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MathGroup Archive 2011

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Oblique coordinates from cartesian coordinates

  • To: mathgroup at smc.vnet.net
  • Subject: [mg119404] Oblique coordinates from cartesian coordinates
  • From: Francisco Miguel Morales Sanchez <fmiguel.morales at gm.uca.es>
  • Date: Thu, 2 Jun 2011 07:15:34 -0400 (EDT)

Hello:
3D plots and contourplots are generated authomatically in a cartesian
base with x
and y axes having 90 degrees between them but I would like this axis
to appear as if it was 60=BA.

I found that a 3D object can be presented with a
different "aparent angle" by using oblique coordinates with "Affine"
or "Geometric Transformation", for example:

gr = {Cuboid[], AbsolutePointSize[10], Opacity[1], {Magenta, Point[{0,
0, 0}]}, {Green,     Point[{1, 1, 1}]}};

Graphics3D[{{Opacity[.35], Blue, gr},
GeometricTransformation[{Opacity[.85], Red,
    gr}, {{{.8, .5, .5}, {0, .8, .5}, {0, 0, .8}}, {.5, .5, 0}}]},
Boxed -> False]


MY QUESTION IS: Why can I not make the same procedure for a Plot3D or
a ContourPlot? Following the same way I get not output. This is an
example of waht I say:

A=Plot3D[Sin[x + y^2], {x, 0, 1}, {y, 0, 1}];
Graphics3D[{GeometricTransformation[A, {{{.8, .5, .5}, {0, .8, .5},
{0, 0, .8}}, {.5, .5, 0}}]}]

I WOULD BE VERY GRATEFUL IF YOU COULD HELP ME!, THANKS IN ADVANCE.
Paco


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