[metapost] envelope proposal 4

[Larry Siebenmann]

Hi Jacko,

You write (Wed, 16 Mar 2005 10:03:20 +0100):

 > But you agree, that a human being is able to find a
 > continuous one-hand envelope, at least in most of
 > practical cases. If so, there must have been an
 > algorithmic approach...

I think you are misunderstanding me from this point on.  Let
me try to be a bit clearer about the difficulty caused by
cusps

You and I can find a rule for defining a continuous
envelope in all cases, algorithmically.  The quandry I
mention at cusps is that we may not agree which curve it
is, say for the 'i' example I gave.  But the worse
difficulty is that because of cusps, nobody can define
continous envelope paths for proposal 4 in all cases SO AS
TO VARY CONTINUOUSLY AS THE PATH CONTROL POINTS VARY
CONTINUOUSLY. That's embarrassing since usually we anly
know the control points approximately.  However, we are
saved by the consideration that (normally/always?) the
discontinuity of envelope variation occurs inside the
inked region, and so has no impact on the the enduser.

Cheers

Laurent S.

PS.  Cusps at integer time are a bit more general and also
more common than cusps at than cusps at non-integer time.