On Sunday, July 1, 2012 2:47:16 AM UTC-7, Andrea Lazzarotto wrote:
>
> I don't know if it can be considered to be related, but I noticed in some 
> cases that when plotting a 3d implicit plot if I put the "mesh=True" in the 
> plot it doesn't show up, but when inside the show method it does show up 
> (in Jmol, not in Tachyon).
>
 
I know nothing about the Jmol code, but
 I don't see how it could be related.  To display a real-time 3d object, 
Jmol has already solved this, and numerous other intermediate problems 
 (viewport, data representation, coordinate transforms).  Somewhere in 
Jmol, a manager/interpreter stands between the solver's output and the 
displayport methods.

For a 2D plot, there is clearly no interpreter at all.  It's not a bug, 
it's just logic that doesn't match the structure of what it's trying to do. 
 For example, the axes might always display correctly, but the parameter 
"axes" is in the wrong place.

This is confusing because it seems natural to define various properties of 
> the plot inside the plot itself, as many other parameters work in both 
> methods. 
>
> -- 
> *Andrea Lazzarotto* - http://andrealazzarotto.com

 
Can we hang on to these words?  I think they're important.

Defining the properties in that display isn't just natural, it is an 
accurate logical structure.  Win-win.  Right now (in 2D) there are no *graph
* data to display.  An equation is rendered to an image container, losing 
all information about the structure of its contents.

It *is* possible to continue this way.  We can hijack the image format and 
use, say, Value to define the height of the curve at a given point, and 
pack the necessary transform information along with it.  This works for 
static objects, but I think it would be a mistake to use it to build 
graphs, because equations change shape as you vary the parameters. 

 Vertex list; connection information.  Points, lines, surfaces. We need to 
manipulate *objects* composed of these elements, then render the result to 
the monitor.  This is what we all want, right?

In the long run, there is no reason to differentiate 2D and 3D plots.  A 2D 
plot has an orthographic camera aligned to one axis.  Say it's aligned to *z
*.  The magnitude of all vectors <0,0,k>, from your point of view is 0.

Or however people normally solve this problem.

I know you all know that.  I'm just reminding you.   There are an *awful lot
* of different plot methods to memorize, and no interpreter-with-display 
structure to manage them.

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