       • To: mathgroup at smc.vnet.net
• Subject: [mg108880] Re: Orientation of Arrowheads
• From: "David Park" <djmpark at comcast.net>
• Date: Mon, 5 Apr 2010 08:02:25 -0400 (EDT)

```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
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],
Arrow[Tube[{{0, 0, 0}, vector/Sqrt}, .02]],
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 at comcast.net
http://home.comcast.net/~djmpark/

From: Roger Koenker [mailto:rkoenker at 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"];
Arrow[Tube[{{0, 0, 0}, {1, 1, 1}/Sqrt}, .02]],
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 at uiuc.edu            Department of Economics
vox:     217-333-4558                University of Illinois
fax:       217-244-6678                Urbana, IL 61801

```

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