Xref: utzoo sci.math:6943 comp.graphics:6046
Path: utzoo!utgpu!jarvis.csri.toronto.edu!rutgers!apple!voder!berlioz!nelson
From: nelson@berlioz (Ted Nelson)
Newsgroups: sci.math,comp.graphics
Subject: Re: Computing Bezier Control Points for an Arc of a Circle
Keywords: bezier, arc, graphics
Message-ID: <317@berlioz.nsc.com>
Date: 7 Jun 89 01:57:34 GMT
References: <108121@sun.Eng.Sun.COM> <10150@watcgl.waterloo.edu>
Reply-To: nelson@berlioz.UUCP (Ted Nelson)
Organization: National Semiconductor, Santa Clara
Lines: 23


In article <10150@watcgl.waterloo.edu> rhbartels@watcgl.waterloo.edu (Richard Bartels) writes:
>This is one of the Golden Oldies.  You can't do a circle exactly
>as a Bezier curve (at least as an integral Bezier curve, you can do
>conic sections as rational Bezier curves).

Yes, but there is nothing to stop you from using 8-way symmetry.  Worst
  case is 2-way symmetry for a rotated ellipse.

We did a simple solution to this problem.  The user would input 3 points
  on the circle and it would draw the circular arc which they define.  All
  we did was to compute the radius of the circle, have a look-up table to
  grab pre-computed Bezier increments which were then stepped up by the
  radius (thus, it would work for ellipses too).  From this it would construct
  a point list in memory of only the octants (use 8-way symmetry) that it
  go through.  It took out the display list before the first point and after
  the third point, and proceeded to draw a line from the first point, the
  complete remaining point list, and then to the third point.

In fact, we did it in assembly language on a NSC Raster Graphics Processor.
  It was only about 12 pages ==> a page or two of C code...

-- Ted.