How to progressively map a plane to a semisphere?

[PhotoComix]

yes in small changes ! as for a animation (and also for animation)

i have already a code for get to the original to the image to the right, but i can not imagine how to achieve the in between transformation, all the small changes from normal to
semi spherical

[NymTevlyn]

Photoshop > Filter > Distort (I think...) > Spherize =)

At least, that's the easy way. Dunno if there's anything at all like that already in GIMP.

[isomage]

If a point has initial position (x0, y0) and final position (x1, y1), you could try just parameterizing the line segment between them.

Let x(t) = x0 + (x1 - x0) t, and y(t) = y0 + (y1 - y0) t. Then as t varies from 0 to 1, (x,y) varies from (x0,y0) to (x1,y1). If you want N steps, generate frames for t = 0, 1/N, 2/N, ..., 1.

[ravells]

For an animation I'd definitely use the spherise filter in photoshop as Nym said. I tried it to begin with but it didn't map the corners of the perimeter of the square to the perimeter of the circle (which is what I thought was wanted), so I went down the UV mapping route.

If want you want to do is an animation and are not too particular about the distortion, then go for spherise in stages saving each image as you go along and increasing the slider a notch, but note the image will still be square with a 'pushed out' sphere in the centre. You'd probably also have to do a warp too to make it move from a square to a circle in shape.

Isomage, when I was taking A level maths, I remember thinking what on earth I'd ever need those skills for in later life. Now I know, but I've forgotten it all!

[Ascension]

I think one of the Adobe programs (Elements or After Effects, not sure but I think the latter) can save an image consisting of many layers as an animated gif. That way you could do the Spherize in increments and put each version on its own layer.

[isomage]

xprime=x/sqrt(1-4*(y/H)*(y/H));
yprime=y/sqrt(1-4*(x/W)*(x/W));

Are you sure about that transformation? If I apply that to each pixel in your image, I get this:

[ravells]

And that's the opening sequence credits to Doctor Who!!!

[isomage]

I failed to find the discussion on the formula to be applied but if may help i have as Mathmap code

filter rel2ellv3(image in)
xprime=x/sqrt(1-4*(y/H)*(y/H));
yprime=y/sqrt(1-4*(x/W)*(x/W));
in(xy:[xprime,yprime])
end

I've just had a brief look at mathmap's documentation and examples, and it appears to be able to do animations; as far as I can tell, if you use a "t" parameter it will automatically generate an animated gif (see http://www.complang.tuwien.ac.at/sch...map/anims.html and http://www.complang.tuwien.ac.at/sch...tml#animations). So assuming your xprime, yprime transformations work correctly in mathmap to give your final image, then I'd guess you might be able to get your desired animation with this:

filter rel2ellv3(image in)
xprime=x/sqrt(1-4*(y/H)*(y/H));
yprime=y/sqrt(1-4*(x/W)*(x/W));
in(xy:[x+t*(xprime-x),y+t*(yprime-y)])
end

I haven't tried it, though.

[RobA]

filter rel2ellv3(image in)
xprime=x/sqrt(1-4*(y/H)*(y/H));
yprime=y/sqrt(1-4*(x/W)*(x/W));
in(xy:[x+t*(xprime-x),y+t*(yprime-y)])
end

I haven't tried it, though.

I tried it. works brilliantly!

Good job.

-Rob A>

[PhotoComix]

filter rel2ellv3(image in)
xprime=x/sqrt(1-4*(y/H)*(y/H));
yprime=y/sqrt(1-4*(x/W)*(x/W));
in(xy:[x+t*(xprime-x),y+t*(yprime-y)])
end

I haven't tried it, though.

@Isomage

I did try...perfect ! ...exactly what i was looking for, thank a lot (and thanks for all the other contribute )

PS the image you posted as example was strange but the code work well !

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About animation gif has to low quality for my taste, but gimp (with a AVI plugin, or with GAP ) may save as uncompressed AVI, then is quite simple apply a codec to shrink the file size or convert to FLV