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  Algorithm for Equirectangular projection (Plate Carre) ?  (Read 3566 times)
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Offline Addictman

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« Posted 2011-06-01 12:54:58 »


I'm dabbling with a spacegame, and I'm working with texturing planets at the moment. I have some tools to create decent-looking planet surfaces, - however they're the typical flat kind based off heightmaps etc. (Square shaped, - 512*512 pixels as an example).

To wrap around spheres seamlessly, I'd like to convert these images into an equirectangular projection so that they map very nicely around spheres. Does anyone have any code that does this, or perhaps can explain the algorithm to me?

Offline Roquen
« Reply #1 - Posted 2011-06-01 14:42:58 »

You're asking for a sampling method for encoding/decoding (roughly) equal area per texel when mapped to a sphere?

If so HEALPix is one method.  I can think of some others if this is the kind of thing that you're looking for.

Or the easy solution is to just use cubemaps.  I think that Spore just used cubemaps, but don't quote me on it.
Offline Addictman

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« Reply #2 - Posted 2011-06-01 15:07:39 »

Oh dear, I'm not even sure of what I am looking for, - there are so many terms and topics I know next to nothing about.

Let's say I have an image A, which is some fractal generated "world map" that I made. It can for instance be 512*512 pixels, with no distortions of any kind.

I want to get to image B, which would be a 1024*512 pixels image, with distortions near the poles, in a equirectangular (or plate carree, equidistant cylindrical, I guess it has many names) projection.

Does that explain better what I am looking for? (Because honestly, I did not understand half what the HEALPix page said).

Thanks for [your attempt] to help ;-)
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Offline Roquen
« Reply #3 - Posted 2011-06-02 15:09:06 »

My reply proves that I have the memory of a may-fly (and that I want to overcomplicate stuff).  I'd forgotten the title of the thread before I reached the end of your post.  Completely ignore my HEALPix comment.  And yeah, the wikipedia page is pretty unreadable.

I'd suggest not doing what you describe.  I (assume) that you'd be grabbing a 2D slice of noise into the 512x512, which is they warped to a 1024*512, which is then rolled into a cylinder and shrink-wrapped to a sphere.  What I'd suggest doing use cube mapping and when calculating the texture faces, project the normal that maps to the given texel back to the surface of the sphere and calculate the 3D noise function at that point.  (But, re-read my first sentence)

(I am trying to help..I promise!)
Offline Addictman

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« Reply #4 - Posted 2011-06-02 18:11:54 »

Now we seem to be on the same page Wink Excellent.

Cube mapping, - check. I'll definitely look further into that. Thanks!

Offline Roquen
« Reply #5 - Posted 2011-06-02 20:19:36 »

BTW: The mapping of a texel to the normal of the sphere should be easy to find.  Search for "normalization map" or cube map (or something of the sort).  Nvidia's SDK used to have code for it.  That'll give you a normalized vector, which you can multiple by some value to get various frequencies plus any offset value you want, etc. etc. when sampling 3D noise.
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