Re: Non-Linear Graphics Scaling

• To: mathgroup at smc.vnet.net
• Subject: [mg86507] Re: Non-Linear Graphics Scaling
• From: dh <dh at metrohm.ch>
• Date: Wed, 12 Mar 2008 05:29:19 -0500 (EST)
• References: <fr7ona\$373\$1@smc.vnet.net>

```
Hi Januk,

a non-linear function will map lines to curves. Therefore, you e.g. may

replace every line by many lines, approximating the curve. E.g.:

graphics /. Line[{{x01_,y01_},{x02_,y02_}}]:>(calculate

x1..n,y1..n;Line[{{x1,y1},..,{xn,yn}}]

If you have more complicated graphics you must also deal with the case:

Line[{pt1,pt2,..ptn}].

Finally you could extend this scheme to geometric shapes like Circle e.t.c

hope this helps, Daniel

Januk wrote:

> Is there a way to have mathematica display a graphic using a non-

> linear scaling function?  I want to scale any point on a 2D graphic by

> some non-linear function of the distance away from the origin.  For a

> list of points, it is trivial to force the issue:

>

> pl3 = Graphics[{Point[

>      RandomReal[{-20, 20}, {1000, 2}]

>      ]

>     }, Frame -> True, PlotRange -> All];

> GraphicsRow@{pl3,

>   pl3 /. (xy : {x_?NumericQ, y_?NumericQ} :>

>      Module[{r, \[Theta]},

>       r = If[Norm[xy] == 0., 0, Log[1+Norm[xy]]];

>       \[Theta] = If[Norm[xy] == 0., 0, ArcTan @@ xy];

>       r {Cos[\[Theta]], Sin[\[Theta]]}

>       ]

>     )}

>

> Is there a way to do this for more complecated graphics (e.g. graphics

> with primitives)?  For example:

>

> pl2 = Graphics[{

>    Red, Point[RandomReal[{-2,2},{100,2}]],

>    Orange, Line[{{-2, .75}, {2, .75}}],

>    Green, Thick , Circle[{0, 0}, 2],

>    Black, Point[{0, 0}]

>    }]

>

> So far the technique of using a ReplaceAll simply transforms the end

> points of the line, not the line shape.

>

> Any thoughts of how to do this for an arbitrary Cartesian 2D graphic

> would be much appreciated.

>

> Thanks,

> Januk

>

```

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