从两个坐标和角点恢复第三个坐标

问题描述

我有3个地理坐标

first_coordinate = [55.266346,25.053268]
second_coordinate = [55.266472,25.053311]
third_coordinate = [55.266370,25.0532]

然后我将它们转换为epsg：3997：

def convert(point):
  return Point(transformer.transform(point[0],point[1]))

first_point_in_meters = convert(first_coordinate)
second_point_in_meters = convert(second_coordinate)
third_point_in_meter = convert(third_coordinate)

然后尝试使用以下方法确定原点第三坐标：

def calculate_third_point(Ax,Ay,Cx,Cy,b,c,A,alt):
  uACx = (Cx - Ax) / b
  uACy = (Cy - Ay) / b

  if alt:
      uABx = uACx * math.cos(A) - uACy * math.sin(A)
      uABy = uACx * math.sin(A) + uACy * math.cos(A)

      Bx = Ax + c * uABx
      By = Ay + c * uABy
  else:
      uABx = uACx * math.cos(A) + uACy * math.sin(A)
      uABy = - uACx * math.sin(A) + uACy * math.cos(A)

      Bx = Ax + c * uABx
      By = Ay + c * uABy

  return Point([Bx,By])

并将这2个坐标转换回epsg：4326。但是最近的坐标距离原点2米

one distance: 2.6033912103159342 m.
anther distance: 19.215538365617018 m.

我做错了什么？

完整代码：

import math
import numpy as np
from pyproj import Transformer

from shapely.geometry import Point

transformer_4326 = Transformer.from_crs(3997,4326,always_xy=True)
transformer = Transformer.from_crs(4326,3997,always_xy=True)

def calculate_third_point(Ax,By])

def find_angle(rone,rtwo,rthree):
  one = np.array(rone)
  two = np.array(rtwo)
  three = np.array(rthree)
  ba = one - two
  bc = three - two
  cosine_angle = np.dot(ba,bc) / (np.linalg.norm(ba) * np.linalg.norm(bc))
  angle = np.arccos(cosine_angle)
  return np.degrees(angle)

def convert(point):
  return Point(transformer.transform(point[0],point[1]))

first_coordinate = [55.266346,25.0532]

first_point_in_meters = convert(first_coordinate)
second_point_in_meters = convert(second_coordinate)
third_point_in_meter = convert(third_coordinate)

angle = find_angle(third_point_in_meter,second_point_in_meters,first_point_in_meters)
distance = first_point_in_meters.distance(second_point_in_meters)
distance2 = first_point_in_meters.distance(third_point_in_meter)

one = calculate_third_point(
  first_point_in_meters.x,first_point_in_meters.y,second_point_in_meters.x,second_point_in_meters.y,distance,distance2,angle,True)

another = calculate_third_point(
  first_point_in_meters.x,False)

print("one distance: {0} m.".format(one.distance(third_point_in_meter)))
print("anther distance: {0} m.".format(another.distance(third_point_in_meter)))

解决方法

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