Display multiple 2D plots in 3D using Graphics in Mathematica? - graphics

Question

Considering the following :
lalist = {{{{1, 1}, 1}, {{3, 3}, 1}, {{5, 5}, 1}},
{{{1, 5}, 1}, {{3, 3}, 1}, {{5, 1}, 1}}}
Row[{
Graphics[{
Opacity[0.5],Red,
Disk ### lalist[[1]]},
Frame -> True],
Graphics[{
Opacity[0.5],Blue,
Disk ### lalist[[2]]},
Frame -> True]}
]
Is it possible that I plot the Blues
Disks "behind" the red ones in a 3 D
plot ?
Below is not what I need :

Answer 1

Like this?
Graphics3D[{{Texture[
Graphics[{Opacity[0.5], Blue, Disk ### lalist[[2]]},
Frame -> True]],
Polygon[{{-1, -1, -1}, {1, -1, -1}, {1, 1, -1}, {-1, 1, -1}},
VertexTextureCoordinates \[Rule] {{0, 0}, {1, 0}, {1, 1}, {0,
1}}]}, {Texture[
Graphics[{Opacity[0.5], Red, Disk ### lalist[[1]]},
Frame -> True]],
Polygon[{{-1, -1, 1}, {1, -1, 1}, {1, 1, 1}, {-1, 1, 1}},
VertexTextureCoordinates \[Rule] {{0, 0}, {1, 0}, {1, 1}, {0,
1}}]}}, Lighting \[Rule] "Neutral"]
Lots of them with opacity .2:
tab = Table[{Opacity \[Rule] .2,
Texture[Graphics[{Opacity[0.5], Blue, Disk ### lalist[[2]]},
Frame -> True]],
Polygon[{{-1, -1, z}, {1, -1, z}, {1, 1, z}, {-1, 1, z}},
VertexTextureCoordinates \[Rule] {{0, 0}, {1, 0}, {1, 1}, {0,
1}}]}, {z, -2, 2, 1}];
plt = Graphics3D[{tab}, Lighting \[Rule] "Neutral"]
and 400 don't seem to be much of a problem in terms of speed (you can easily modify the code above to see it).
EDIT: OK, just to be silly, try this
Dynamic[Graphics3D[{{Texture[#],
Polygon[{{-1, -1, -1}, {1, -1, -1}, {1, 1, -1}, {-1, 1, -1}},
VertexTextureCoordinates \[Rule] {{0, 0}, {1, 0}, {1, 1}, {0,
1}}]}, {Texture[Rotate[#, \[Pi]/2]],
Polygon[{{-1, -1, 1}, {1, -1, 1}, {1, 1, 1}, {-1, 1, 1}},
VertexTextureCoordinates \[Rule] {{0, 0}, {1, 0}, {1, 1}, {0,
1}}]}}, Lighting \[Rule] "Neutral"] &#Binarize[CurrentImage[]]]
which gives
(or something like that), rotatable, updated in real time etc.

Answer 2

See the solution presented on "Lunchtime Playground: Fun with Mathematica" here: http://mathgis.blogspot.com/2009/02/howto-display-2d-plot-in-3d.html

Answer 3

Using transparent textures to render these circles in layers as ACL does is a nice solution, unless one wants to interact with the resulting 3D object. Rendering of 3D objects that contain transparent elements is done in software whereas otherwise it would have been done in hardware:
The 3D renderer uses two different
methods of sorting polygons. For
graphics scenes that include no
transparency, a hardware-accelerated
depth buffer is used. Otherwise, the
renderer uses a binary space partition
tree to split and sort polygons from
any viewpoint. The BSP tree is slower
to create and is not hardware
accelerated, but it provides the most
general ability to support polygons.
On my laptop, interaction with 3D graphics is incredibly slow as soon as transparent objects start to appear.
The solution would be to use 3D disks instead of semi transparent planes with 2D disks in them. Since MMA doesn't have 3D Disks or Circles if you want to do something like that, you have to roll your own. A bare-bones version would be something like:
myDisk[{x_, y_, z_}, r_] :=
Polygon#Table[
{x, y, z} + r {Cos[\[Phi]], Sin[\[Phi]], 0} // N,
{\[Phi], 0, 2 \[Pi], 2 \[Pi]/200}
]
Your layers would then be generated as follows:
Graphics3D[
{
EdgeForm[],
{
Red,
myDisk[{1, 1, 0.5}, 0.5],
myDisk[{0, 0, 0.5}, 0.5],
myDisk[{-1, -1, 0.5}, 0.5]
},
{
Blue,
myDisk[{1, -1, -0.5}, 0.5],
myDisk[{0, 0, -0.5}, -0.5],
myDisk[{-1, 1, -0.5}, 0.5]}
}
]