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#1
STH

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Hi all.. I need to depict 'beams' leaving a point on Earth at different angles and travelling around the Earth.
Is there any way I can show a 'beam' leaving a point on a map and have it as a stright line? Even on a mercator map where a line of a constant bearing does stay straight this doesn't line up with my 'beam' which is presumably part of a 'Great Circle' and curved on a Mercator map. (IS THIS CORRECT?)
Does anyone have any ideas/links to help?

Many thanks STH

#2
Kartograph

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A great circle arc (orthodrome) will always be curved on a Mercator-projected Map. A loxodrome (same bearing) is a straight line in a Mercator map.

Use a gnomonic projection for the straight display of an orthodrome.

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Hope that helps,

Andreas

#3
frax

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I have no idea what you are asking for, do you think you could specify it in more detail, and/or show some (similar) examples...

Is it that you are preparing the navigational charts for the upcoming alien invasion?
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#4
bchubb

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I can never quite get my head around projections, :unsure: but perhaps azimuthal equidistant?

There are a couple other suggestions on this page which might be what you are looking for? :

On some map projections, great-circle arcs are represented as straight lines, making them quite convenient to use for determining great-circle distances, directions, or courses. The following is a summary of some ....

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#5
mdenil

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In part it depends on where the 'beams' originate from. If they originate from one place then any azimuthal projection centered on the origin will do. There are also two point azimuthal projections that will give you correct azimuths from two points. Two examples Snyder gives are from Maurer and from Close.

For straight minimal-distance lines (Great Circles), starting anywhere and heading any way, you will need a gnomonic. Over large distances, the distance exaggeration on this is extreme, and they get to be awkward.

there exist also retroazimuthal projections where all directions to the focus are true. Snyder cites the Craig Mecca, the wonderfully strange Hammer (which seems to be involuted like a möbious strip), plus one or two others. They work well when you need to determine direction TO a fixed place (Mecca, for instance, or a radio transmitter).

M.Denil

#6
Martin Gamache

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Here is a link to the publication mentioned by Mr. Denil.

Snyder book and other USGS projection pubs.

#7
mdenil

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in facI, I was referring to
Flattening the Earth: two thousand years of map projections

http://www.amazon.co...279846?v=glance

by the by, there are several great circles depict able as straight lines on a Mercator map: the equator and all meridians. This though, is common to all standard rectangular projections

#8
frax

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/me wonders if this solves STH's dilemma
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#9
Kartograph

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Probably we made him flee? :(

#10
frax

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he will be back on the day of the alien invasion, when the spaceship will be shooting highly charged laser beams at different angles and the mother ships will be travelling around the Earth :)

unless the alien cartographer made some mistake, and they get lost.

(me likes to say the word gnomonic)
Hugo Ahlenius
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#11
Kartograph

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(me likes to say the word gnomonic)


Phew! It´s so good to hear that I am not alone eith this funny habit! :P

BTW Does anybody remember Beavis and Butthead?

"HeHehe...He said gnomonic...HeHeHe..."




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