I submit this for the consideration of interested parties.

While reading up on a version of a subdivision surface scheme, I
developed the idea of using a simplified version of it to provide
smooth interpolation of height field data.

The method builds a small quartic patch around each of the interior
points of the height field.  The coefficients for this quartic are
based on the value of that point and each of its eight neighbors.
When clipped properly the patches all meet perfectly, and there are
no discontinuities in the surface normal across the borders.

The result is a smooth surface across the entire height field with
no creases or seams.

The advantages are:
* There is no "stepping" as is commonly observed in height fields,
  especially 8-bit height fields.  A gently rising set of data
  points yields a gently sloping surface.

* There is no need for smoothing calculations; the patches are
  naturally smooth.

The disadvantages are:

* Slightly more data is needed to generate the same number of squares.
  In a normal height field, an M x N image will produce a (M-1) x (N-1)
  set of squares, which are comprised to two triangles.  This new
  method produces a (M-2) x (N-2) set of patches.

* The patches are mostly quartic objects; however some of them will be
  cubic, quadratic, or even linear.  Furthermore, a bounding box is
  very easy to calculate for each patch.  The method will be slower in
  any event.

I have posted some code that demonstrates this method, and an MPG
animation of it, in p.t.s-f and p.b.a.

So, what do you think?

Regards,
John
-- 
ICQ: 46085459

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