();
        by = a.lat();
    }
    // alter longitude to cater for 180 degree crossings
    if (px < 0) { px += 360 };
    if (ax < 0) { ax += 360 };
    if (bx < 0) { bx += 360 };
    if (py == ay || py == by) py += 0.00000001;
    if ((py > by || py < ay) || (px > Math.max(ax, bx))) return false;
    if (px < Math.min(ax, bx)) return true;
    var red = (ax != bx) ? ((by - ay) / (bx - ax)) : Infinity;
    var blue = (ax != px) ? ((py - ay) / (px - ax)) : Infinity;
    return (blue >= red);
}
};

// Variables ===============
// =========================
var $map = document.getElementById('map_canvas'),
defaultLocation = new google.maps.LatLng(-37.813553, 144.96341899999993), // Melbourne CBD
directions = {
    display: new google.maps.DirectionsRenderer(),
    service: new google.maps.DirectionsService()
},
initialLocation = defaultLocation,
map = null,
options = {
    center: initialLocation,
    mapTypeId: google.maps.MapTypeId.ROADMAP,
    zoom: 13
},
zones = {
    a: {
        options: {
            path: [
                new google.maps.LatLng(-37.839848,144.916192),
                new google.maps.LatLng(-37.831374,144.911557),
                new google.maps.LatLng(-37.822358,144.911128),
                new google.maps.LatLng(-37.806627,144.908038),
                new google.maps.LatLng(-37.794148,144.914218),
                new google.maps.LatLng(-37.787636,144.924518),
                new google.maps.LatLng(-37.788586,144.947520),
                new google.maps.LatLng(-37.787365,144.950953),
                new google.maps.LatLng(-37.789536,144.958507),
                new google.maps.LatLng(-37.793063,144.966060),
                new google.maps.LatLng(-37.792656,144.975501),
                new google.maps.LatLng(-37.807983,144.972239),
                new google.maps.LatLng(-37.815035,144.975158),
                new google.maps.LatLng(-37.833069,144.971210),
                new google.maps.LatLng(-37.836594,144.968463),
                new google.maps.LatLng(-37.849066,144.950438),
                new google.maps.LatLng(-37.839848,144.916192)
            ],
            fillColor: "#00FF00",
            fillOpacity: 0.35,
            strokeColor: "#00FF00",
            strokeOpacity: 1,
            strokeWeight: 2
        },
        polygon: null
    }, // End zone a
    b: {
        options: {
            path: [
                new google.maps.LatLng(-37.840119,144.915591),
                new google.maps.LatLng(-37.865465,144.914561),
                new google.maps.LatLng(-37.867905,144.908467),
                new google.maps.LatLng(-37.871970,144.902974),
                new google.maps.LatLng(-37.859096,144.873277),
                new google.maps.LatLng(-37.867498,144.843064),
                new google.maps.LatLng(-37.870208,144.838944),
                new google.maps.LatLng(-37.815984,144.849587),
                new google.maps.LatLng(-37.812187,144.860230),
                new google.maps.LatLng(-37.781531,144.864350),
                new google.maps.LatLng(-37.770134,144.865724),
                new google.maps.LatLng(-37.757378,144.859544),
                new google.maps.LatLng(-37.728872,144.867097),
                new google.maps.LatLng(-37.734574,144.904176),
                new google.maps.LatLng(-37.732673,144.920999),
                new google.maps.LatLng(-37.746791,145.022622),
                new google.maps.LatLng(-37.764706,145.020562),
                new google.maps.LatLng(-37.764435,145.027085),
                new google.maps.LatLng(-37.790485,145.027429),
                new google.maps.LatLng(-37.792927,145.031205),
                new google.maps.LatLng(-37.826561,145.025369),
                new google.maps.LatLng(-37.837136,145.026742),
                new google.maps.LatLng(-37.836865,145.037042),
                new google.maps.LatLng(-37.845812,145.039445),
                new google.maps.LatLng(-37.847710,145.042535),
                new google.maps.LatLng(-37.871292,145.038415),
                new google.maps.LatLng(-37.879693,145.034295),
                new google.maps.LatLng(-37.884571,145.038758),
                new google.maps.LatLng(-37.903807,145.035325),
                new google.maps.LatLng(-37.927371,145.029145),
                new google.maps.LatLng(-37.931433,145.025712),
                new google.maps.LatLng(-37.975560,145.015412),
                new google.maps.LatLng(-37.969606,145.008546),
                new google.maps.LatLng(-37.961485,145.011292),
                new google.maps.LatLng(-37.944701,144.995843),
                new google.maps.LatLng(-37.937932,144.996873),
                new google.maps.LatLng(-37.925476,144.984857),
                new google.maps.LatLng(-37.911392,144.984857),
                new google.maps.LatLng(-37.894054,144.985200),
                new google.maps.LatLng(-37.881861,144.977647),
                new google.maps.LatLng(-37.856927,144.966660),
                new google.maps.LatLng(-37.849066,144.951554),
                new google.maps.LatLng(-37.837136,144.969064),
                new google.maps.LatLng(-37.833340,144.971810),
                new google.maps.LatLng(-37.814899,144.976274),
                new google.maps.LatLng(-37.807847,144.973527),
                new google.maps.LatLng(-37.792384,144.976274),
                new google.maps.LatLng(-37.791299,144.967004),
                new google.maps.LatLng(-37.785873,144.952584),
                new google.maps.LatLng(-37.786958,144.947434),
                new google.maps.LatLng(-37.786144,144.924088),
                new google.maps.LatLng(-37.791842,144.915162),
                new google.maps.LatLng(-37.805135,144.906236),
                new google.maps.LatLng(-37.820052,144.908982),
                new google.maps.LatLng(-37.831171,144.910012),
                new google.maps.LatLng(-37.840119,144.915591)
            ],
            fillColor: "#0000FF",
            fillOpacity: 0.35,
            strokeColor: "#0000FF",
            strokeOpacity: 1,
            strokeWeight: 2
        }
    } // End zone b
};

// Load reference to map
map = new google.maps.Map($map, options);
// Load zones
zones.a.polygon = new google.maps.Polygon(zones.a.options);
zones.a.polygon.setMap(map);
zones.b.polygon = new google.maps.Polygon(zones.b.options);
zones.b.polygon.setMap(map);
// Load route
calcRoute(
    'Dandenong',
    'South Melbourne'
);