       Scaling a part of a composite image

• To: mathgroup at smc.vnet.net
• Subject: [mg98748] Scaling a part of a composite image
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Fri, 17 Apr 2009 04:31:13 -0400 (EDT)

```Dear community,

In an image composed of at least two (or more) parts combined using
Show, I would like to programmatically scale one of these two images
with respect to the size of the whole composite image.
Do you know, how to do this in Mathematica 6?

Is it possible in Mathematica 6 to determine programmatically the total size of the Image?

To be more concrete: the function below draws a 3D trajectory - a
solution of a system of three ODE. In addition it draws a triangle
attached to the trajectory. The latter plays the role of an arrow head
showing the direction of the trajectory. Parameters in the argument
are:  point is a list of initial values {x0,y0,z0} of the trajectory,
tmax is the calculation time, col is the color of both the trajectory
and the arrow head, arrpos is the time fixing the position of the arrow
on the trajectory, and arrsize scales the arrow size. The subfunction
arr defines the arrow using 2 closely-lying points taken on the trajectory.

directedTrajectory3D[point_List, tmax_, col_, arrpos_, arrsize_] :=
Module[{p0, eq4, eq5, eq6, pt1, pt2, s},
arr[pt1_List, pt2_List] := Module[{r},
r = (pt1 - pt2)2 /. List -> Plus // Sqrt;
Graphics3D[ {col,
Polygon[{pt1, {pt2[], pt2[] - 0.2*r,
pt2[] - 0.2*r}, {pt2[], pt2[] + 0.3*r,
pt2[] + 0.2*r} }]}]];

eq4 = x == point[];
eq5 = y == point[];
eq6 = z == point[];
s = NDSolve[{eq1, eq2, eq3, eq4, eq5, eq6}, {x, y, z}, {t, 0,
tmax}];
p0 = ParametricPlot3D[
Evaluate[{x[t], y[t], z[t]} /. s], {t, 0, 30}, PlotRange -> All,
PlotStyle -> col, AxesLabel -> {"x", "y", "z"}];

Show[{p0,
arr[Evaluate[{x[arrpos], y[arrpos], z[arrpos]} /. s] // Flatten,
Evaluate[{x[arrpos - 0.5*arrsize], y[arrpos - 0.5*arrsize],
z[arrpos - 0.5*arrsize]}] /. s // Flatten]}]
];

One can try with the example of Lorentz system from help:

Clear[eq1, eq2, eq3];
eq1 =
\!\(\*SuperscriptBox["x", "\[Prime]",
MultilineFunction->None]\)[t] == -3 (x[t] - y[t]);
eq2 =
\!\(\*SuperscriptBox["y", "\[Prime]",
MultilineFunction->None]\)[t] == -x[t] z[t] + 26.5 x[t] - y[t];
eq3 =
\!\(\*SuperscriptBox["z", "\[Prime]",
MultilineFunction->None]\)[t] == x[t] y[t] - z[t];

directedTrajectory3D[{1, 0, 1}, 30, Red, 5, 0.1]

A strong drawback is that in this function one needs to rescale the
arrow sizes by hand each time. Compare two images with the same
trajectory in which the arrow is placed the first time at t=5 and then
at t=15 with the same arrsize=0.1.

directedTrajectory3D[{1, 0, 1}, 30, Red, 5, 0.1]
directedTrajectory3D[{1, 0, 1}, 30, Red, 15, 0.1]

I would like to find a programmatic way of scaling the arrows so that
they would be always visible and the same size.

Thank you, Alexei

--
Alexei Boulbitch, Dr., habil.
Senior Scientist

IEE S.A.
ZAE Weiergewan
11, rue Edmond Reuter
L-5326 Contern
Luxembourg

Phone: +352 2454 2566
Fax:   +352 2454 3566

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```

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