将纬度/经度转换为XY [英] Convert Lat/long to XY

问题描述

我想将经/纬度转换为XY坐标。我捡起了这个方程，但没有得到想要的输出：

I want to convert lat/long to XY coordinates. I picked up this equation but can't get the desired output:

x = r λ cos(φ0)
y = r φ

这两个点的度量是：

point1 = (-37.8206195, 144.9837765)
point2 = (-37.8193712, 144.9837765) 

尝试：

import math

avg = (-37.8206195 + -37.8193712)/2
rad_avg = math.pi / 180

point1 = (-37.8206195, 144.9837765)
point2 = (-37.8193712, 144.9837765) 

dist = rad_avg * math.cos(avg)

print(dist)

出局：

0.01732592680044846

输出应该在1.6亿左右

The output should be around 160m

推荐答案

首先 math.cos 期望以弧度表示的角度参数。要从度数转换为弧度，您需要执行以下操作：

First of all math.cos expects angle argument in radians. To convert from degrees to radians you need to do:

rad_avg = avg * math.pi / 180

甚至：

math.radians(<angle_in_degrees>)

基本上，这意味着您正在使用<$ c映射180º $ c> pi 并取您的角度部分。

Basically it means you're mapping 180º with pi and taking the portion for your angle.

我假设您要通过首先转换来计算两个点之间的距离到 xy坐标（根据您的参考）。

I assume then that you want to compute distance between both points by converting it first to "xy" coordinates (according to your reference).

首先需要在同一坐标系中获得两个点。如链接所示，对于小区域，可以通过以下方式估算它们：

You need to get first both points in the same coordinate system. As the link states, for small areas, they can be estimated by:

• x = rλcos（φ0）


• y = rφ

所以您需要这样做：

import math

point1 = (-37.8206195, 144.9837765) # Lat/Long (lambda/phi)
point2 = (-37.8193712, 144.9837765) # Lat/Long (lambda/phi)

r = 6371000 # meters
phi_0 = point1[1]
cos_phi_0 = math.cos(math.radians(phi_0))

def to_xy(point, r, cos_phi_0):
    lam = point[0]
    phi = point[1]
    return (r * math.radians(lam) * cos_phi_0, r * math.radians(phi))

point1_xy = to_xy(point1, r, cos_phi_0)
point2_xy = to_xy(point2, r, cos_phi_0)

最后，要计算笛卡尔坐标的距离，您需要使用皮塔哥拉斯定理 d = sqrt（delta_x ^ 2 + delta_y ^ 2）

Finally, to compute distance in cartesian coordinates you need to use the Pitagoras Theorem d = sqrt(delta_x^2 + delta_y^2)

在您的示例中：

dist = math.sqrt((point1_xy[0] - point2_xy[0])**2 + (point1_xy[1] - point2_xy[1])**2)

其中结果： 113.67954606562853 。

此外，还有一种捷径可以使距离公式正确：

Plus, there's a shortcut to get it right to the distance formula:

• d = r * sqrt（x²+y²）其中， x =（λ2-λ1）*数学。 cos（φ0）和 y =（φ2-φ1）

• d = r * sqrt(x² + y²) where x = (λ2 - λ1) * math.cos(φ0) and y = (φ2 - φ1)

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