[MUD-Dev] Re: Nested coorindate space model

Michael Hohensee michael at sparta.mainstream.net
Mon Jun 15 18:31:38 New Zealand Standard Time 1998


J C Lawrence wrote:
> 
> On Fri, 05 Jun 1998 18:40:04 -0400
> Michael Hohensee<michael at sparta.mainstream.net> wrote:
> 
> > Sorry it took me so long to respond to this message.  I've had to do
> > some heavy number crunching. :)
> 
> Unfortunately you still missed a key point.
> 

No, I realize that what I put forth doesn't work yet.  I tried to
explain why in my previous post.  What you've described here is
essentially another example of why my original idea doesn't work.  I
haven't missed that. :)  As I said, I'm still trying to find the correct
algorithm.  Perhaps it doesn't exist, but it's interesting to try.

> > J C Lawrence wrote:
> 
> >> On Sat, 30 May 1998 12:07:44 -0400 Michael
> >> Hohensee<michael at sparta.mainstream.net> wrote:
> >
>
> Understood.  Unfortunately perceived distance is a function of
> geometry and that geometry occurs in hard coordinates.
> 

True.  And as I said in my previous post, the fact that I was relying on
hard coordinates as if they were "percieved" coordinates was why I was
getting the wrong answer.  I've since found the solution to my first two
"non-ideal" cases (i.e. the ones I made up and posted) but I've found
those two solutions don't work for more complex situations (including,
by the way, the one you just described)  It seems that as you complicate
things, you find that each case is really just a simplified case of the
pervious one.  I'm currently working on an "N space solution."  If I
find it, I'll let you guys know.  (And I'll even make sure that it
works, before I show it to you. ;)

> > So, if you do the math, you find that as the angle subtended by the
> > stick decreases, the distance that the observer's vision-path
> > travels through Y increases.  If we use the right formula, we get
> > the same length of the stick no matter where we look at it from.
> 
> This is conveniently only true except when the translation layer is
> parallel to the line of sight.  It becomes less true as the angle
> between the line of sight and the translation layer moves approaches a
> normal.

Yes, and if you do the geometry, (O my aching hands) you find that
unless you take additional steps beyond the simple Side-Angle-Side
formula, you end up measuring a length which is not the stick.  The
trick is to then take that length, and turn it into the length of the
stick. (or, take that length, and the stick's length, and use them to
reverse-engineer your way to a simple formula.)

--
Michael Hohensee       michael at mainstream.net
http://www.geocities.com/SiliconValley/Heights/9025/
      Finger me for my PGP Public Key, or use: 
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