How do I find real co-ordinates from Map images

How large is the area covered by each map, and how accurate do you need the points to be?

hi steve,

it would be good to find a method that can be applied to a variety of maps (or sizes), -say the UK as a single image and Australia as another.

I would say that Australia would be the largest map size I would need to consider, however if I have to scale my expectations down to suit the math then so-be-it.

I also presume that map images would need to correctly oriented True North so that the central line of Longitude (relative to the map) is 'straight' and vertical.

Hope that has answered your question.

You are utterly lost unless you know the type of map projection that is used. There are literally hundreds of different projections used for cartography. Each has its own advantage.

I consider John P. Snyder's 'Map Projections – A Working Manual', which was published by the US Geological Survey as a professional paper (#1395), the bible on the subject. However, it has gone out of print. Fortunately, there is someone that reproduces it, but I can't recall who. A search on the web is how I found them. It was about $60.

This book contains a detailed discussion of all the different map projections and then the math equations to translate between polar and rectilinear coordinates. I have used these formulas extensively for aircraft FMS (Flight Management Systems) I have built.

However, step one is to identify the projection type that you have, then the book will give you the equations you need to do what you want.

Nice tip. IT's available online from USGS at: http://pubs.er.usgs.gov/usgspubs/pp/pp1395

you shoud use the concept of graph colouring

Huh? This seems like a straightforward problem in spherical geometry and interpolation. I'm not sure how graph coloring applies. Can you explain further?

Steve,

I don't think you can get there from here. Spherical geometry will not work. Every map has a form of distortion built into it. There is no way to map a sphere, or even a portion of a sphere on a flat surface (i.e., a map) without distortion.

The type of distortion used depends on what the function of the map is. Once the map projection type is known you can use mathematical formulas to translate from one coordinate system to another as well as the inverse equations to go back.

The original poster wanted an accurate way to do this given known coordinates at specific points on the map. You need to know the map projection type, the map scale, and the equations for the projection used, and then crunch the numbers. Some of the map projections have some pretty complex equations associated with them, so beware. Been there, done that, and got the T-Shirt.

Hero - Interesting. Intuitively it would seem that if you know the lat/lon coordinates of all four corners of the map, and you know you're on the surface of a sphere, you could work out the interpolation. At that point it's a pretty constrained problem.

From what you say it seems like it's more complicated than "intuition" says. I downloaded the book you pointed out earlier and will take a look at it when I get a chance to see if I can learn more.

The reason I asked Ian initially what size map and how accurate he needed to be is that for small enough maps and rough enough accuracy, fairly simple interpolation might work well enough.

I found a source for John P Snyder's 'Map Projections - A Working Copy', but they have a limited supply of the book. It is part # 1636 and it is $31.00! That is a half price blowout.

http://www.navtechgps.com/supply/books.asp?Line=mapping

See my comment above, it's available in electronic format from the USGS at

http://pubs.er.usgs.gov/usgspubs/pp/pp1395

You can download it, save it, and print it yourself.

Steve

Nice detective work, Steve!

hero, steve, Many thanks for your thoughts & suggestions to my question/posting. my first leaning was that spherical geometry would have held the answer, -just too long since school and all those formulae have gone rather rusty! -but i can understand that if some maps have already been 'pre-adjusted' (according to projection) then the basic geometry will no longer give the desired results. Many thanks again for your time, i'll download/purchase 'the bible' and take it from there. Regards Ian.

Your question seems to be unclear. Position of what? What map projection are you using? Or is it a 7.5 Min. quandrangle (or larger) USGA topographical? (which seems to be the case)...in which case you could readily (simply) measure along the boundaries to obtain the position to a reasonable degree of accuracy. If you have an equal area projection such as Mercator (a navigation map), you can readily plot directions with a plotting magnet since all lines of constant direction (rhumb lines) straight, just like the compass or ruler edge. More specifics about what you are trying to achieve might be helpful.

Way back before we used computers to do it, we used 30cm rulers (that had mm marked as well - you know, the clear plastic ones with inches on one side and metric on the other) to make paper scales. We used it to use geo. coordinates when the maps were marked with military grids. The maps had goe. reference marks, so we drew in boxes and then used the rules to make a scale/protractor on paper. It was slow and tedious and only worked on that sheet and a few surrounding sheets, but we weren't traveling across the globe - just in a pretty small local area.

The whole 60 seconds in a minute, 60 minutes in a degree system is really well suited for a 30cm (300mm) ruler. Now to get a 30cm ruler into a 23cm long box, we would just lean it over until it fit. Then you make soe tick marks on the paper, then slide in another paper and transpose your marks onto a new scale. Laminate it and it holds up well to the elements in the field.

One problem with this method is that depending where on the planet you happen to be, you usually have to make two scales - one for lattitude and one for longitude. Not very high-tech I agree, but sometimes paper and pencil is still the best way.