mcdonald@uxe.cso.uiuc.edu (02/19/89)
>Assumptions: Your ellipse is aligned vertically (i.e. not rotated), and > the center (h, k) is given in rational numbers with denominator d. > Also, the eccentricity is small (since you say it's for a raster device, > I assume the pixel aspect ratio (length/width) is near one). I also assume > that the major and minor radii (a and b) are rational with denominator d. Wrong, Wrong, and I guess that's OK. In other words, I would like the answer for arbitrary orientation (e.g. major axis at 23 degrees to the horizontal) and eccentricity. I have found no usefully fast answers for this. Anybody out there have the answer? I have looked in several textbooks and never found any help. Doug McDonald
stanford@aostra.UUCP (curtis stanford) (02/22/89)
In article <46900031@uxe.cso.uiuc.edu>, mcdonald@uxe.cso.uiuc.edu writes: > > > >Assumptions: Your ellipse is aligned vertically (i.e. not rotated), and > > the center (h, k) is given in rational numbers with denominator d. > > Also, the eccentricity is small (since you say it's for a raster device, > > I assume the pixel aspect ratio (length/width) is near one). I also assume > > that the major and minor radii (a and b) are rational with denominator d. > > In other words, I would like the answer for arbitrary orientation > (e.g. major axis at 23 degrees to the horizontal) and eccentricity. > I have found no usefully fast answers for this. Anybody out there > have the answer? I have looked in several textbooks and never found > any help. > > Doug McDonald I don't know how fast this is or if anyone else has mentioned it but in the November, 1988 issue of Computer Language there is a good article on Ellipses, Parabolas, & Hyperbolas including a routine "xyellipse" to draw so called "vertical" ellipses and a routine "angellipse" to draw ellipses at an arbitrary angle from the x axis. It involves calling cos and sin just once at the beginning of the routine. I plan on trying it soon but at the moment I have no idea how fast it is. The only problem is that "angellipse" overlaps pixels and may leave pixel wide gaps making it inappropriate for flood fills. Later... Curtis Stanford Alberta Oil Sands Technology and Research Authority Calgary, AB calgary!aostra!stanford