graphics zoom inaccuracy
- To: mathgroup at smc.vnet.net
- Subject: [mg27932] graphics zoom inaccuracy
- From: Gianluca Gorni <gorni at dimi.uniud.it>
- Date: Sat, 24 Mar 2001 00:48:57 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Hello!
I have just discovered that I cannot trust the FrontEnd graphics
display to decide whether a point is inside a circle or not, when
it is very close to the border: visually the answer seems to depend
on options like PlotRange and AspectRatio!
Here is my example:
{radius, px, py} = {235/239, 79/4441, (385743*Sqrt[3])/14624213};
obj = Graphics[{Disk[{1, 0}, radius], PointSize[.04], RGBColor[1, 0, 0],
Point[{px, py}]}];
With the following options the point appears outside the disk, as it should:
Show[obj, PlotRange -> {px + {-1, 1}/(1*10^4), py + {-1, 1}/(1*10^4)},
AspectRatio -> Automatic]
Show[obj, PlotRange -> {px + {-1, 1}/(2*10^4), py + {-1, 1}/(2*10^4)}];
With the next choice of options the point looks as if it is *inside*
the disk:
Show[obj, PlotRange -> {px + {-1, 1}/(2*10^4), py + {-1, 1}/(2*10^4)},
AspectRatio -> Automatic];
I exported the third picture as eps, and looked at it in
Illustrator and FreeHand: the point is still inside, but by quite
different margins. So perhaps the problem is with
PostScript interpreters in general and not restricted to Mathematica.
What about extra-accurate graphics for the next major Mathematica version,
that protect us users from the vagaries of PostScript? I mean, when
the graphics primitives have infinite precision, Mathematica should take over
the zooming calculations and not leave them to the PostScript interpreter.
My version is "4.1 for Power Macintosh (November 2, 2000)"
Gianluca Gorni