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altasilvapuer
04-08-2009, 05:56 PM
When I was beginning work on the climate portions of my world map of Geidor ('http://www.cartographersguild.com/showthread.php?t=4971'), I needed to convert latitudes into pixel heights to figure out where to lay my guidelines in Photoshop, and grew quickly tired of the mental contortions from crunching every number by hand, so I made this.

Attached is an Excel spreadsheet that can calculate those latitude heights for given map dimensions and planetary axial tilt. I'm not 100% sure my numbers are right, but they appear to be close enough for a ballpark for the few axial tilts I checked. It definitely appears to be reasonably correct for axial tilt of 23.5, or that of Earth.

If anyone would like to refine my math to allow a wider range of axial tilts, please feel free to do so. My mind is still a little contorted because of all the dead ends I went down with this, due to being tired when I made it.

My math is actually based almost entirely on observations of the approximate corresponding latitude lines for Earth, so that is likely why it works best for 23.5.

-asp

Sigurd
04-08-2009, 07:53 PM
Hey, thanks for sharing!


I'd love to have a better work path towards a photoshop random world :)


Have some rep.


Sigurd

isomage
04-08-2009, 10:10 PM
If t is your axial tilt in degrees, then the tropics are at latitudes t and -t, and the Arctic circles are at latitudes 90 - t and t - 90.

If your image is such that the bottom edge (y = 0) corresponds to the South pole and the top edge (y = h, where h is the image height) corresponds to the North pole (and latitude is linear between them) then you can convert latitudes to y coordinates with y = h * (latitude + 90) / 180.

For example, if the axial tilt is t = 23.5 degrees, then the tropics are at 23.5 and -23.5 degrees and the Arctic circles are at 66.5 and -66.5 degrees. If your image height is h = 3300, then these latitudes correspond to image coordinates of y = 2080, y = 1219, y = 2869, and y = 430 respectively.

altasilvapuer
04-08-2009, 10:13 PM
Awesome. Thanks for the reply, isomage; that's the math I've used here. I went through so many approximate iterations before noticing that simple fact that the whole thing was rather fuddled in my brain.

I will probably add more to this "Number-Cruncher" as I start to get more ambitious with world generation, and think of more things for it to generate.

If anyone has any ideas for something to add, let me know. Collaboration was my main reason for uploading this, anyway.

-asp

isomage
04-08-2009, 10:37 PM
Awesome. Thanks for the reply, isomage; that's the math I've used here.

For image height 3300 and axial tilt 22.5 (the default parameters in the spreadsheet), I get y coordinates of 2887, 2062, 1237, 412; these are different from the values calculated by the spreadsheet.

Just to verify, 67.5 degrees is (90 + 67.5) / 180 = 87.5% of the total height, and 3300 * 0.875 = 2887.5.

guyanonymous
04-08-2009, 10:42 PM
I'm attaching the spreadsheets (Excel 2007 format) that I was fiddling with a while back.

They're for generating planets with realistic details based on random star generation, planet size, and distance etc.

Feel free to take anything you can from them...

I had it setup, if memory serves, to randomly generate a few hundred thousand stars, and 500000 planets to orbit those random stars at random distances etc....I just deleted all but the first 10 generations though (it was just a copy paste of each row I think) so that the file was actually small enough to fit on here).

I also tossed in, for good measure, a rough invention time-line based on wikipaedia. Dates, though, were in the process of being tweaked for my own planet....but what the hey - perhaps it's useful.

altasilvapuer
04-09-2009, 10:31 AM
For image height 3300 and axial tilt 22.5 (the default parameters in the spreadsheet), I get y coordinates of 2887, 2062, 1237, 412; these are different from the values calculated by the spreadsheet.

Just to verify, 67.5 degrees is (90 + 67.5) / 180 = 87.5% of the total height, and 3300 * 0.875 = 2887.5.

I should rephrase, then, apparently: that's the pattern I caught in my head and attempted to use. My brain was so discombobulated from the many failed calculations before noticing the relationships to the axial tilt (I noticed that of the tropics almost immediately, but the arctic circles came much later) that I probably over complicated things. I'll mess around and update it. Thanks!


I'm attaching the spreadsheets (Excel 2007 format) that I was fiddling with a while back.

They're for generating planets with realistic details based on random star generation, planet size, and distance etc.

Feel free to take anything you can from them...

I had it setup, if memory serves, to randomly generate a few hundred thousand stars, and 500000 planets to orbit those random stars at random distances etc....I just deleted all but the first 10 generations though (it was just a copy paste of each row I think) so that the file was actually small enough to fit on here).

I also tossed in, for good measure, a rough invention time-line based on wikipaedia. Dates, though, were in the process of being tweaked for my own planet....but what the hey - perhaps it's useful.

They sound amazing! Perhaps we can form some combination of the two? I definitely think I am going to have to download OpenOffice, already. I extremely dislike the new Microsoft Office, so I'm still using 2000. I used have a copy of 2003 around here somewhere that I preferred, but it is AWOL, so oh well. I'll grab OO, poke around in your file, and see what might be useful to merge.

altasilvapuer
04-09-2009, 02:00 PM
(pardon the double-post)

Wow, I see what my error was in the math, now, isomage. Thanks for pointing that out. It looks really obviously incorrect, now that you've pointed it out.

guyanonymous:
I finally downloaded OpenOffice (which is quite nicer than I remember it; I may be tempted to switch wholesale) and opened your spreadsheets. All I can say at first is, "Wow." This is exactly the sort of thing I was looking to build, eventually, but I hadn't done enough research to incorporate things of that nature, yet. One thing I like most about your spreadsheet is the horizontal layout, permitting multiple entries per page. Mine as it currently stands permits only one entry per page. I think I'm going to reformat mine to allow for multiple entries, as well, if possible.

I'm going to go back to the grindstone with this for a while, and I'll repost it after I've got my math fixed and my layout a little more optimized.
In the meantime, here is an updated version with what should be corrected math.

-asp

guyanonymous
04-09-2009, 07:07 PM
By the way - I can't vouch for what I did being 100% accurate - but it seemed to pan out when I put in a few known quantities.