6
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To visualize an eigenvector and value calculation I tried to display the eigenvectors (scaled by the eigenvalues) as arrows in a Graphics3D plot using Manipulate. The (symmetric) matrix is a function of three variables, so I used the sliders to set the point at which I evaluated the matrix.

This worked rather nicely, but as I change the Manipulate sliders, the box size and orientation and scaling changes which kills the effectiveness of the animation attempt.

I'm looking for a Graphics3D option that would prevent this dynamic scaling of the bounding box size and orientation. ViewAngle and ViewCenter looked the most appropriate, but didn't produce the result I expected.

Any idea how to do this?

For reference (and possible experimentation), here's the notebook content for the visualization:

Clear[o, e, e1, e2, e3, standardBasis, ee, ev, arrows, \
arrowsReference,  x, y , z , p]
o := {0, 0, 0}
e1 := {1, 0, 0}
e2 := {0, 1, 0}
e3 := {0, 0, 1}
standardBasis := {e1, e2, e3}
Manipulate[
 e := {{2 y, x, x}, {x, 0, z}, {x, z, -1}} ;
 p := {x, y, z} ;
 ev = Eigenvalues[e] ;
 (*
 Taking the orthonormal eigenvectors, and scaling them by their \
eigenvalues to get a feel for their magnitude and direction.
  *)
 ee := ev Map[ Normalize, Eigenvectors[e]]  //
   N ; (* note: sneaky multiplication of lists, pairwise eigenvalue \
times eigenvector as in:
 a = {1.5, 2}
 b = {2, 3}
  a b

 which produces: {3, 6}
 *)
 arrows = Table[Arrow[{p, p + Part[ee, i]}], {i, 3}] ;
 arrowsReference =
  Table[Arrow[{p, p + Part[standardBasis, i]}], {i, 3}] ;
 Graphics3D[{Red, Arrowheads[.05], arrows, Blue, Arrow[{o, p}],
   Green, arrowsReference}, Boxed -> True, Axes -> True],
 {{x, 1}, -10, 10},
 {{y, 2}, -10, 10},
 {{z, 4}, -10, 10}]
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  • 2
    $\begingroup$ Have you tried setting SphericalRegion -> True in Graphics3D[]? $\endgroup$ – J. M. will be back soon Feb 8 '12 at 3:00
  • $\begingroup$ I hadn't tried SphericalRegion, but it doesn't change things noticeably. $\endgroup$ – Peeter Joot Feb 8 '12 at 3:10
3
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Have you tried setting PlotRange->10 ?

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