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From: Roger Koenker on 4 Apr 2010 07:46
For a teaching demo, I'm trying to plot Arrowheads as Octahedrons, but --as documented--
Mathematica wants to orient the Arrowhead according to the orientation of the Arrow
and I would like the Octahedron to be oriented "vertically". Here is my current version:

<< Graphics`polyhedra`
octo = PolyhedronData["Octahedron"];
Graphics3D[{Opacity[.75], Arrowheads[{{.06, 1, octo}}],
Arrow[Tube[{{0, 0, 0}, {1, 1, 1}/Sqrt[3]}, .02]],
Arrowheads[{{.01, 1, Graphics3D[Sphere[]]}}],
Arrow[{{0, 0, 0}, {.577, .577, .1154}}],
Polygon[{{0, 0, 0}, {0, 2, .2}, {2, 2, .4}, {2, 0, .2}}]},
PlotRange -> {{0, 2}, {0, 2}, {0, 2}}, Boxed -> True]

Any suggestions would be most welcome.

url: www.econ.uiuc.edu/~roger Roger Koenker
email rkoenker(a)uiuc.edu Department of Economics
vox: 217-333-4558 University of Illinois
fax: 217-244-6678 Urbana, IL 61801


From: David Park on 5 Apr 2010 08:02
Roger,

This kind of stuff is basically a mess because there is a lot of graphics
level jumping, that is between graphics primitives and Graphics3D. It would
make a lot more sense to me if PolyhedronData returned graphics primitives.

In any case, the basic trick is:
1) Arrowhead works so that what points along the x-axis is rotated to point
along the vector axis. (Help tells us that in MORE INFORMATION for
Arrowheads.)
2) We have to undo this so we rotate the object such that what points along
the vector axis is rotated to point along the x-axis.

octo = PolyhedronData["Octahedron"]

vector = {1, 1, 1};
octo2 = MapAt[Rotate[#, {vector, {1, 0, 0}}] &, octo, 1]

Graphics3D[{Opacity[.75],
Arrowheads[{{.06, 1, octo2}}],
Arrow[Tube[{{0, 0, 0}, vector/Sqrt[3]}, .02]],
Arrowheads[{{.01, 1, Graphics3D[Sphere[]]}}],
Arrow[{{0, 0, 0}, {.577, .577, .1154}}],
Polygon[{{0, 0, 0}, {0, 2, .2}, {2, 2, .4}, {2, 0, .2}}]},
PlotRange -> {{0, 2}, {0, 2}, {0, 2}},
Boxed -> True]


David Park
djmpark(a)comcast.net
http://home.comcast.net/~djmpark/



From: Roger Koenker [mailto:rkoenker(a)uiuc.edu]


For a teaching demo, I'm trying to plot Arrowheads as Octahedrons, but --as
documented--
Mathematica wants to orient the Arrowhead according to the orientation of
the Arrow
and I would like the Octahedron to be oriented "vertically". Here is my
current version:

<< Graphics`polyhedra`
octo = PolyhedronData["Octahedron"];
Graphics3D[{Opacity[.75], Arrowheads[{{.06, 1, octo}}],
Arrow[Tube[{{0, 0, 0}, {1, 1, 1}/Sqrt[3]}, .02]],
Arrowheads[{{.01, 1, Graphics3D[Sphere[]]}}],
Arrow[{{0, 0, 0}, {.577, .577, .1154}}],
Polygon[{{0, 0, 0}, {0, 2, .2}, {2, 2, .4}, {2, 0, .2}}]},
PlotRange -> {{0, 2}, {0, 2}, {0, 2}}, Boxed -> True]

Any suggestions would be most welcome.

url: www.econ.uiuc.edu/~roger Roger Koenker
email rkoenker(a)uiuc.edu Department of Economics
vox: 217-333-4558 University of Illinois
fax: 217-244-6678 Urbana, IL 61801




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