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[Timotei Dolean <>]

Well, I'll try and research a bit about that "constant curvature" thingy, with the positively curved and negatively curved. Hope it i what the teacher wants. I cannot speak with him yet.
I found this on Wikipedia: "The standard surface geometries of constant curvature are elliptic geometry (or spherical geometry) which has positive curvature, Euclidean geometry which has zero curvature, and hyperbolic geometry (pseudosphere geometry) which has negative curvature.". So I think that's what I have to do, since the euclidean geometry has no curvature, and we see the object in their "real" form.

Thanks
Timotei

Akanksh Vashisth wrote:

>From what I could gather about the description, you want to simulate the view from a viewers perspective depending on the rays travelling within a certain metric being refracted by the medium they travel in. So if the space is Minkowski, it will look like it looks normally without glasses, but if the space has positive curvature, then the image shall start looking like a convex lens? is that correct? 

If it is, then you will have to do some ray tracing to generate rays from the eyes going through the "pixels" in you image and seeing if and where they intersect. And the behaviour of rays in the metric could be simulated by mixing the behaviour of both the Fresnel terms, and step integration of the the ray through the participating medium. Or you could simple transform the vertices of the object into the metric you want and then project them using perspective projection onto a plane.

Although I do not think that my understanding of the problem is correct as ray tracing is a domain in itself and I don't think any teacher shall give this as a simple "program" assignment. I believe what will be of much help in getting the solution is giving a few test cases, for instance, what will I see if I see a Box through these glasses? If the space is Minkowski, Positively curved, Negatively Curved etc.?

Hope this helped.

Cheers!

- Akanksh 

2010/1/11 Timotei Dolean <>

Well, I'll try to reformulate it.

So we a pair of eyeglasses. When we look through them, the eyeglasses closes to or away the point at which we look. The closing and awaying of the points are based on a defined metric (lets say in Minkowski metric).
For an easier start, let's presume we are looking at a sphere. I have to generate an image (perspective) based on HOW it will look that sphere if we would look through that eyeglasses.
So practically every pair of eyeglasses (from the real world) based on the diopter of the lens, make the people looking through them see the "focused" image.
So in almost the same fashion I should generate a sphere viewed from a point in space, based on the Minkowski metric.

Is that better?:)

Timotei

Bernd Gaertner wrote:

Timotei Dolean wrote:

So... nobody know where I should start?:)

Given this fuzzy description I'm afraid not. I have no clue what you are exactly supposed to do.

This is what I have to do: "Suppose we have some glasses that closes or aways the points at what we are looking, in respect with a metric, let it be for example: Minkowski.  HOW we see from a certain point, a sphere for example? "

Bernd.