奇怪的大圆距离计算

发布于 2024-09-29 09:35:36 字数 1376 浏览 7 评论 0原文

我在使用地图计算大圆距离时遇到一些问题。

上下文：http://airports.palzkill.de/search/

地图应该作为大圆距离搜索地图 - 您移动圆心标记或半径标记，圆就会变小或变大。出于调试目的，框标题字段显示计算出的距离（以公里为单位）。

仅当圆心接近 0/0 并且半径标记距它不太远时，此功能才可以正常工作。你将任何一个标记移动到“极端”的次数越多，整个事情就会越偏离，只会产生垃圾。

这是用于计算更新的代码，您还可以在 JS 文件 js.js 中找到整个代码，第 146 到 184 行：

function searchmapupdate()
{   
rad_lat_radiuspos = (circleradiusmarker.getPosition().lat()*Math.PI/180);
rad_lon_radiuspos = (circleradiusmarker.getPosition().lng()*Math.PI/180);
rad_lat_circlecenter = (circlecentermarker.getPosition().lat()*Math.PI/180);
rad_lon_circlecenter = (circlecentermarker.getPosition().lng()*Math.PI/180);

circleradiusvar = Math.acos(Math.sin(rad_lat_circlecenter)*Math.sin(rad_lat_radiuspos)+Math.cos(rad_lat_circlecenter)*Math.cos(rad_lon_radiuspos)*Math.cos(rad_lon_circlecenter-rad_lon_radiuspos))*6371.01*1000;

if (isNaN(circleradiusvar)==false) circle.setOptions({center:circlecentermarker.getPosition(), radius:circleradiusvar});

document.getElementById("mapsearchhead").innerHTML = Math.round(circleradiusvar/1000);
}

由于整个过程确实计算了一些正确的输出，我认为数学本身并不是完全错误的，我猜猜只是缺少一些“矫正”的东西？不幸的是，我在三角学方面非常糟糕，所以我不知道这里可能出了什么问题，甚至不知道从哪里开始寻找如何解决它的想法。

Marco

P.S.：我知道由于投影的球形性质，整个事物必须在极点周围表现“反直觉”。但这并不能真正解释当您将两个标记移动到靠近赤道周围的日期变更线（0/179、0/-179）时会发生什么。

原文

I have some problems with a great circle distance calculation using a map.

Context: http://airports.palzkill.de/search/

The map is supposed to work as a great circle distance search map - you move the circles center marker or the radius marker, and the circle gets smaller or larger. For debug purposes, the boxes title field shows the calculated distance in km.

This only works fine as long as the circle center is close to 0/0, and the radius marker is not too far away from it.
The more you move either of the markers to "extremes", the more off some tangent the whole thing goes and produces nothing but crap.

This is the code used for calculating the updates, you can also find the entire code in the JS file js.js, lines 146 to 184:

function searchmapupdate()
{   
rad_lat_radiuspos = (circleradiusmarker.getPosition().lat()*Math.PI/180);
rad_lon_radiuspos = (circleradiusmarker.getPosition().lng()*Math.PI/180);
rad_lat_circlecenter = (circlecentermarker.getPosition().lat()*Math.PI/180);
rad_lon_circlecenter = (circlecentermarker.getPosition().lng()*Math.PI/180);

circleradiusvar = Math.acos(Math.sin(rad_lat_circlecenter)*Math.sin(rad_lat_radiuspos)+Math.cos(rad_lat_circlecenter)*Math.cos(rad_lon_radiuspos)*Math.cos(rad_lon_circlecenter-rad_lon_radiuspos))*6371.01*1000;

if (isNaN(circleradiusvar)==false) circle.setOptions({center:circlecentermarker.getPosition(), radius:circleradiusvar});

document.getElementById("mapsearchhead").innerHTML = Math.round(circleradiusvar/1000);
}

Since the whole thing does calculate some correct output I assume the math itself is not totally wrong, I guess there is just some "correctional" stuff missing?
Unfortunately I am absolutely lousy at trigonometry, so I dont have a clue what might be wrong here, or even where to start searching for ideas about how to fix it.

Marco

P.S.: I know that due to the spherical nature of the projection, the whole thing has to act "counter-intuitive" around the poles. But that doesnt really explain what happens when you move both markers close to the date line around the equator (0/179, 0/-179).

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