Question

我在某个纬度和经度选择了一个POI兴趣点，我想要非常准确地生成一些最远50英尺远的随机点。我不想超过50英尺，但我也希望随机点均匀分布到50英尺。

到目前为止，这是我所拥有的，它看起来相当不错，但它会产生距离太远的距离。

到目前为止，我最好的猜测是，我认为我的许多假设都是基于圈子而不是球体。

x0 = Longitude of POI
y0 = Latitude of POI
u = Uniformly random number between [0,1)
v = Uniformly random number between [0,1)

r = 50*0.3048/111,300
r = maximum 50 foot radius distance new point is away from POI
    0.3048 is to convert feet to meters
    111,300 is to convert meters to degrees for earth

θ (or t) = 2π*v
θ (or t) = Uniformly random rotation around the polar axis

w = r*sqrt(u)
w = Non-uniformly random distance based on polar coordinate system
    so points don’t clump near the center.

Δy = w*sin(θ)
Δy = New random delta change to latitude
     standard w*sin(θ) for converting from polar to Cartesian coordinates

y1 = y0+Δy
y1 = New random latitude of new point

Δx = w*cos(θ)/cos(y1*π/180)
Δx = New random delta change to longitude
     cos(y1*π/180) used to adjust for shrinking east west distances
     as you move further away from the equator

x1 = x0+Δx
x1 = New random longitude of new point

只是为了添加更多上下文，我在SQL Server内部使用WKID 4326地理坐标系并使用STDistance检查我的工作。

Answer 1

刚刚找到解决方案，我的数学没有任何问题，这是在SQL服务器中将float转换为VARCHAR的错误，我将在下面包含我的固定SQL Server代码。在我拥有之前：

CONVERT(VARCHAR(50),xxx,3)

我有：

CAST(xxx AS VARCHAR(50))

将float转换为varchar时default只有6位有效数字，所以我需要传递一个format参数。有一点非常奇怪的是CAST不应该截断，但无论如何它确实！也许这是SQL Server 2016 RC0中的一个错误。

WITH
LoopTable AS (
    SELECT 1 AS i
    UNION ALL
    SELECT i + 1
    FROM LoopTable
    WHERE
    (i + 1) <= 100000
),
InitialPOI AS (
    SELECT geography::STPointFromText('POINT(-81.2545 44.1244)',4326) POI
    FROM LoopTable
)
SELECT NewPoint.Lat NewLat, NewPoint.Long NewLong, Distance
FROM (
    SELECT POI, NewPoint, POI.STDistance(NewPoint)/0.3048 Distance
    FROM (
        SELECT POI, geography::STPointFromText('POINT('+CONVERT(VARCHAR(50),POI.Long+x,3)+' '+CONVERT(VARCHAR(50),POI.Lat+y,3)+')',4326) NewPoint
        FROM (
            SELECT POI, w*COS(t)/COS(POI.Lat*PI()/180) x, w*SIN(t) y
            FROM (
                SELECT POI, 25*0.3048/111300*SQRT(RAND(CHECKSUM(NEWID()))) w, 2*PI()*RAND(CHECKSUM(NEWID())) t
                FROM InitialPOI
            ) i1
        ) i2
    ) i3
) i4
OPTION (MAXRECURSION 0)

从点开始在给定半径内的球体上均匀生成点

1 个答案: