Oblique coordinates for ContourPlots and Plot3D

Discussion in 'Mathematica' started by Francisco Miguel Morales Sanchez, May 29, 2011.

1. Francisco Miguel Morales SanchezGuest

Hi everybody:

I am new in this group and just found it, so I do not know if this or
a similar question was solved before here and if it is easy to solve.
I am trying to make a kind of ternary plot of a function, so plotting
x vs y adding the excemption x+y<1 I am able to get what I need, since
I consider the line joining x=0,y=1 my z axis for a AxByCz mix where x
+y+z=1. I did not close my task since these graphs are often presented
with an equilateral triangular shape base and my graphs look with x
and y axes having the coomon 90=BA between them for cartesian
coordinates. Well, I found that a 3D object can be presented with a
different "aparent angle" by using oblique coordinates with "Affine"
or "Geometric Transformation", I copy bellow the example for a
transformation applied to a 3D shape, a cuboid, found in Wolfram
documentation:

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

In[2]:= 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 FOR A 3DPLOT OR A
COUNTOURPLOT?, IF I FOLLOW THE SAME WAY I HAVE NOT OUTPUT, I WOULD BE
VERY GRATEFUL IF YOU COULD HELP ME!, THANKS IN ADVANCE. ps: A simple
example not working:

In1: A=Plot3D[Sin[x + y^2], {x, 0, 1}, {y, 0, 1}]
In2: Graphics3D[{GeometricTransformation[A, {{{.8, .5, .5}, {0, .8, .
5}, {0, 0, .8}}, {.5, .5, 0}}]}]

Francisco Miguel Morales Sanchez, May 29, 2011