Message #413

From: Roice Nelson <roice@gravitation3d.com>
Subject: Re: [MC4D] On Rendering the Elusive 8th "Face" of the 4D Puzzle
Date: Tue, 21 Aug 2007 17:19:23 -0500

Fair enough, it wouldn’t hurt to have the "box with lid off" option (and the
additional option Alex suggested with altered sticker-shrink and face-grow
for the out face). Those like me who don’t prefer it for their own personal
aesthetic reasons simply don’t have to turn it on. Good points about the
artificial nature of the shrink settings too. As Einstein said, "Everything
should be made as simple as possible, but not simpler." I guess we just
have different opinions on where to draw the line in this case. Ultimately,
I think it is fair for the implementer to impose their own preference,
especially when the source code is available for modification to anyone who
would like to alter it otherwise.

There are some questions in my mind about the proper way to display a
removed lid. Do you flip it over, like you were opening a flap on a box? or
just cut the lid completely off and slide it over to the side as you
suggest? (in other words, does the representation of that face need to be
mirrored or not?) I can’t think of a great reason to truly favor one over
the other, so perhaps it would need to be an option? Also, if you want to
open the lid like a flap, maybe there is a case to be made that you should
go ahead and flatten the entire box, not by a mixture of projection and
unfolding, but entirely by unfolding. The resulting representation would be
a 3D cross, and none of the faces would have the severe distortion we see on
some of the faces in the current projection (since they would all lie in one
3D hyperplane and no 4D->3D projection would even be required). Such a
representation would seem a little more logically pure to me than one that
mixes projection/unfolding. Maybe I’ve just circuitously given an argument
for sliding the lid over instead of unfolding it :)

On the inside/outside semantics discussion, yes, it is a dynamic animation
effect I was describing. When I watch this:

http://www.mathematik.com/4DCube/4DCubePovray.html

and keep my eye on one of the faces moving down through the center, it
appears (to me) as if the cube turns inside out. This was all I was
saying. To accept this language, you must interpret the scene as if it was
3D only, and look at the face like it had an inside and an outside (the
terms in this case are not being used for "describing the position of the
eyepoint relative to a hyperface"). I recognize this appearance effect is
also due to the simplicity of the face geometry for a 4D cube. If you
placed a more complicated shape like me inside one of the faces, the
animation of the projection wouldn’t appear to turn me inside out and show
my guts. It would flatten me, then mirror me, as you’ve described. And the
possibility of the effect is sensitive to the movement of the viewpoint as
well. So anyway, I’ll concede on this too. You’ve made a good argument
that your language is more precise here…

Roice