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Re: Scaling a part of a composite image
*To*: mathgroup at smc.vnet.net
*Subject*: [mg98843] Re: Scaling a part of a composite image
*From*: dh <dh at metrohm.com>
*Date*: Mon, 20 Apr 2009 05:41:04 -0400 (EDT)
*References*: <gs9eo8$n10$1@smc.vnet.net>
Hi Alexei,
to specify your arrow, you may use a mix of coordinates and scaled
coordinates like e.g.:
Polygon[{pt1, Scaled[10^-2 {0, -2, -2}, pt2],
Scaled[10^-2 {0, 3, 2}, pt2]}]
Daniel
Alexei Boulbitch wrote:
> 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[[1]], pt2[[2]] - 0.2*r,
> pt2[[3]] - 0.2*r}, {pt2[[1]], pt2[[2]] + 0.3*r,
> pt2[[3]] + 0.2*r} }]}]];
>
> eq4 = x[0] == point[[1]];
> eq5 = y[0] == point[[2]];
> eq6 = z[0] == point[[3]];
> 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
>
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