将纬度和经度转换为 3D 空间中的点 [英] Convert Latitude and Longitude to point in 3D space

问题描述

我需要将纬度和经度值转换为 3 维空间中的一个点.我已经尝试了大约 2 个小时，但我没有得到正确的结果.

Equirectangular 坐标来自 页面.完成它的工作的代码如下:

def llarToWorld(lat, lon, alt, rad):# 见:http://www.mathworks.de/help/toolbox/aeroblks/llatoecefposition.htmlf = 0 # 展平ls = atan((1 - f)**2 * tan(lat)) # lambdax = rad * cos(ls) * cos(lon) + alt * cos(lat) * cos(lon)y = rad * cos(ls) * sin(lon) + alt * cos(lat) * sin(lon)z = rad * sin(ls) + alt * sin(lat)返回 c4d.Vector(x, y, z)

实际上，我切换了y 和z 因为当时地球在旋转，但是，它有效！结果是这样的:

解决方案

作为 TreyA statet，LLA to ECEF 是解决方案.请参阅 http://www.mathworks.de/help/toolbox/aeroblks/llatoecefposition.html

I need to convert latitude and longitude values to a point in the 3-dimensional space. I've been trying this for about 2 hours now, but I do not get the correct results.

The Equirectangular coordinates come from openflights.org. I've tried several combinations of cos and sin, but the result did never look like our little beloved earth.

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In the following, you can see the result of applying the conversion Wikipedia suggests. I think one can guess from context what c4d.Vector is.

def llarToWorld(latit, longit, altid, rad):
    x = math.sin(longit) * math.cos(latit)
    z = math.sin(longit) * math.sin(latit)
    y = math.cos(longit)
    v = c4d.Vector(x, y, z)
    v = v * altid + v * rad
    return v

Red: X, Green: Y, Blue: Z

One can indeed identify North- and South America, especially the land around the Gulf of Mexico. However, it looks somewhat squished and kind of in the wrong place..

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As the result looks somewhat rotated, I think, I tried swapping latitude and longitude. But that result is somewhat awkward.

def llarToWorld(latit, longit, altid, rad):
    temp = latit
    latit = longit
    longit = temp
    x = math.sin(longit) * math.cos(latit)
    z = math.sin(longit) * math.sin(latit)
    y = math.cos(longit)
    v = c4d.Vector(x, y, z)
    v = v * altid + v * rad
    return v

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This is what the result looks like without converting the values.

def llarToWorld(latit, longit, altid, rad):
    return c4d.Vector(math.degrees(latit), math.degrees(longit), altid)

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Question: How can I convert the longitude and latitude correctly?

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Solution

Thanks to TreyA, I found this page on mathworks.com. The code that does it's work is the following:

def llarToWorld(lat, lon, alt, rad):
    # see: http://www.mathworks.de/help/toolbox/aeroblks/llatoecefposition.html
    f  = 0                              # flattening
    ls = atan((1 - f)**2 * tan(lat))    # lambda

    x = rad * cos(ls) * cos(lon) + alt * cos(lat) * cos(lon)
    y = rad * cos(ls) * sin(lon) + alt * cos(lat) * sin(lon)
    z = rad * sin(ls) + alt * sin(lat)

    return c4d.Vector(x, y, z)

Actually, I switched y and z because the earth was rotated then, however, it works! That's the result:

解决方案

As TreyA statet, LLA to ECEF is the solution. See http://www.mathworks.de/help/toolbox/aeroblks/llatoecefposition.html

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