地図の縮尺をウェブ地図のズームレベルに変換する方法

Question

こんにちは。特定の地図縮尺を、主要なウェブ地図サービスで使われている最も近いズーム縮尺に変換する方法を知りたいです。たとえば、1:100,000に最も近い既定の縮尺、またはキャッシュされている縮尺のうち最も近いものを使ってウェブ地図を開きたいと考えています。次のような縮尺の一覧があり、答えが10だとわかっている場合、ズームレベルはどう計算すればよいでしょうか？ 20 : 1128.497220
19 : 2256.994440
18 : 4513.988880
17 : 9027.977761
16 : 18055.955520
15 : 36111.911040
14 : 72223.822090
13 : 144447.644200
12 : 288895.288400
11 : 577790.576700
10 : 1155581.153000
9 : 2311162.307000
8 : 4622324.614000
7 : 9244649.227000
6 : 18489298.450000
5 : 36978596.910000
4 : 73957193.820000
3 : 147914387.600000
2 : 295828775.300000
1 : 591657550.500000 これを求めるうまい方法があるはずですが、学校を出て何年もたち、会議ばかりで頭がすっかり鈍ってしまったので、数学は苦手です。助けていただき、ありがとうございます。 Ryan

DerrickWestoby1 · Answer

This (5 year old) post helped me a lot.  Thanks David!

calculateconvert_zoom1Testing         log(591657550.500000 div (${map_scale} div 2)) calculateconvert_zoom2testing         log(2) calculateconvert_zoom3testing         ${convert_zoom1} div ${convert_zoom2} calculateweb_zoomtesting         round(${convert_zoom3}, 0)

DavidAglietti · Answer

Ah ha!  I found the key to the answer by applying some google-foo, wine, and much confused panic recall of algebra i thought i would never use.    I'll post the answer so I become rich and famous, as all GIS old guys should do.

Here is where I found the logic for the cached map scale logic:

What ratio scales do Google Maps zoom levels correspond to? - Geographic Information Systems Stack Exchange

and this response led to the answer:

http://gis.stackexchange.com/a/81390‌

Many thanks to these folks as this would have been impossible for me to figure out on my own.

For posterity in javascript form:

alert(Math.round(Math.log(591657550.500000 /(<your map scale>/2))/Math.log(2)));

This should return an integer value that corresponds to the zoom level (rounded) once you supply the scale.

Try it in JsFiddle:

Edit fiddle - JSFiddle

Hope this helps someone else, I was lost on this one for a time and considered knitting as an alternative career.

D. Ryan