spherical texture mapping

ok, I also asked this in the textures and design forum, but I'm stuck. How do textures get mapped onto the surface of a sphere in mathematical terms? I have some maps I'd like to put on a globe. The maps are already conically projected onto textures, so I need some way to transform those conical projections to something that will map nicely onto a sphere.

ANy ideas? Or is this just too mathematical?

- C

...my experience of texturing is that rewrapping around the same shape works.

Most maps of the world are distorted. They squeeze or stretch the countries overall, focus on the country or region that the map was produced in, etc. Some of the satellite maps have been a revelation to me, at least.

For maps to be accurate they have to be stretched and flattened out on a flat surface, with the distortions ironed out. I didn't understand your reference to "conically produced". I don't know that knowing how things are mapped will help a lot...but a texture I have of a Foster roof, which is spherical, reproduces perfectly when used on a spherical roof, and looks rubbish on any other shape in-world, and distorted as a flat texture.

My feeling is that untill we get different controls for controlling textures on spherical surfaces (and unless there is something I am missing) your best option is to have two round textures taken from spherical objects on the same texture, butting up to each other, each with a different side of the map you want. I think something with a plain blue sea which extends across the rest of the texture outside the rounded map portions would work best.

There are a number of globes in world, so someone else surely must have the answer to this question.

I have found generally that textures of 3d surfaces do work in world on 3d shapes of the same shape. Failing ready-made textures from some other source, take digital photographs of a globe, and use that after you put them together into the one texture. It might take a few experiments.
HTH and isn't just the early-morning ramblings of a woman who went to bed at 4.30am and got up at 7.30am, lol.
Cali

I think this is what you are looking for:

http://www.vgd.co.uk/pages/notebook/mapsphere.html

- Jon

I'll start out with a basic explanation of concept, and then I'll explain the math as best I can. I can't give you the actual equasions, but I can give a general understanding of the process. Assuming you're more of a mathmatician than I am, you can probably work it out from there.

Think of the a texture on a sphere the same way you'd think of a map wrapping around a globe. On the 2D map, the very top and bottom represent the poles, and the center represents the equator. In 3D space, the poles of the globe each take up only one point while the equator takes up the entire circumference of the globe. On the map however, the poles and the equator are identical in size.

What this means is that when you apply the map to the globe, the map will shrink in places by various amounts ranging from zero shrinkage at the equator to 100% shrinkage at the poles. It's important to note that only the width of the map will shrink. The height will stay fixed. To put it more simply for the sake of your math, the very top and bottom of the map will end up with a width value of zero, while the very middle will end up with a width value of 1. The parts inbetween will end up with width values inversely proportional to their distance from the equator. The height value for all areas will always be 1.

So here are your variables:

X = height
Y = width

polesSizeY = 0
equatorSizeY = 1
allSizeX=1

northPoleLocationX = 1
equatorLocationX = 0
southPoleLocationX= -1

As |locationX| increases, sizeY proportionally decreases.

I think the width falls off quadratically, not linearly. If it were linear, I'm pretty sure you'd end up with two opposing cones instead of two hemispheres. As I said though, I'm not really qualified to give you the exact equasions. Hopefully this will get you on your way though.

Good luck.



Oh, and by the way, I'm not a big fan of that polar coordinates filter in Photoshop. It destroys entire sections of your image in its effort to forcefit the 2D image that it does understand onto its interpretation of a 3D sphere that it doesn't understand. So my advice if you were thinking about it is stay away from it.

I know this is an old thread but i have one word...

Mercator!

if you want a globe, just scan a Mercator projection out of any atlas.
apply to shpere as is.

Yes, Dianne is correct. Using any projection with the name Mercator in it will give you good results.