Path: utzoo!attcan!uunet!oddjob!uwvax!husc6!mailrus!chianti!shane
From: shane@chianti.cc.umich.edu (Shane Looker)
Newsgroups: comp.graphics
Subject: Bezier Surface computations
Message-ID: <618@mailrus.cc.umich.edu>
Date: 8 Aug 88 14:25:41 GMT
Sender: usenet@mailrus.cc.umich.edu
Reply-To: shane@um.cc.umich.edu (Shane Looker)
Distribution: comp.graphics
Organization: University of Michigan Computing Center, Ann Arbor
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Well, yesterday I was reading my textbook on graphics (3D stuff), and 
was going through the section on Bezier lines and surfaces.  I implimented
the basic functions with no problem, and as I suspected, they are real
dogs computationally.

There was also a nice section on converting the functions to using only
integer math (it implies) and using function step differences to compute
the next value of the function.  There is an explination of how a 4 point
Bezier curve is a cubic polynomial of the form:
         f(u) = a[0]*u^3 + a[1]*u^2 + a[2]*u + a[3]

The real problem with this nice bit of math is that it NEVER gives a clue as
to what the coefficients a[0]...a[3] are related to!!!  I spend over an hour
yesterday trying to figure out how to derive these and how to write the
necessary translation functions for x, y, and z.

The book was:
  Computer Graphics           (how do they come up with these clever names?)
  Hearn and Baker.            (From Illinois)


If anybody can tell me the answers to my questions, you will get a good deal
of thanks.

Shane Looker
Looker@um.cc.umich.edu