Convert Lat/long to XY

问题:

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

The measurements of the two points are:

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

Attempt:

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)

Out:

0.01732592680044846

The output should be around 160m

回答1:

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

Or even:

math.radians(<angle_in_degrees>)

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

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

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 = r λ cos(φ0)
• y = r φ

So you need to do:

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)

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

In your example:

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

Which results: 113.67954606562853. Closer to what you're looking for.

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

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