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Re: Parametric Function with Lines Instead of Points

  • Subject: Re: Parametric Function with Lines Instead of Points
  • From: Kenneth Evans <evans@xxxxxxxxxxx>
  • Date: Thu, 29 Mar 2007 14:42:57 -0500
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<font size="-1"><font face="Helvetica, Arial, sans-serif">Don,<br>
<br>
&nbsp;&nbsp;&nbsp;&nbsp; Well, I'm sure glad I asked that question. I 
previously thought
the GriddedNDSet was the same as the LinearNDSet except with irregular
spacing.&nbsp; It's amazing how much you can miss just reading the JavaDoc
and technical references.&nbsp; In any event, whether my mind is fully
"wrapped around it" or not, my understanding has greatly increased.&nbsp;
Attached is a Figure 8 Klein Bottle using the Gridded3DSet with
manifold dimension =&nbsp; 2 as proof.&nbsp; I attached it to see if that solves
the email problem I was having. ;-)<br>
<br>
&nbsp;&nbsp;&nbsp;&nbsp; I was also confused about the manifold 
dimension.&nbsp; There appear to
be two dimensions, the domain dimension and the manifold dimension.&nbsp;
The domain is also a manifold (or can be) I think, and that is what I
thought was meant by manifold dimension.<br>
<br>
&nbsp;&nbsp;&nbsp;&nbsp; I found the following reference helpful, although it 
is a bit
terse and missing the figures:<br>
<br>
<a class="moz-txt-link-freetext" 
href="http://www.unidata.ucar.edu/staff/caron/papers/CoordMath.htm";>http://www.unidata.ucar.edu/staff/caron/papers/CoordMath.htm</a><br>
<br>
&nbsp;&nbsp;&nbsp;&nbsp; Thanks for the help and information,<br>
<br>
&nbsp;&nbsp;&nbsp; -Ken<br>
</font></font><br>
Don Murray wrote:
<blockquote cite="mid460AD2B5.7010305@xxxxxxxxxxxxxxxx" type="cite">Hi
Ken-
  <br>
  <br>
It is all very confusing, but once you wrap your mind around
  <br>
it, it's an incredibly powerful and flexible data model.
  <br>
  <br>
Here's the way I try to think of it.&nbsp; A domain can have a dimension
  <br>
(number of components of the RealTupleType) and a manifold dimesion
  <br>
(the structure of that data).&nbsp; For a given manifold dimension:
  <br>
  <br>
1 = line
  <br>
2 = plane
  <br>
3 = volume
  <br>
  <br>
That's an oversimplification, but it's how I rationalize what
  <br>
to use.
  <br>
  <br>
So a Gridded2DSet (dim=2) with a manifold dimension = 1 is useful
  <br>
for depicting things like map lines. The points have 2 dimensions
  <br>
(lat,lon), but the single manifold dimension gives them the
  <br>
structure of lines connecting the points.&nbsp; A Gridded3DSet on a
  <br>
2D manifold would be a slice through a volume (i.e. a plane).
  <br>
  <br>
A LinearNDSet inherently has the same manifold dimension as
  <br>
its domain dimension, thus you can't use it to depict a crosshair
  <br>
which is a 2 or 3D set on a 1D manifold.
  <br>
  <br>
As for wrapping your head around this all, at Unidata we say that
  <br>
when you can say from memory (paraphrased from the FlatField javadoc):
  <br>
  <br>
A FlatField range type may be either a RealType, a RealTupleType, or a
TupleType of RealType-s and RealTupleType-s.
  <br>
  <br>
AND understand it, you'll have reached that VisAD enlightenment. ;-)
  <br>
  <br>
Don
  <br>
  <br>
Kenneth Evans wrote:
  <br>
  <blockquote type="cite">&nbsp;&nbsp;&nbsp;&nbsp; It is more that it is 
counterintuitive
to me to be using ((x,y,z) -&gt; t) rather than (t -&gt; (x,y,z)).&nbsp;
However, I guess the same thing appears on the plot.&nbsp; The reason for
reversing the order seems to be to get the correct topology.&nbsp; So I now
have a recipe, but I am not sure I understand what is happening.&nbsp; Is it
written up somewhere what has and doesn't have a topology and what that
topology is.&nbsp; I haven't come across it.
    <br>
    <br>
&nbsp;&nbsp;&nbsp; It is also interesting about the manifold dimension = 
1.&nbsp; It seems
to me that the domain, which is the part that goes with the
Gridded3DSet, has manifold dimension = 3, and that it is the range that
has manifold dimension = 1.&nbsp; (When using your order.)&nbsp; Or am I just
confused.
    <br>
    <br>
&nbsp;&nbsp;&nbsp; I did try to make a cursor consisting of two crossed lines
recently.&nbsp; I noticed that I needed to use a Gridded2DSet, whereas a
Linear2D set should have served.&nbsp; I believe the later gave points, not
lines.&nbsp; I assume this is the same problem.&nbsp; (I ended up using a 
shape.)
    <br>
    <br>
&nbsp;&nbsp;&nbsp;&nbsp; Thanks for the information,
    <br>
  </blockquote>
  <br>
*************************************************************
  <br>
Don 
Murray&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 UCAR Unidata Program
  <br>
<a class="moz-txt-link-abbreviated" 
href="mailto:dmurray@xxxxxxxxxxxxxxxx";>dmurray@xxxxxxxxxxxxxxxx</a>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 P.O. Box 3000
  <br>
(303) 
497-8628&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 Boulder, CO 80307
  <br>
<a class="moz-txt-link-freetext" 
href="http://www.unidata.ucar.edu/staff/donm";>http://www.unidata.ucar.edu/staff/donm</a>
  <br>
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