Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ames!eos!shelby!polya!rokicki
From: rokicki@polya.Stanford.EDU (Tomas G. Rokicki)
Newsgroups: comp.sys.amiga
Subject: Re: Dmouse 1.20 and DLineArt
Keywords: neat stuff!
Message-ID: <11542@polya.Stanford.EDU>
Date: 25 Aug 89 23:31:17 GMT
References: <1451@esunix.UUCP> <123627@sun.Eng.Sun.COM>
Sender: Tomas G. Rokicki <rokicki@Polya.Stanford.EDU>
Organization: Stanford University
Lines: 33

raz%kilowatt@Sun.COM (Steve -Raz- Berry) writes:
> >Steve, you really ought to see your lineart run on a 68020, it goes nuts!
> >The Elipse moves along at a moderate pace, but the others are hyperactive.
> If I can figure out how to generate ellipses with splines, they will cruise
> along nicely too.

Two ways to do ellipses with splines, the first is faster but less
accurate, the second is slower but more accurate.

In both, the spline is centered at (x,y) with x-axis a and y-axis b.

First method:  two splines, they are
   [(x-a, y), (x-a, y-4b/3), (x+a, y-4b/3), (x+a, y)]
   [(x-a, y), (x-a, y+4b/3), (x+a, y+4b/3), (x+a, y)]
This isn't exactly an ellipse, but is probably close enough for most
people.  Please, round the 4b/3 terms *towards* the center of the
screen, or the extrema may go off the screen.  Also, reverse the second
so that it gets drawn clockwise instead of in halves from left to right.

Second method, four splines, they are:
   [(x-a, y), (x-a, y+cb), (x-ca, y+b), (x, y+b)]
   [(x, y+b), (x+ca, y+b), (x+a, y+cb), (x+a, y)]
   [(x+a, y), (x+a, y-cb), (x+ca, y-b), (x, y-b)]
   [(x, y-b), (x-ca, y-b), (x-a, y-cb), (x-a, y)]
in all of these, c=4(sqrt(2)-1)/3 or something like 0.55.
This is highly accurate, off less than r/3600 at the worst point.

You should check out the latest mackie (Radical Eye Radio, (415) 32-RADIO)
and see how it generates a random set of patterns . . . also make *sure*
that the spline code is the version in the latest mackie; the old
version would hang if the four points happened to be coincident . . .

-tom