地理空间 $nearSphere 运算符如何与 LineString 和 Polygon 交互

Question

根据文档，2dSphere geospatial index 也可用于复杂的 GeoJSON 形状，例如由多个节点组成的 LineString 和 Polygon。

当您使用 $nearSphere 搜索填充了此类复杂形状的字段以查找与另一个 GeoJSON 对象（也可能是复杂形状）的接近度时，如何计算这些形状的距离？

它会比较形状的最近节点吗？最远的节点？节点的一些平均值？形状的任何边缘上的最近点？

Answer 1

$nearSphere 运算符仅允许您指定一个点（您可以通过提供maxDistance 参数来定义“球体”的中心）。因此，唯一有意义的答案可能是关于形状如何排序最近到最远。

答案是，所有具有等距“最近”点的形状都将排在距离最近点较远的形状之前。换句话说，点到形状的距离就是点到形状上最近点的距离。

我们可以看到，通过运行$nearSphere 的变体$geoNear 命令，它返回计算出的距离，然后我们可以检查。

我们的样本数据：

> db.near.find()
{ "_id" : 10, "loc" : { "type" : "Polygon", "coordinates" : [ [ [ 0, 0 ], [ 0, 5 ], [ 5, 5 ], [ 5, 0 ], [ 0, 0 ] ] ] } }
{ "_id" : 11, "loc" : { "type" : "Polygon", "coordinates" : [ [ [ 1, 1 ], [ 1, 5 ], [ 5, 5 ], [ 5, 1 ], [ 1, 1 ] ] ] } }
{ "_id" : 12, "loc" : { "type" : "Polygon", "coordinates" : [ [ [ 0, 0 ], [ 0, 6 ], [ 6, 6 ], [ 6, 0 ], [ 0, 0 ] ] ] } }
{ "_id" : 13, "loc" : { "type" : "Polygon", "coordinates" : [ [ [ 0, 0 ], [ 0, 6 ], [ 6, 6 ], [ 6, 0 ], [0, 0 ] ], [ [ 1, 1 ], [ 1, 5 ], [ 5, 5 ], [ 5, 1 ], [ 1, 1 ] ] ] } }
{ "_id" : 14, "loc" : { "type" : "Polygon", "coordinates" : [ [ [ 0, 0 ], [ 0, 6 ], [ 6, 6 ], [ 6, 0 ], [ 0, 0 ] ], [ [ 0.1, 0.1 ], [ 0.1, 5 ], [ 5, 5 ], [ 5, 0.1 ], [ 0.1, 0.1 ] ] ] } }
{ "_id" : 15, "loc" : { "type" : "Polygon", "coordinates" : [ [ [ 0, 0 ], [ 0, 1 ], [ 1, 1 ], [ 1, 0 ], [0, 0 ] ],  [ [ 0.1, 0.1 ], [ 0.1, 0.5 ], [ 0.5, 0.5 ], [ 0.5, 0.1 ], [ 0.1, 0.1 ] ] ] } }
{ "_id" : 16, "loc" : { "type" : "LineString", "coordinates" : [ [ 0, 0 ], [ 0.1, 0.1 ] ] } }
{ "_id" : 17, "loc" : { "type" : "LineString", "coordinates" : [ [ 0, 0 ], [ 0, 0.1 ] ] } }
{ "_id" : 18, "loc" : { "type" : "LineString", "coordinates" : [ [ 0, 0 ], [ 0.1, 0 ] ] } }

我们使用 $nearSphere 的结果：

{ "_id" : 16, "loc" : { "type" : "LineString", "coordinates" : [  [ 0, 0 ],  [  0.1,  0.1 ] ] } }
{ "_id" : 18, "loc" : { "type" : "LineString", "coordinates" : [  [ 0, 0 ],  [  0.1,  0 ] ] } }
{ "_id" : 14, "loc" : { "type" : "Polygon", "coordinates" : [  [  [ 0, 0 ], [ 0, 6 ], [     6,  6 ],    [   6,  0 ],    [   0,  0 ] ],  [   [   0.1,    0.1 ],  [   0.1,    5 ],    [   5,  5 ],    [   5,  0.1 ],  [   0.1,    0.1 ] ] ] } }
{ "_id" : 13, "loc" : { "type" : "Polygon", "coordinates" : [  [  [ 0, 0 ], [ 0, 6 ], [     6,  6 ],    [   6,  0 ],    [   0,  0 ] ],  [   [   1,  1 ],    [   1,  5 ],    [   5,  5 ],    [   5,  1 ],    [   1,  1 ] ] ] } }
{ "_id" : 15, "loc" : { "type" : "Polygon", "coordinates" : [  [  [ 0, 0 ], [ 0, 1 ], [     1,  1 ],    [   1,  0 ],    [   0,  0 ] ],  [   [   0.1,    0.1 ],  [   0.1,    0.5 ],  [   0.5,    0.5 ],  [   0.5,    0.1 ],  [   0.1,    0.1 ] ] ] } }
{ "_id" : 12, "loc" : { "type" : "Polygon", "coordinates" : [  [  [ 0, 0 ],  [  0,  6 ],  [  6,  6 ],  [  6,  0 ],  [  0,  0 ] ] ] } }
{ "_id" : 17, "loc" : { "type" : "LineString", "coordinates" : [  [ 0, 0 ],  [  0,  0.1 ] ] } }
{ "_id" : 10, "loc" : { "type" : "Polygon", "coordinates" : [  [  [ 0, 0 ],  [  0,  5 ],  [  5,  5 ],  [  5,  0 ],  [  0,  0 ] ] ] } }
{ "_id" : 11, "loc" : { "type" : "Polygon", "coordinates" : [  [  [ 1, 1 ],  [  1,  5 ],  [  5,  5 ],  [  5,  1 ],  [  1,  1 ] ] ] } }

并运行$geoSphere命令，我们可以确认点到形状的距离（出于空间考虑，省略坐标）：

> db.runCommand({geoNear:"near", near: {type:"Point", coordinates:[0,0]}, spherical:true})
[
    {
        "dis" : 0,
        "obj" : {
            "_id" : 16,
            "loc" : {
                "type" : "LineString"
            }
        }
    },
    {
        "dis" : 0,
        "obj" : {
            "_id" : 18,
            "loc" : {
                "type" : "LineString"
            }
        }
    },
    {
        "dis" : 0,
        "obj" : {
            "_id" : 14,
            "loc" : {
                "type" : "Polygon"
            }
        }
    },
    {
        "dis" : 0,
        "obj" : {
            "_id" : 13,
            "loc" : {
                "type" : "Polygon"
            }
        }
    },
    {
        "dis" : 0,
        "obj" : {
            "_id" : 15,
            "loc" : {
                "type" : "Polygon"
            }
        }
    },
    {
        "dis" : 0,
        "obj" : {
            "_id" : 12,
            "loc" : {
                "type" : "Polygon"
            }
        }
    },
    {
        "dis" : 0,
        "obj" : {
            "_id" : 17,
            "loc" : {
                "type" : "LineString"
            }
        }
    },
    {
        "dis" : 0,
        "obj" : {
            "_id" : 10,
            "loc" : {
                "type" : "Polygon"
            }
        }
    },
    {
        "dis" : 157424.6238723255,
        "obj" : {
            "_id" : 11,
            "loc" : {
                "type" : "Polygon"
            }
        }
    }
]

如您所见，每个形状（除了从 [1,1] 开始的最后一个形状）到点 [0,0] 的距离都是 0，尽管这些形状的大小和形状都不同。在到指定点的距离相同的文档中，没有定义顺序。这意味着即使它看起来是确定性的，也不能保证是相同的。