Don Hatch wrote:
> Maybe it's obvious by now, but what I meant was, how would you
> augment our front-face-removed perspective picture to represent
this?
> It seems pointless to me to even think about the 4D case without
> understanding what you would want in the 3D case first.
>
> Don
you're totally correct that any solution should start with a proper 3d
analogy, and i did learn from the process.
so here's another attempt. this time as an attachment for a smaller
message, and with colors roughly matching the initial mc4d colors
including the green hidden face. the dotted lines are not part of the
diagram but are there for clarity of the diagram showing where the
invisible faces would be if they were to be drawn. notice how the
mirror
looks "through" the purple face to show the invisible face. that's
because from the mirror's perspective the purple face is inverted and
therefore is correctly not drawn. i also included the face expansion
but
left out sticker shrink for ease of modeling. now perhaps the main
view
didn't need to be rotated slightly and therefore foreshortened, but
hopefully you'll all get the general idea.
regarding christian's message, the current view is not an "unfolding"
of
any sort. it's an accurate projection of the inside of a 4d box. it's
an
admittedly strange box because it has the property that the faces are
only visible when viewed from the inside and are transparent from the
other side. that's clearly a strange definition, but it has a common
and
perfect analogy in 3d computer graphics called "backface removal", or
in
this case "frontface removal" which is occasionally used in scientific
visualization, especially for the interactive viewing of 3d charts.
i'd
definitely want any 4d mirror to be equally accurate and consistent.
what do you think?
-daniel
--- End forwarded message ---