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Porklet
06-13-2011, 06:54 PM
I have tried to create a realistic river system for the world I am working on based on the information I got from the Sticky post "How to get you rivers in the right place" by Ryan K. I think I have done that, but I wondered if some more experienced map makers might take a look at my work. The map is 6,000 miles by 6,000 miles and is representative, at this point. The rivers shown are major river systems. I have included the 30th parallel in order to show the dry/arid zones and the wet zones to the north.

The area marked "A" is an experiment. I don't know if it can function this way. The south side of the mountain chain is in a rain shadow. The rivers flowing out of it are from the substantial snow melt cascading out of the valleys south. There are a few elevated mountain lakes, and the system then flows in to an expansive and very dry savannah. I intended for the map to show a varying flow river system collecting in a dry lake bed, filling, and evaporating seasonally (much like the African savannah without the torrential storms). I am wondering if that situation is realistic, and, if so, is it clear on as presented on the map?

Thanks for any help.

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Hai-Etlik
06-13-2011, 08:37 PM
That river looks fine. There are plenty of 'endorheic' lakes like the Caspian Sea, Great Salt Lake, etc, and there are also rivers that simply spread out into an inland flood plain and evaporate like the Okavango.

The long river in the northeast though seems to be following along a raised area of hills (though it's hard to interpret without contours) Those huge lakes up in the mountains without much of a catchment area feel a bit off too.

Overall, you've got the basic idea.

As a bonus bit of criticism, you've got a problem with your projection. You seem to be using a Equidistant Cylindrical projection (Parallels are all evenly spaced and vertical distances are all to scale.) However, that would produce severe distortion at the higher latitudes.

Take a look at the map of Earth here: http://en.wikipedia.org/wiki/Equirectangular_projection

See how the parallels (Horizontal grid lines) are evenly spaced, but horizontal distance gets stretched out more and more as you move away from the equator.

Along the N 60 parallel near the top of your map, distances are only half what they are at the equator (So the map is only 3000 miles wide at 60). And at the very top, which appears to be about N 75, it's just a little over one quarter the width at the equator, 1553 miles wide. Even at just N 30 the map is 5196 miles wide. There's no way to have a square 6000 miles on a side on the surface of a sphere 3820 miles in radius.

Unfortunately there's no easy solution or rule of thumb. All projections cause distortion. If you are most concerned with shape, don't care much about distance, and aren't worried about the poles, Mercator is your best bet. It stretches in BOTH directions as you move away from the equator which means things tend to stay the same shape.

My recommendation would be to move the N 60 line upward and call it a Mercator map. You'd be able to retain '6000 miles' along the equator, but away from the equator the scale would change.

You can get a graticule (Grid) for a Mercator map here: http://www.cartographersguild.com/showthread.php?14805-Mecator-Map-Vector-Template

Porklet
06-13-2011, 09:36 PM
That river looks fine. There are plenty of 'endorheic' lakes like the Caspian Sea, Great Salt Lake, etc, and there are also rivers that simply spread out into an inland flood plain and evaporate like the Okavango.

The long river in the northeast though seems to be following along a raised area of hills (though it's hard to interpret without contours) Those huge lakes up in the mountains without much of a catchment area feel a bit off too.

Overall, you've got the basic idea.


If the river you are referring to is to the right of the forest,then it's flowing between the raised hills and the raised elevation from the mountains to the east. I am not fond of that river. It was one of the first ones I attempted, and I had already considered removing it altogether or redesigning it.

Are you referring to the lakes in the hills north of site "A"?

Porklet
06-13-2011, 09:38 PM
As a bonus bit of criticism, you've got a problem with your projection. You seem to be using a Equidistant Cylindrical projection (Parallels are all evenly spaced and vertical distances are all to scale.) However, that would produce severe distortion at the higher latitudes.

Take a look at the map of Earth here: http://en.wikipedia.org/wiki/Equirectangular_projection

See how the parallels (Horizontal grid lines) are evenly spaced, but horizontal distance gets stretched out more and more as you move away from the equator.

Along the N 60 parallel near the top of your map, distances are only half what they are at the equator (So the map is only 3000 miles wide at 60). And at the very top, which appears to be about N 75, it's just a little over one quarter the width at the equator, 1553 miles wide. Even at just N 30 the map is 5196 miles wide. There's no way to have a square 6000 miles on a side on the surface of a sphere 3820 miles in radius.

Unfortunately there's no easy solution or rule of thumb. All projections cause distortion. If you are most concerned with shape, don't care much about distance, and aren't worried about the poles, Mercator is your best bet. It stretches in BOTH directions as you move away from the equator which means things tend to stay the same shape.

My recommendation would be to move the N 60 line upward and call it a Mercator map. You'd be able to retain '6000 miles' along the equator, but away from the equator the scale would change.

You can get a graticule (Grid) for a Mercator map here: http://www.cartographersguild.com/showthread.php?14805-Mecator-Map-Vector-Template

That had not even occurred to me. This is my first map that wasn't drawn on graph paper. I have downloaded your svg file for use with GIMP. I have two days off so I will try to post something soon. Thanks for all of the help.

EDIT:
I have added my Mercator work thus far. Am I doing this right? I had to move it south in order for the equator to match my earlier works. The relative latitudes are going to change a lot about the world I thought I was building.

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Hai-Etlik
06-14-2011, 12:15 AM
EDIT:
I have added my Mercator work thus far. Am I doing this right? I had to move it south in order for the equator to match my earlier works. The relative latitudes are going to change a lot about the world I thought I was building.

I'd say you've got it quite a bit too small.

I would suggest you try to line up the equator with where you had the equator before, and the N 30 meridian (The second one up from the equator) with where you had it before. All the others will be different, but as those were apparently the ones you were focusing on, it makes sense to keep them same.

To simplify it, I've chopped out the part of the graticule you need to do that:

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waldronate
06-14-2011, 12:52 AM
Imm not sure that a Mercator projection would be a particularly good choice because of the rather extreme distortion heading northward. A simpler cylindrical projection might work, as might something like a Mollweide projection. I pulled out my elderly and creaky ReprojectImage program ( http://www.ridgenet.net/~jslayton/ReprojectImage.zip - although something like Hugin or any number of other image reprojection programs would also work here) and used a Mollweide projection on the basic image. Pulling back onto a sphere gives the last screenshot. If you have a flat map that you're starting from and aren't terribly worried about some distortion, then I really recommend picking a projection that will keep the latitudes at a slight expense of longitudes (unless it's absolutely critical that some points be exactly north or south of others).

As far as the river that you were asking about, two real-world examples are the Okavango delta in Africa ( http://en.wikipedia.org/wiki/Okavango_Delta ) and what was Tulare Lake in California's central valley ( http://en.wikipedia.org/wiki/Tulare_Lake ). Both had annual floods that spread out over many, many square miles and revert to grassland and/or marshes after that passes. Neither one has a whole lot of rainfall in the actual areas that flood, but collect rain from elsewhere.

Hai-Etlik
06-14-2011, 01:08 AM
Imm not sure that a Mercator projection would be a particularly good choice because of the rather extreme distortion heading northward. A simpler cylindrical projection might work, as might something like a Mollweide projection.

Yes, Normal Mercator really isn't the best option for a continent map, but I suggested it as it's far and away the simplest option that can be implemented without needing additional software. If I were trying to map a continent this size and shape for general reference, I'd probably use a Chamberlain Trimetric projection but that's well beyond what I want to throw at a newbie.

waldronate
06-14-2011, 01:10 AM
I'm a firm believer in additional software!

Hai-Etlik
06-14-2011, 01:22 AM
I'm a firm believer in additional software!

In the long run, I certainly agree: my most recent map used about 7 different programs, two which I wrote myself. But I didn't want to overwhelm Porklet by introducing too much at once.

Porklet
06-14-2011, 01:51 PM
Imm not sure that a Mercator projection would be a particularly good choice because of the rather extreme distortion heading northward. A simpler cylindrical projection might work, as might something like a Mollweide projection. I pulled out my elderly and creaky ReprojectImage program ( http://www.ridgenet.net/~jslayton/ReprojectImage.zip - although something like Hugin or any number of other image reprojection programs would also work here) and used a Mollweide projection on the basic image. Pulling back onto a sphere gives the last screenshot. If you have a flat map that you're starting from and aren't terribly worried about some distortion, then I really recommend picking a projection that will keep the latitudes at a slight expense of longitudes (unless it's absolutely critical that some points be exactly north or south of others).

I am frightened. I had no idea the chain of islands in the NW was on the other side of the planet.

I have downloaded the Reproject software. I am toying with it now. I have a sense of how to use the X/Y/Scale stats on the left using your original picture as a guide. I am using this software to accurately show where land masses lie on a sphere of a particular size, no? This may sound ignorant, but I am still a little confused. Thanks for your help.

Porklet
06-14-2011, 02:07 PM
Yes, Normal Mercator really isn't the best option for a continent map, but I suggested it as it's far and away the simplest option that can be implemented without needing additional software. If I were trying to map a continent this size and shape for general reference, I'd probably use a Chamberlain Trimetric projection but that's well beyond what I want to throw at a newbie.

I have implemented your Mercator fix, see below. Do I understand this correctly? Every line north of the Equator is 15 degrees on the globe, or am I wrong? Thanks for the help.

36525

Is there something I could do with the scale to make Mercator work better? I want the mechanics of the world to be believable, and I want environments in the tropics and near arctic without creating a massive world system. The idea was born years ago on notebook paper, portrait style. The map was only recently changed to fit in a square. What if I altered the scale to 6,000 x 3,000, or vice versa now that I think about it? Would that alleviate some of the distortion near the poles?

I am beginning to understand the use of the Reproject software by waldronate, but if I can use Mercator to establish the world system in its final form I want to go ahead and do that. Then I can play around with other aspects.

I saw an episode of "The West Wing" where C.J. had a meeting with the Cartographers for Social Equality. They maintained that the Mercator map was Euro-centrist and did not give adequate props to the southern hemisphere. They showed the Peterson (or Pederson or Pedersen) Projection and it freaked C.J. out. I thought they were exaggerating just to be funny, but apparently they weren't fooling around. I am beginning to understand why C.J. was freaking.

waldronate
06-14-2011, 04:57 PM
I am frightened. I had no idea the chain of islands in the NW was on the other side of the planet.

I have downloaded the Reproject software. I am toying with it now. I have a sense of how to use the X/Y/Scale stats on the left using your original picture as a guide. I am using this software to accurately show where land masses lie on a sphere of a particular size, no? This may sound ignorant, but I am still a little confused. Thanks for your help.

Where the islands end up will depend on the projection used. I used Mollweide for that particular example as it has evenly-spaced straight lines of latitude, unlike Mercator, which has a hyperbolic tangent spacing between lines of latitude. On a Mercator projection they would end up on the same side of the globe, but be greatly reduced in size. Your original map showed equally-spaced lines of latitude and I picked Mollweide as an example of a projection without worrying too much about final distortion. Mercator will keep the shape of the coastlines, but will radically distort the size of polar regions; the Mollweide projection keeps the latitude scale, but starts to distort the shape as it heads poleward.

Most folks draw a map with the goal of making it look good and later try to shoehorn it into some sort of "realistic" projection. The essence of mapmaking is to produce a work of art that is suited for a particular purpose and that balanced the technical and visual aspects. Given a choice, most folks will fudge the technical to get the visual. Mountains, for example, may be represented as groups of small pictures, or as chains of hachures, or some other way entirely. None of these are technically accurate representations, but they convey the sense and general location of mountains, which is often an important part of the goal of the map. Such a representation for mountains is most likely totally unsuitable for map used to plan the route of a road or canal; those purposes require a different sort of map, usually one carefully surveyed and reference to ground truth with a precise projection.

The reason I mention that is that if you're concerned about technical accuracy, you're probably better off deciding where you want things and how you'd like them to relate and then redrawing your map to take into account your understanding of the way you want them to be against your understanding of the overall globe. Early maps are often inaccurate representations of reality because accurate longitude surveying requires good timekeeping. Changing the map a little to match a newfound understanding won't change the underlying reality of the world (such as it is) and inaccuracies in early map editions can be explained as the work of some not-so-good surveyors that were further distorted by someone who wanted to make certain areas more important.

ReprojectImage assumes a spherical world, which differs from earth by about 1 part in 300 (pretty much close enough for any reasonable visual work). It doesn't know or care about a world size because the math here is all about the angles, not the actual distances.

waldronate
06-14-2011, 05:39 PM
A little fiddling with the images gives the results shown below. The Mercator-based one shows the distortion in latitude that you have in the map posted above. The Plate-Carree one shows your original map pasted directly onto a globe with its attendant distortions in shape. The Mercator one has slightly different climate zones than your original map; the Plate Carree one has the same climate zones but slightly different shapes. The only reason why I show things on an Orthographic projection is that it's one familiar to users of a globe and it often helps when trying to see things like an excess of rivers in an area that aren't immediately obvious in an area-distorted projection.

Hai-Etlik
06-14-2011, 07:06 PM
I have implemented your Mercator fix, see below. Do I understand this correctly? Every line north of the Equator is 15 degrees on the globe, or am I wrong? Thanks for the help.

36525


Yes, all the lines are at 15 increments, so the dark lines are 0 and the next line is 15 then 30 and so on.



Is there something I could do with the scale to make Mercator work better? I want the mechanics of the world to be believable, and I want environments in the tropics and near arctic without creating a massive world system. The idea was born years ago on notebook paper, portrait style. The map was only recently changed to fit in a square. What if I altered the scale to 6,000 x 3,000, or vice versa now that I think about it? Would that alleviate some of the distortion near the poles?


The "best" solution would probably be to make a rough world map, as in the WHOLE world with your continent where you want it. Then reproject it to a projection suitable for a map of JUST the continent like say, Lambert Conformal Conic, or Chamberlain Trimetric then refine it. Unfortunately, that would mean throwing out your existing map except as a reference.

As to the scale. For a map this size, there is no consistent scale. It's just not possible. Certain projections do manage consistency for particular cases. Equidistant Cylindrical has a consistent scale for measurements north-south and along the equator. Equidistant Azimuthal has a consistent scale for measurements from a single point. Covering a smaller area does help, but you want to cover the equator to the arctic which rather constrains you to being big. You could make the map less wide which would help. If the continent were shaped more like South America, for instance.

If you go with my Mercator option as is, you get equator to subarctic (A bit shy of 60). I could adjust it to cover true arctic if you don't mind the 30 parallel moving down a bit.

With Waldonrate's Mollweide option, you do reach the arctic easily.

Another option is a conic like this Equidistant Conic:

36541

Like your original map, it spans from S 15 to N 75 and preserves north-south distances. It also preserves east-west distances at N 15 and N 60 (the 'Standard Parallels' for this conic). As before the graticule is spaced at 15 intervals.

Unlike the previous options Waldronate and I have suggested, this is a projection specifically created for this continent.



I am beginning to understand the use of the Reproject software by waldronate, but if I can use Mercator to establish the world system in its final form I want to go ahead and do that. Then I can play around with other aspects.

I saw an episode of "The West Wing" where C.J. had a meeting with the Cartographers for Social Equality. They maintained that the Mercator map was Euro-centrist and did not give adequate props to the southern hemisphere. They showed the Peterson (or Pederson or Pedersen) Projection and it freaked C.J. out. I thought they were exaggerating just to be funny, but apparently they weren't fooling around. I am beginning to understand why C.J. was freaking.

The Equal Area Cylindrical projection (Aka. Gall-Peters which I think is what they are talking about) is a projection for the whole world that preserves areas, but massively distorts shapes and directions.

The equal area thing was a big issue for some a while back, but it's pretty much been dealt with. Mercator was initially designed for marine navigation by dead reckoning. A navigator needs to know which direction Greenland is, not how big it is relative to Africa. Equal Area projections are great if you need to know how big something is, but useless for anything else. Compromise projections like Robinson and Winkel Tripel ended up winning out as the projections of choice for world reference maps as they balance the various distortions out rather than trying to eliminate just one at the expense of the others. Mercator is making something of a comeback in web maps since it lets you easily "zoom in" while retaining shapes and directions.

Porklet
06-14-2011, 10:40 PM
A little fiddling with the images gives the results shown below. The Mercator-based one shows the distortion in latitude that you have in the map posted above. The Plate-Carree one shows your original map pasted directly onto a globe with its attendant distortions in shape. The Mercator one has slightly different climate zones than your original map; the Plate Carree one has the same climate zones but slightly different shapes. The only reason why I show things on an Orthographic projection is that it's one familiar to users of a globe and it often helps when trying to see things like an excess of rivers in an area that aren't immediately obvious in an area-distorted projection.

I am okay with adjusting climate zones. I was working on that while waiting for a response to my questions concerning the river system. In regards to technical accuracy, I only need the NW island chain to fall on the 65th parallel. That is something I can easily fix. The 30th parallel's dry zone falls near the same latitude as before.

Although the continent is based on a world have developed over many years I am rebuilding it from the bottom up. Most of the other issues regarding scale and space are easily altered. Most of the northern portion of the continent is uninhabited and undeveloped so if it becomes smaller in scale it won't affect much.

The Mercator Projection you provided does help to bring it into perspective. What is Fractal Terrain Pro? Did you place the .jpg on a 3-D model like a texture map? Thanks again for your help.

Porklet
06-14-2011, 11:10 PM
The "best" solution would probably be to make a rough world map, as in the WHOLE world with your continent where you want it. Then reproject it to a projection suitable for a map of JUST the continent like say, Lambert Conformal Conic, or Chamberlain Trimetric then refine it. Unfortunately, that would mean throwing out your existing map except as a reference.

As to the scale. For a map this size, there is no consistent scale. It's just not possible. Certain projections do manage consistency for particular cases. Equidistant Cylindrical has a consistent scale for measurements north-south and along the equator. Equidistant Azimuthal has a consistent scale for measurements from a single point. Covering a smaller area does help, but you want to cover the equator to the arctic which rather constrains you to being big. You could make the map less wide which would help. If the continent were shaped more like South America, for instance.

If I were to continue with this map as pictured below (with your new graphics thank you very much). Could I at a later date use it as a reference to then make it a part of a larger global map? I don't envision ever taking that step, but it would be nice to have that option. I had originally thought that the planet I would be working on would be half the dimensions of our earth. That would've made the 6,000 by 6,000 map roughly half of the planet. That seems like a bit much. I would prefer to leave the rest of the planet alone for now. I suppose the longitude shown on the image below would give me the relative percentage of the global map covered in my continental map.

I am satisfied with knowing the relative global positions of the locations on the map so that I can interpret things such as climate, relative temperatures, and celestial events such as the midnight sun. If I have to alter the scale at different latitudes that's okay with me. It's a work in progress.

Speaking of scale: What does happen to scale closer to the poles? I know the scale is reduced, but is it uniform based on the degrees from the equator? Is their an equation that can be used to convert distance from point to point? I assume scale at the equator is 1:1, or is the center point arbitrary? I have already noticed that some locales that were directly north of others are now far off to the east/west. It's unsettling, but north/south relationships are inconsequential.

I apologize if I am being dense. With the graphic that you gave me, along with waldronate's projections in a previous post, it's beginning to become clear. I should have made my world flat. Just kidding. I can see the map I have made as a spherical domain for the first time.

The only logistical issue I have is moving the island chain (area "A") so that its midpoint lies on the 65th parrallel (which I assume is north of the line just above it). Ugh, South America, huh?

36546

Hai-Etlik
06-15-2011, 01:05 AM
If I were to continue with this map as pictured below (with your new graphics thank you very much). Could I at a later date use it as a reference to then make it a part of a larger global map? I don't envision ever taking that step, but it would be nice to have that option. I had originally thought that the planet I would be working on would be half the dimensions of our earth. That would've made the 6,000 by 6,000 map roughly half of the planet. That seems like a bit much. I would prefer to leave the rest of the planet alone for now. I suppose the longitude shown on the image below would give me the relative percentage of the global map covered in my continental map.

Yes, getting a clear idea of the projection and how your continent sits on the globe now will save you massive headaches if you ever try to fit it into a larger map later. Your original map (The whole thing, not just the continent) actually covered a roughly triangular region of about 1/8th of the planet's surface.

The Mercator graticule had it covering a bit less. It was about the same width as it was before, but not as tall and the region covered was more like a trapezoid.

With Waldronate's Mollweide interpretation of the map, the area covered was larger and the shape is well, hard to describe in Euclidean terms.

Finally, with the Equidistant Conic interpretation. Area covered is again increased, but not as much.



I am satisfied with knowing the relative global positions of the locations on the map so that I can interpret things such as climate, relative temperatures, and celestial events such as the midnight sun. If I have to alter the scale at different latitudes that's okay with me. It's a work in progress.


That's what I figured. The problem is that scale WILL vary with ANY projection if you cover a large enough area, and yours is certainly large enough. In conformal projections (Like Mercator), it will only vary with location. With other projections it will vary with location, and the direction you are looking.

For instance, in your original Equidistant Projection, Any measurement along the equator or straight north-south, was to scale. Other measurements got larger as you move away from the equator and turned away from north or south.

With Mercator it's relatively simple, the scale factor at a latitude is the secant of the latitude. Since most calculators don't have Secant, divide 1 by the cosine of the latitude to get it. 1/cos(φ) where φ is the latitude. And yes, that's relatively simple compared to most other projections.

With the conic projection. The scale is true north-south (As it's an 'Equidistant' projection) and along parallels N 15 and N 60 Between them, east-west distances are slightly reduced, and outside them they are increased, and stretch out more rapidly the further you go. On a positive note, the overall distortion for this projection, in the area covered by the map is much less than the others. As long as you don't need to be too precise, you should be fairly safe measuring straight line distances on it in any direction as if it had a consistent scale


Speaking of scale: What does happen to scale closer to the poles? I know the scale is reduced, but is it uniform based on the degrees from the equator? Is their an equation that can be used to convert distance from point to point? I assume scale at the equator is 1:1, or is the center point arbitrary? I have already noticed that some locales that were directly north of others are now far off to the east/west. It's unsettling, but north/south relationships are inconsequential.


That's what I figured you were after. The problem is that scale WILL vary with ANY projection if you cover a large enough area, and yours is certainly large enough. In conformal projections (Like Mercator), it will only vary with location. With other projections it will vary with location, and the direction you are looking.

For instance, in your original Equidistant Projection, Any measurement along the equator or straight north-south, was to scale. Other measurements got larger as you move away from the equator and turned away from north or south.

With Mercator it's relatively simple, the scale factor at a latitude is the secant of the latitude. Since most calculators don't have Secant, divide 1 by the cosine of the latitude to get it. 1/cos(φ) where φ is the latitude. And yes, that's relatively simple compared to most other projections.

With the conic projection I made for you. The scale is true north-south (As it's an 'Equidistant' projection) and along parallels N 15 and N 60. Between them, east-west distances are slightly reduced, and outside them they are increased, and stretch out more rapidly the further you go. The overall distortion for this projection, in the area covered by the map, is much less than the others. As long as you don't need to be too precise, you should be fairly safe treating it as if it were 'flat' when measuring distance and area.


I apologize if I am being dense. With the graphic that you gave me, along with waldronate's projections in a previous post, it's beginning to become clear. I should have made my world flat. Just kidding. I can see the map I have made as a spherical domain for the first time.

Well, if it's a fantasy world, there really is no problem with making it flat, and it really does make mapping much easier. You certainly aren't being dense; this really is a very different way of thinking about geometry. We figured out euclidean (flat) geometry back in ancient times. It wasn't until the 19th century that non-euclidean geometries were widely accepted as even being geometry. Plenty of fantasy mappers never worry about this, and for most fantasy maps most of the time, it doesn't really matter as most such maps cover much smaller areas where distortion is minimal.



The only logistical issue I have is moving the island chain (area "A") so that its midpoint lies on the 65th parrallel (which I assume is north of the line just above it). Ugh, South America, huh?


Yep, just a little ways. I could give you a graticule with a bit more room in the north, or you could move it a bit to the right. If you moved it straight right to the W 30 meridian (second from the centre), you would have it at right about N 65.

Porklet
06-15-2011, 04:19 PM
For instance, in your original Equidistant Projection, Any measurement along the equator or straight north-south, was to scale. Other measurements got larger as you move away from the equator and turned away from north or south.

With Mercator it's relatively simple, the scale factor at a latitude is the secant of the latitude. Since most calculators don't have Secant, divide 1 by the cosine of the latitude to get it. 1/cos(φ) where φ is the latitude. And yes, that's relatively simple compared to most other projections.

With the conic projection. The scale is true north-south (As it's an 'Equidistant' projection) and along parallels N 15 and N 60 Between them, east-west distances are slightly reduced, and outside them they are increased, and stretch out more rapidly the further you go. On a positive note, the overall distortion for this projection, in the area covered by the map is much less than the others. As long as you don't need to be too precise, you should be fairly safe measuring straight line distances on it in any direction as if it had a consistent scale.

So, if 1 pixel = 1 mile at the equator, for example. Then where the Secant =.5 one pixel would equal 1/2 a mile?
My father is a math teacher. I know he has several calculators lying around from Grad School. I will see if he has one with a Secant function. Distances in my case do not have to be precise as long as they are believable.



Yep, just a little ways. I could give you a graticule with a bit more room in the north, or you could move it a bit to the right. If you moved it straight right to the W 30 meridian (second from the centre), you would have it at right about N 65.

If it's not too much trouble, please. I would expect that incorporating a map into a global system where the map shows the pole would be much easier. I can extend the map north to include the pole. Thanks again. You and waldronate have been Repped. Let me know if I can help you in any way, maybe I could clean out your gutters or something.

Here's the map with the islands moved. I do want it roughly north of the two small islands south and to the west of the mainland so I went ahead and moved it anyway.

36560

Hai-Etlik
06-15-2011, 06:15 PM
So, if 1 pixel = 1 mile at the equator, for example. Then where the Secant =.5 one pixel would equal 1/2 a mile?
My father is a math teacher.

Where sec(φ) = 2, one pixel would be half a mile. Mercator stretches distances out as you move away from the equator.



If it's not too much trouble, please. I would expect that incorporating a map into a global system where the map shows the pole would be much easier. I can extend the map north to include the pole.


Ah, extending the conic projection all the way to the pole would be problematic unfortunately. The distortion gets quite severe as you approach it (it's INFINITE at the pole as the singe point of the pole is stretched out into an arc.) and there's also a discontinuity (the 'cut' that allows the cone to be unrolled into a flat map) I could reduce the distortion by moving the northern standard parallel up to the pole, but that wouldn't fix the discontinuity, and it would increase the distortion in the <em>middle</em> of the map significantly

If you take a look at this full globe graticule in the conic projection, the north pole is the innermost circle, and the south pole is the outermost one. The area at the top of the image where there are no meridians is the discontinuity.
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In fact, all the projections we've suggested so far have problems at the poles because they treat them as discontinuities. Normal Mercator pushes the poles away to infinity, Mollweide does leave the poles as points, but there is still a discontinuity at the poles and severe shape distortion, Equidistant Cylindrical stretches the poles out to the entire width of the map. And my conic stretches them to arcs of circles. Real life maps of the poles tend to be in special polar projections, like Polar Stereographic Azimuthal.

If you want a projection that can cover 90 of longitude at the equator, AND the north pole, without much distortion, I don't think such a thing is possible. The best I can suggest are Chamberlain Trimetric which is rather complex, and Transverse Mercator, which is like the Normal Mercator I've spoken about, but instead of wrapping the map in a cylinder around the equator, you wrap it around the poles.

I've attached the SVG source file for the conic graticule if you want to play with it yourself.

Porklet
06-16-2011, 11:34 AM
Normal Mercator pushes the poles away to infinity...

The only thing that frightens me more than euclidean geometry is mapping infinity. The more I learn, it seems, the less I know. I thank you for the conic graticule, your patience, and your knowledge. The news continues to disturb me, however, and before I witness a rupture in my own personal space/time; I must leave. To quote the great philosopher Monty "the Python" Descartes, "I run away; therefore I am."