Re: Escher perspective

Andy Norris (andyn@texas.net)
Thu, 04 May 1995 19:49:46 -0400

At 12:35 PM 5/3/95 -0700, vworlds-list@netcom.com wrote:
>
> From: vanevery@rbdc.rbdc.com (Brandon Van every):
>
> But you guys keep missing the point: computer graphics is _not_ 3d.
> It's all 2d _projections_ of stuff. Just because you can't build a 3d
> model of many Escher works, does _not_ mean you can't create
> continuously moving 2d perspective illusions which resemble his works.
> There is probably a mathematically correct way to do this. Even if
> there isn't, it can probably be simulated through extra processing of
> the viewer's perspective as he/she moves. So you run out of illusion
> after traversing 180 degrees or whatever. Big deal, you can always
> put up a wall to block the user from moving any farther than that.
>
>Well, actually that's getting into implementation specifics, which is
>somewhat outside of the charter for this list, I believe.

I think he's just saying that it could be done.

>Sterographic
>viewing is NOT strictly 3d transformed to 2d, and may be what many
>people invision when they think of VR.

This is the central problem. Assuming a stereographic view, it
probably doesn't work.

>Also, the problem with doing
>the Escher transform, is that the actual physical representation of
>the space would change based on the 2d results as the viewer moved,
>basically a reverse of how the transform normally works. The point is
>developing a 3d model to represent Esherian space and have a standard
>viewing transform for it, which is most likely not possible. What your
>suggesting would involve more than one viewing engine, basically one
>for every view produced, as there is no standard algorithm for
>producing Escherian effects.

If you assume a, um, monographic perspective, then it might be
possible. What it would mean is that instead of generating a 3D world
up front and just navigating it in real time, you would have to have
some kind of transform that generates the world on the fly as you
navigate it. This isn't how we normally think about a virtual world,
but there's no real reason you couldn't build one this way (technical
limitations not withstanding).

>What would be more interesting, I think, is to take the 3d space and
>play games with representing 4d space... i.e. extrapolate what Escher
>might do with the same tools.

Tell me what you're thinking of with 4D worlds. It's interesting
conceptually, but I'm not sure what it means in practical--or, for
that matter, even visual--terms.

--Andy