mongo/jstests/core/geo_big_polygon2.js

//
//  Big Polygon related tests
//  - Tests the capability for a geo query with a big polygon object (strictCRS)
//    $geoWithin & $geoIntersects
//  - Big polygon objects cannot be stored
//    Try all different shapes queries against various stored geo points, line & polygons

var crs84CRS = {
    type: "name",
    properties: {
        name: "urn:ogc:def:crs:OGC:1.3:CRS84"
    }
};
var epsg4326CRS = {
    type: "name",
    properties: {
        name: "EPSG:4326"
    }
};
var strictCRS = {
    type: "name",
    properties: {
        name: "urn:x-mongodb:crs:strictwinding:EPSG:4326"
    }
};
// invalid CRS name
var badCRS = {
    type: "name",
    properties: {
        name: "urn:x-mongodb:crs:invalid:EPSG:4326"
    }
};

// helper to generate a line along a longitudinal
function genLonLine(lon, startLat, endLat, latStep) {
    var line = [];
    for (var lat = startLat; lat <= endLat; lat += latStep) {
        line.push( [ lon, lat ] );
    }
    return line;
}

// Main program
// Clear out collection
var coll = db.geo_bigpoly;
coll.drop();

// GeoJson Objects to be inserted into collection
// coordinates are longitude, latitude
// strictCRS (big polygon) cannot be stored in the collection
var objects = [
    {
        name: "boat ramp",
        geo: {
            type: "Point",
            coordinates: [ -97.927117, 30.327376 ]
        }
    },
    {
        name: "on equator",
        geo: {
            type: "Point",
            coordinates: [ -97.9 , 0 ]
        }
    },
    {
        name: "just north of equator",
        geo: {
            type: "Point",
            coordinates: [ -97.9 , 0.1 ]
        }
    },
    {
        name: "just south of equator",
        geo: {
            type: "Point",
            coordinates: [ -97.9 , -0.1 ]
        }
    },
    {
        name: "north pole - crs84CRS",
        geo: {
            type: "Point",
            coordinates: [ -97.9 , 90.0 ],
            crs: crs84CRS
        }
    },
    {
        name: "south pole - epsg4326CRS",
        geo: {
            type: "Point",
            coordinates: [ -97.9 , -90.0 ],
            crs: epsg4326CRS
        }
    },
    {
        name: "short line string: PA, LA, 4corners, ATX, Mansfield, FL, Reston, NYC",
        geo: {
            type: "LineString",
            coordinates: [
                [ -122.1611953, 37.4420407 ],
                [ -118.283638, 34.028517 ],
                [ -109.045223, 36.9990835 ],
                [ -97.850404, 30.3921555 ],
                [ -97.904187, 30.395457 ],
                [ -86.600836, 30.398147 ],
                [ -77.357837, 38.9589935 ],
                [ -73.987723, 40.7575074 ]
            ]
        }
    },
    {
        name: "1024 point long line string from south pole to north pole",
        geo: {
            type: "LineString",
            coordinates: genLonLine(2.349902, -90.0, 90.0, 180.0 / 1024)
        }
    },
    {
        name: "line crossing equator - epsg4326CRS",
        geo: {
            type: "LineString",
            coordinates: [
                [ -77.0451853, -12.0553442 ],
                [ -76.7784557, 18.0098528 ]
            ],
            crs: epsg4326CRS
        }
    },
    {
        name: "GeoJson polygon",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ -80.0, 30.0 ],
                  [ -40.0, 30.0 ],
                  [ -40.0, 60.0 ],
                  [ -80.0, 60.0 ],
                  [ -80.0, 30.0 ] ]
            ]
        }
    },
    {
        name: "polygon w/ hole",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ -80.0, 30.0 ],
                  [ -40.0, 30.0 ],
                  [ -40.0, 60.0 ],
                  [-80.0, 60.0 ],
                  [ -80.0, 30.0 ] ],
                [ [ -70.0, 40.0 ],
                  [ -60.0, 40.0 ],
                  [ -60.0, 50.0 ],
                  [ -70.0, 50.0 ],
                  [ -70.0, 40.0 ] ]
            ]
        }
    },
    {
        name: "polygon w/ two holes",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ -80.0, 30.0 ],
                  [ -40.0, 30.0 ],
                  [ -40.0, 60.0 ],
                  [ -80.0, 60.0 ],
                  [ -80.0, 30.0 ] ],
                [ [ -70.0, 40.0 ],
                  [ -60.0, 40.0 ],
                  [ -60.0, 50.0 ],
                  [ -70.0, 50.0 ],
                  [ -70.0, 40.0 ] ],
                [ [ -55.0, 40.0 ],
                  [ -45.0, 40.0 ],
                  [ -45.0, 50.0 ],
                  [ -55.0, 50.0 ],
                  [ -55.0, 40.0 ] ]
            ]
        }
    },
    {
        name: "polygon covering North pole",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ -120.0, 89.0 ],
                  [ 0.0, 89.0 ],
                  [ 120.0, 89.0 ],
                  [ -120.0, 89.0 ] ]
            ]
        }
    },
    {
        name: "polygon covering South pole",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ -120.0, -89.0 ],
                  [ 0.0, -89.0 ],
                  [ 120.0, -89.0 ],
                  [ -120.0, -89.0 ] ]
            ]
        }
    },
    {
        name: "big polygon/rectangle covering both poles",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ -130.0, 89.0 ],
                  [ -120.0, 89.0 ],
                  [ -120.0, -89.0 ],
                  [ -130.0, -89.0 ],
                  [ -130.0, 89.0 ] ]
            ],
            crs: strictCRS
        }
    },
    {
        name: "polygon (triangle) w/ hole at North pole",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ -120.0, 80.0 ],
                  [ 0.0, 80.0 ],
                  [ 120.0, 80.0 ],
                  [-120.0, 80.0 ] ],
                [ [ -120.0, 88.0 ],
                  [ 0.0, 88.0 ],
                  [ 120.0, 88.0 ],
                  [-120.0, 88.0 ] ]
            ]
        }
    },
    {
        name: "polygon with edge on equator",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ -120.0, 0.0 ],
                  [ 120.0, 0.0 ],
                  [ 0.0, 90.0 ],
                  [ -120.0, 0.0 ] ]
            ]
        }
    },
    {
        name: "polygon just inside single hemisphere (Northern) - China, California, Europe",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ 120.0, 0.000001 ],
                  [ -120.0, 0.000001 ],
                  [ 0.0, 0.000001 ],
                  [ 120.0, 0.000001 ] ]
            ]
        }
    },
    {
        name: "polygon inside Northern hemisphere",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ 120.0, 80.0 ],
                  [ -120.0, 80.0 ],
                  [ 0.0, 80.0 ],
                  [ 120.0, 80.0 ] ]
            ]
        }
    },
    {
        name: "polygon just inside a single hemisphere (Southern) - Pacific, Indonesia, Africa",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ -120.0, -0.000001 ],
                  [ 120.0, -0.000001 ],
                  [ 0.0, -0.000001 ],
                  [ -120.0, -0.000001 ] ]
            ]
        }
    },
    {
        name: "polygon inside Southern hemisphere",
        geo: {
            type: "Polygon",
            coordinates: [
                [ [ -120.0, -80.0 ],
                  [ 120.0, -80.0 ],
                  [ 0.0, -80.0 ],
                  [ -120.0, -80.0 ] ]
            ]
        }
    },
    {
        name: "single point (MultiPoint): Palo Alto",
        geo: {
            type: "MultiPoint",
            coordinates: [
                [ -122.1611953, 37.4420407 ]
            ]
        }
    },
    {
        name: "multiple points(MultiPoint): PA, LA, 4corners, ATX, Mansfield, FL, Reston, NYC",
        geo: {
            type: "MultiPoint",
            coordinates: [
                [ -122.1611953, 37.4420407 ],
                [ -118.283638, 34.028517 ],
                [ -109.045223, 36.9990835 ],
                [ -97.850404, 30.3921555 ],
                [ -97.904187, 30.395457 ],
                [ -86.600836, 30.398147 ],
                [ -77.357837, 38.9589935 ],
                [ -73.987723, 40.7575074 ]
            ]
        }
    },
    {
        name: "two points (MultiPoint): Shenzhen, Guangdong, China",
        geo: {
            type: "MultiPoint",
            coordinates: [
                [ 114.0538788, 22.5551603 ],
                [ 114.022837, 22.44395 ]
            ]
        }
    },
    {
        name: "two points (MultiPoint) but only one in: Shenzhen, Guangdong, China",
        geo: {
            type: "MultiPoint",
            coordinates: [
                [ 114.0538788, 22.5551603 ],
                [ 113.743858, 23.025815 ]
            ]
        }
    },
    {
        name: "multi line string: new zealand bays",
        geo: {
            type: "MultiLineString",
            coordinates: [
                [ [ 172.803869, -43.592789 ],
                  [ 172.659335, -43.620348 ],
                  [ 172.684038, -43.636528 ],
                  [ 172.820922, -43.605325 ] ],
                [ [ 172.830497, -43.607768 ],
                  [ 172.813263, -43.656319 ],
                  [ 172.823096, -43.660996 ],
                  [ 172.850943, -43.607609 ] ],
                [ [ 172.912056, -43.623148 ],
                  [ 172.887696, -43.670897 ],
                  [ 172.900469, -43.676178 ],
                  [ 172.931735, -43.622839 ] ]
            ]
        }
    },
    {
        name: "multi polygon: new zealand north and south islands",
        geo: {
            type: "MultiPolygon",
            coordinates: [
                [
                  [ [ 165.773255, -45.902933 ],
                    [ 169.398419, -47.261538 ],
                    [ 174.672744, -41.767722 ],
                    [ 172.288845, -39.897992 ],
                    [ 165.773255, -45.902933 ] ]
                ],
                [
                  [ [ 173.166448, -39.778262 ],
                    [ 175.342744, -42.677333 ],
                    [ 179.913373, -37.224362 ],
                    [ 171.475953, -32.688871 ],
                    [ 173.166448, -39.778262 ] ]
                ]
            ]
        }
    },
    {
        name: "geometry collection: point in Australia and triangle around Australia",
        geo: {
            type: "GeometryCollection",
            geometries: [
                {
                    name: "center of Australia",
                    type: "Point",
                    coordinates: [ 133.985885, -27.240790 ]
                },
                {
                    name: "Triangle around Australia",
                    type: "Polygon",
                    coordinates: [
                        [ [ 97.423178, -44.735405 ],
                          [ 169.845050, -38.432287 ],
                          [ 143.824366, 15.966509 ],
                          [ 97.423178, -44.735405 ] ]
                    ]
                }
            ]
        }
    }
];


// Test various polygons which are not queryable
var badPolys = [
    {
        name: "Polygon with bad CRS",
        type: "Polygon",
        coordinates: [
            [ [ 114.0834046, 22.6648202 ],
              [ 113.8293457, 22.3819359 ],
              [ 114.2736054, 22.4047911 ],
              [ 114.0834046, 22.6648202 ] ]
        ],
        crs: badCRS
    },
    {
        name: "Open polygon < 3 sides",
        type: "Polygon",
        coordinates: [
            [ [ 114.0834046, 22.6648202 ],
              [ 113.8293457, 22.3819359 ] ]
        ],
        crs: strictCRS
    },
    {
        name: "Open polygon > 3 sides",
        type: "Polygon",
        coordinates: [
            [  [ 114.0834046, 22.6648202 ],
               [ 113.8293457, 22.3819359 ],
               [ 114.2736054, 22.4047911 ],
               [ 114.1, 22.5 ] ]
        ],
        crs: strictCRS
    },
    {
        name: "duplicate non-adjacent points",
        type: "Polygon",
        coordinates: [
            [  [ 114.0834046, 22.6648202 ],
               [ 113.8293457, 22.3819359 ],
               [ 114.2736054, 22.4047911 ],
               [ 113.8293457, 22.3819359 ],
               [ -65.9165954, 22.6648202 ],
               [ 114.0834046, 22.6648202 ] ]
        ],
        crs: strictCRS
    },
    {
        name: "One hole in polygon",
        type: "Polygon",
        coordinates: [
            [  [ -80.0, 30.0 ],
               [ -40.0, 30.0 ],
               [ -40.0, 60.0 ],
               [ -80.0, 60.0 ],
               [ -80.0, 30.0 ] ],
            [  [ -70.0, 40.0 ],
               [ -60.0, 40.0 ],
               [ -60.0, 50.0 ],
               [ -70.0, 50.0 ],
               [ -70.0, 40.0 ] ]
        ],
        crs: strictCRS
    },
    {
        name: "2 holes in polygon",
        type: "Polygon",
        coordinates: [
            [  [ -80.0, 30.0 ],
               [ -40.0, 30.0 ],
               [ -40.0, 60.0 ],
               [ -80.0, 60.0 ],
               [ -80.0, 30.0 ] ],
            [  [ -70.0, 40.0 ],
               [ -60.0, 40.0 ],
               [ -60.0, 50.0 ],
               [ -70.0, 50.0 ],
               [ -70.0, 40.0 ] ],
            [  [ -55.0, 40.0 ],
               [ -45.0, 40.0 ],
               [ -45.0, 50.0 ],
               [ -55.0, 50.0 ],
               [ -55.0, 40.0 ] ]
        ],
        crs: strictCRS
    },
    {
        name: "complex polygon (edges cross)",
        type: "Polygon",
        coordinates: [
            [  [ 10.0, 10.0 ],
               [ 20.0, 10.0 ],
               [ 10.0, 20.0 ],
               [ 20.0, 20.0 ],
               [ 10.0, 10.0 ] ]
        ],
        crs: strictCRS
    }
];


// Closed polygons used in query (3, 4, 5, 6-sided)
var polys = [
    {
        name: "3 sided closed polygon",
        type: "Polygon",  // triangle
        coordinates: [ [
            [ 10.0, 10.0 ],
            [ 20.0, 10.0 ],
            [ 15.0, 17.0 ],
            [ 10.0, 10.0 ]
        ] ],
        crs: strictCRS,
        nW: 0, nI: 1
    },
    {
        name: "3 sided closed polygon (non-big)",
        type: "Polygon",  // triangle
        coordinates: [ [
            [ 10.0, 10.0 ],
            [ 20.0, 10.0 ],
            [ 15.0, 17.0 ],
            [ 10.0, 10.0 ]
        ] ],
        nW: 0, nI: 1
    },
    {
        name: "4 sided closed polygon",
        type: "Polygon",  // rectangle
        coordinates: [ [
            [ 10.0, 10.0 ],
            [ 20.0, 10.0 ],
            [ 20.0, 20.0 ],
            [ 10.0, 20.0 ],
            [ 10.0, 10.0 ]
        ] ],
        crs: strictCRS,
        nW: 0, nI: 1
    },
    {
        name: "4 sided closed polygon (non-big)",
        type: "Polygon",  // rectangle
        coordinates: [
            [ [ 10.0, 10.0 ],
              [ 20.0, 10.0 ],
              [ 20.0, 20.0 ],
              [ 10.0, 20.0 ],
              [ 10.0, 10.0 ] ]
        ],
        nW: 0, nI: 1
    },
    {
        name: "5 sided closed polygon",
        type: "Polygon",  // pentagon
        coordinates: [ [
            [ 10.0, 10.0 ],
            [ 20.0, 10.0 ],
            [ 25.0, 18.0 ],
            [ 15.0, 25.0 ],
            [ 5.0,  18.0 ],
            [ 10.0, 10.0 ]
        ] ],
        crs: strictCRS,
        nW: 0, nI: 1
    },
    {
        name: "5 sided closed polygon (non-big)",
        type: "Polygon",  // pentagon
        coordinates: [ [
            [ 10.0, 10.0 ],
            [ 20.0, 10.0 ],
            [ 25.0, 18.0 ],
            [ 15.0, 25.0 ],
            [ 5.0,  18.0 ],
            [ 10.0, 10.0 ]
        ] ],
        nW: 0, nI: 1
    },
    {
        name: "6 sided closed polygon",
        type: "Polygon",  // hexagon
        coordinates: [ [
            [ 10.0, 10.0 ],
            [ 15.0, 10.0 ],
            [ 22.0, 15.0 ],
            [ 15.0, 20.0 ],
            [ 10.0, 20.0 ],
            [ 7.0,  15.0 ],
            [ 10.0, 10.0 ]
        ] ],
        crs: strictCRS,
        nW: 0, nI: 1
    },
    {
        name: "6 sided closed polygon (non-big)",
        type: "Polygon",  // hexagon
        coordinates: [ [
            [ 10.0, 10.0 ],
            [ 15.0, 10.0 ],
            [ 22.0, 15.0 ],
            [ 15.0, 20.0 ],
            [ 10.0, 20.0 ],
            [ 7.0,  15.0 ],
            [ 10.0, 10.0 ]
        ] ],
        nW: 0, nI: 1
    }
];

// helper function to create n-sided polygon
function nGonGenerator(N, D, clockwise, LON, LAT) {
    // compute N points on a circle centered at LAT,LON
    // with diameter = D
    // and lat*lat + lon*lon = (D/2)*(D/2)
    // lat range is -10 to +10
    // lon = sqrt( (D/2)*(D/2) - lat*lat )
    // N = number of edges
    // N must be even!
    // edge lengths will be uneven with this quick & dirty approach
    N = (N % 2 == 1) ? N + 1 : N;
    var eps = 2 * D / N;
    var lat=0;
    var lon=0;
    var pts = [];
    var i = 0;
    // produce longitude values in pairs
    // traverse with left foot outside the circle (clockwise) to define the big polygon
    for (i = 0, lat = D / 2; i <= N / 2; ++i, lat -= eps) {
        if ( lat < (-D / 2) ) {
            // set fixing lat
            lat = (-D / 2);
        }
        lon = Math.sqrt( (D / 2) * (D / 2) - (lat * lat) );
        newlat = lat + LAT;
        newlon = lon + LON;
        conjugateLon = LON - lon;
        pts[i] = [ newlon, newlat ];
        pts[N-i] = [ conjugateLon, newlat ];
    }
    // Reverse points if counterclockwise
    if (!clockwise) {
        pts = pts.reverse();
    }
    // ensure we connected the dots
    assert(tojson(pts[0]) == tojson(pts[N]));
    return pts;
}

// helper function to return number of valid objects
function getNumberOfValidObjects(objects) {
    var i = 0;
    objects.forEach(function(o) {
        // strictCRS cannot be stored
        if (!o.geo.crs || o.geo.crs != strictCRS) {
            i++;
        }
    });
    return i;
}

var totalObjects = getNumberOfValidObjects(objects);

// test various n-sided polygons in query, (n: <number of sides>, d: <diameter>)
// Try them in both clockwise & counterclockwise order
var nsidedPolys = [
    // Big Polygon centered on 0, 0
    {
        name: "4 sided polygon centered on 0, 0",
        type: "Polygon",
        coordinates: [
            nGonGenerator(4, 30, true, 0, 0)
        ],
        crs: strictCRS,
        nW: totalObjects - 3,
        nI: totalObjects
    },
    // Non-big polygons have counterclockwise coordinates
    {
        name: "4 sided polygon centered on 0, 0 (non-big)",
        type: "Polygon",
        coordinates: [
            nGonGenerator(4, 30, false, 0, 0)
        ],
        nW: 0,
        nI: 3
    },
    {
        name: "100 sided polygon centered on 0, 0",
        type: "Polygon",
        coordinates: [
            nGonGenerator(100, 20, true, 0, 0)
        ],
        crs: strictCRS,
        nW: totalObjects - 3,
        nI: totalObjects
    },
    {
        name: "100 sided polygon centered on 0, 0 (non-big)",
        type: "Polygon",
        coordinates: [
            nGonGenerator(100, 20, false, 0, 0)
        ],
        nW: 0,
        nI: 3
    },
    {
        name: "5000 sided polygon centered on 0, 0 (non-big)",
        type: "Polygon",
        coordinates: [
            nGonGenerator(5000, 89.99, false, 0, 0)
        ],
        nW: 0,
        nI: 3
    },
    {
        name: "25000 sided polygon centered on 0, 0",
        type: "Polygon",
        coordinates: [
            nGonGenerator(25000, 89.99, true, 0, 0)
        ],
        crs: strictCRS,
        nW: totalObjects - 3,
        nI: totalObjects
    },
    // Big polygon centered on Shenzen
    {
        name: "4 sided polygon centered on Shenzen",
        type: "Polygon",
        coordinates: [
            nGonGenerator(4, 5, true, 114.1, 22.55)
        ],
        crs: strictCRS,
        nW: totalObjects - 3,
        nI: totalObjects - 2
    },
    {
        name: "4 sided polygon centered on Shenzen (non-big)",
        type: "Polygon",
        coordinates: [
            nGonGenerator(4, 5, false, 114.1, 22.55)
        ],
        crs: strictCRS,
        nW: 2,
        nI: 3
    }
];

// Populate with 2dsphere index
assert.commandWorked(coll.ensureIndex({geo: "2dsphere"}), "create 2dsphere index");

// Insert objects into collection
objects.forEach(function(o) {
    // strictCRS objects cannot be stored
    if (o.geo.crs && o.geo.crs == strictCRS) {
        assert.writeError(coll.insert(o), "insert " + o.name);
    } else {
        assert.writeOK(coll.insert(o), "insert " + o.name);
    }
});

// Try creating other index types
assert.commandWorked(
    coll.ensureIndex({geo: "2dsphere", a: 1}),
    "compound index, geo");
// These other index types will fail because of the GeoJSON documents
assert.commandFailed(
    coll.ensureIndex({geo: "2dsphere", a: "text"}),
    "compound index, geo & text");
assert.commandFailed(
    coll.ensureIndex({geo: "geoHaystack" }, {bucketSize:1}),
    "geoHaystack index");
assert.commandFailed(
    coll.ensureIndex({geo: "2d"}),
    "2d index");

totalObjects = coll.count();

// Test with none & 2dsphere index
var indexes = ["none", "2dsphere"];

indexes.forEach(function(index) {

    // Reset indexes on collection
    assert.commandWorked(coll.dropIndexes(), "drop indexes");

    if (index != "none") {
        // Create index
        assert.commandWorked(coll.ensureIndex({geo: index}), "create " +  index + " index");
    }

    // These polygons should not be queryable
    badPolys.forEach(function(p) {

        // within
        assert.throws(function() {
            coll.count({geo: {$geoWithin: {$geometry: p}}});},
            null,
            "within " + p.name);

        // intersection
        assert.throws(function() {
            coll.count({geo: {$geoIntersects: {$geometry: p}}});},
            null,
            "intersects " + p.name);
    });


    // Tests for closed polygons
    polys.forEach(function(p) {

        // geoWithin query
        var docArray = [];
        var q = {geo: {$geoWithin: {$geometry: p}}};
        // Test query in aggregate
        docArray = coll.aggregate({$match: q}).toArray();
        assert.eq(p.nW, docArray.length, "aggregate within " + p.name);
        docArray = coll.find(q).toArray();
        assert.eq(p.nW, docArray.length, "within " + p.name);

        // geoIntersects query
        q = {geo: {$geoIntersects: {$geometry: p}}};
        // Test query in aggregate
        docArray = coll.aggregate({$match: q}).toArray();
        assert.eq(p.nI, docArray.length, "aggregate intersects " + p.name);
        docArray = coll.find(q).toArray();
        assert.eq(p.nI, docArray.length, p.name + " intersects");
        // Update on matching docs
        var result = coll.update(q, {$set: {stored: ObjectId()}}, {multi: true});
        // only check nModified if write commands are enabled
        if ( coll.getMongo().writeMode() == "commands" ) {
            assert.eq(p.nI, result.nModified, "update " + p.name);
        }
        // Remove & restore matching docs
        assert.eq(p.nI, coll.remove(q).nRemoved, "remove " + p.name);
        var bulk = coll.initializeUnorderedBulkOp();
        docArray.forEach(function(doc) {
            bulk.insert(doc);
        });
        assert.eq(docArray.length, bulk.execute().nInserted, "reinsert " + p.name);

    });

    // test the n-sided closed polygons
    nsidedPolys.forEach(function(p) {

        // within
        assert.eq(p.nW,
            coll.count({geo: {$geoWithin: {$geometry: p}}}),
            "within " + p.name);

        // intersects
        assert.eq(p.nI,
            coll.count({geo: {$geoIntersects: {$geometry: p}}}),
            "intersection " + p.name);

    });

});