Re: DEMs, TINs, orthos, draping

[Tapani Sarjakoski <Tapani.Sarjakoski@fgi.fi>]

Crispen, Bob wrote:
> 
> > Tapani Sarjakoski[SMTP:Tapani.Sarjakoski@fgi.fi] sez:
> >
> > A. Digital elevation models (DEMs)
> >
> > There are two main approaches for representing elevation
> > of the ground in digital form: a) regular grids and b)
> > irregular triangulation networks (TINs).
> [much good stuff snipped]

Yes, I have ignored much like spline-surfaces etc. 
However, regarding ready made data sets that have been 
greated by GIS-releted software and delivered by some 
organization or company, these two approaches seem to be
dominating. Regular grids and TINs are also simple enough 
that it is usually not too difficult to transfere a data
set from one system to another, at least in my experience.
  
> If you've got a series of points that are not on
> a regularly spaced grid and want to end up with
> a regularly spaced grid (in VRML terms, going
> from an IndexedFaceSet to an ElevationGrid),
> am I correct in concluding that you create the grid
> using bilinear interpolation even though you're
> virtually certain to miss the high and low points
> in the terrain (I'm assuming that the elevation
> data you're starting with has been sampled at
> "interesting" points). 

Yes you can loose. The process of creating a regular
grid from a "random" set of sampled elevation points
can be considered to be a surface approximation and
filtering (smooting) process. How accurately a regular-grid 
based surface representation describes the "true" surface is
obviously critically dependent on the spacing of the
grid and also on the smoothness of the terrain,
because within a mesh the surface is assumed to be 
a "bilinear surface". Especially, regular grids are
not capable in reprenting accurately "breaklines" of
the terrain surface. TINs are good in that because the
sides of the triangles can be forced to follow these
breaklines. This is one reason why TIN are often
favoured in task related e.g. road design and similar.
There are also hybrid approaches, combining the good 
features of both methods.

> What algorithms do you use for thinning?  If
> I want a lower LOD, should I simply pick, say,
> every tenth point, or is there a better way that
> most folks use?

The are so many studies and methods available for the
task that it is simply not possible evaluate them here.
However, for me a reasonable method is based on some kind
of surface fitting (spline surface, polynomial surface).
Once we have a surface patch, we can compute the z-value
from it the z-values for grid points. 
For me it also essential that the 
method must cope with a situation in which have gaps
in our sampled point set (thicking instead of thinning?).
What does mean LOD?

> What about going the other way -- from elevation
> data on a regular grid to thinned elevation data
> with irregularly spaced points (in VRML, from
> ElevationGrid to IndexedFaceSet)?  Is there a
> conventional way to do this?  I think graphics
> folks would use a mesh decimation algorithm
> here.

I have not faced this problem by myself. A reasonable
approach could be to interpolate the z for the center
point of each mesh and form four trinangles of it, like
this:

0--------1
|\      /|
| \    / |
|  \  /  |
|   \/   |
|    z   |
|   /\   |
|  /  \  |
| /    \ |
|/      \|
3--------2

Tapani