如何为 n 公里的方位角方向创建一个矩形

Question

假设我有 item,item_latitude,item_longitude 和 azimuth.

三列四列

我正在尝试为 +/-35 度和 2 公里的方位角方向的每个纬度和经度创建一个矩形。

例子。站点 x 的方位角为 45 度，因此 +35 和 -35 度到 45 度将是 15 度和 80 度，距离为 2 KM

我正在尝试获取 area.I 使用 jts.util.GeometricShapeFactory 库的所有多边形，但它总是创建一个如下所示的圆。我将 scala 与 jts.util.GeometricShapeFactory 库一起使用。

def generatePolygoan(lat:String,long:String,diameterINKM:Double):Option[String] = {
    val latitude = lat.toDouble
    val longitude = long.toDouble
    val diameterInMeters = diameterINKM * 1000
    val shapeFactory = new GeometricShapeFactory()
    //shapeFactory.setNumPoints(64) // adjustable
    shapeFactory.setCentre(new Coordinate(latitude, longitude))
    // Length in meters of 1° of latitude = always 111.32 km
    shapeFactory.setWidth(diameterInMeters / 111320d)
    // Length in meters of 1° of longitude = 40075 km * cos( latitude ) / 360
    shapeFactory.setHeight(diameterInMeters / (40075000 * Math.cos(Math.toRadians(latitude)) / 360))
    val circle = shapeFactory.createCircle()
    Some(circle.toString)
  }

上面的代码围绕纬度和经度创建了圆，但我只需要在方位角方向创建矩形 +/- 35 度。

请帮助我，我是几何学的新手。代码可能在任何程序中，如 JAVA/SCALA/PHP/PYTHON/MYSQL/POSTGRES/MONGODB 甚至数学伪代码

Answer 1

您需要创建一个函数来计算某个点与特定方位角和特定距离内的另一个点（参见 geographic distance and azimuth 第 1C 章]然后调用该函数：

从项目点到方位角的循环 - 距离方位角的增量
从方位角 - 增量方位角到方位角 + 距离处的增量方位角循环
从方位角 + 到项目点距离的增量循环：

代码：

import math

earthRadius = 6371.0 # earth radius in km

# utility functions working in degrees
def cos(d):
    return math.cos(math.radians(d))

def sin(d):
    return math.sin(math.radians(d))

def arccos(d):
    return math.degrees(math.acos(d))

def arcsin(d):
    return math.degrees(math.asin(d))

def printLatLon(lat,lon,prefix="",sep=" "):
    print(str.format("{}{:10.8}{}{:11.9}",prefix,lat,sep,lon))

# function to compute a point at some distance in some direction
def pointFrom(lat1, lon1, azimuth, distance):
    b = math.degrees(distance / earthRadius)
    a = arccos(cos(b)*cos(90 - lat1) + sin(90 - lat1)*sin(b)*cos(azimuth))
    B = arcsin(sin(b)*sin(azimuth)/sin(a))
    lat2 = 90 - a
    lon2 = B + lon1

# set initial point
p0Lat = 18.3965 # latitude in degrees 
p0Lon = 74.7274 # longitude in degrees 
azimuth = 20.0 # azumuth in degrees 
distance = 2.0 # distance in km (sane unit as earth radius)
deltaAzimuth = 35.0

pList = [[p0Lat,p0Lon]]

# conpute arc from point 0 to azimuth - 35
nbPoints = 5
deltaDistance = distance / nbPoints
print(str.format("delta distance {:.3} km",deltaDistance))
azi = azimuth - deltaAzimuth
for i in range(1,nbPoints+1):
    disti = deltaDistance * i
    #print("disti = "+str(disti))
    piLat,piLon = pointFrom(p0Lat,p0Lon,azi,disti)
    printLatLon(piLat,piLon,prefix=str.format("{:.3} {:.3} : ",azi,disti))
    pList.append([piLat,piLon])

# compute n points point at distance from azimuth - 35 to aximuth + 35
deltaAzPoint  = 5.0
nbPoints = int(2.0  * deltaAzimuth / deltaAzPoint)

print(str.format("delta azimuth {:.3} deg",deltaAzPoint))
az0 = azimuth - deltaAzimuth
for i in range(1,nbPoints+1):
    azi = az0 + i*deltaAzPoint
    #print("az : "+str(azi))
    piLat,piLon =  pointFrom(p0Lat,p0Lon,azi,distance)
printLatLon(piLat,piLon,prefix=str.format("{:.3} {:.3} : ",azi,distance))
    pList.append([piLat,piLon])

# compute points from distance to 0 (p0) for azimuth + 35
nbPoints = 5
print(str.format("delta distance {:.3} km",deltaDistance))
azi = azimuth + deltaAzimuth
for i in range(nbPoints-1,0,-1):
    disti = deltaDistance * i
    piLat,piLon = pointFrom(p0Lat,p0Lon,azi,disti)
    printLatLon(piLat,piLon,prefix=str.format("{:.3} {:.3} : ",azi,disti))
    pList.append([piLat,piLon])

# return to origin
pList.append([p0Lat,p0Lon])

# print result
for latLon in pList:
    printLatLon(latLon[0],latLon[1])

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