Manipulate [ Show [graphics ]]]
- To: mathgroup at smc.vnet.net
- Subject: [mg108267] Manipulate [ Show [graphics ]]]
- From: leigh pascoe <leigh at evry.inserm.fr>
- Date: Fri, 12 Mar 2010 07:09:51 -0500 (EST)
Dear Experts,
I am plotting some frequencies and a function in a 3D graph. Each
frequency is a real number between [0,1], so I am plotting these in a
tetrahedron where the frequency is measured along the sides of the unit
tetrahedron. The basic tetrahedral axes and transformations are encoded
as follows:
First define a linear transform to put points in tetrahedral coordinates
and draw the tertrahedral box
v1 = {0, 0, 0};
v2 = {1, 0, 0};
v3 = {0, 1, 0};
v4 = {0, 0, 1};
lintrans[v_] :=
Module[{mat = {{1/2, -1/2, 0}, {-1/(2*Sqrt[3]), -1/(2*Sqrt[3]),
1/Sqrt[3]}, {-Sqrt[2/3], -Sqrt[2/3], -Sqrt[2/3]}},
tr = {0, 0, Sqrt[2/3]}}, mat.v + tr]
tetrahedron[{v1_, v2_, v3_, v4_}] := {Line[{v1, v2, v3, v1}],
Line[{v1, v2, v4, v1}], Line[{v1, v4, v3, v1}],
Line[{v4, v2, v3, v1}]};
g2 = Graphics3D[{Thickness[0.01],
tetrahedron[
lintrans /@ {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}]}];
Then plot the surface x2*x3==x1*(1-x2-x3-x1)
g1 = ParametricPlot3D[ lintrans[{x1, x2, (x1 - x1^2 - x1*x2)/(x1 +
x2)}], {x1, 0, 1}, {x2, 0, 1}, Mesh -> All, WorkingPrecision -> 20];
and show these together
Show[g1, g2, PlotRange -> {0, 1}]
The first problem I have is that the function is not collinear with the
axis of the tetrahedron as it should be (rounding error?), although it
is basically correct. It is necessary to rotate the graphic to see the
full bend of the surface in 3D. Is there a way to correct this minor
imperfection?
Then I would like to plot some individual points in the same graphic.
Eventually these points will be complicated functions of parameters that
can be Manipulated to show the movement of the points relative to the
curve as the parameters are changed. I tried for example
g3 = ListPointPlot3D[ lintrans /@ {{.2, .3, .4}, {.2, .5, .1}, {.3, .7,
.1}, {.4, .5, .1}}];
Show[g1, g2, g3, PlotRange -> {0, 1}]
which plots the points inside the tetrahedron.
Firstly, how can I make the individual points more visible (e.g. red
filled circles)? A 3D point would be nice.
When I try to manipulate this graphic it doesn't work
g3 := ListPointPlot3D[
lintrans /@ {{.2*w1, .3, .4}, {.2, .5*w2, .1}, {.3, .7, .1*
w3}, {.4, .5*w1, .1}}];
Manipulate[
Show[g1, g2, g3, PlotRange -> {0, 1}], {w1, 0,
1}, {w2, .2, .9}, {w3, .4, .5}]
In fact I don't see the points at all. How do I make these points
display dynamically?
Finally, it is possible that the individual points will be complex for
some parameter values. Can I conditionally make these disappear inside a
Manipulate statement?
Thanks for any suggestions.
Leigh