Hey, great to see this explained. The POV-Ray Scene help file shows this too, I
finally
looked it up there (again). This is what I wasn't quite getting about it, the fact
that
only a pair of triangles gets made from 4 pixels of the originating image. The
vertexes
are centrally based then after all, but not a pair of triangles per pixel as I was
thinking of it. This explains the sawtooth form my hf testing script was taking, since
they "stepped" from one to the other as a group of 4, or you could even say as a
"pair"
of black and white pixels (high and low points). Which would create only a slope.
Interesting thing is the slope appears to be made from one direction, I suppose
starting
from the origin <0,0,0>.
This certainly has given me new insight to this, thanks Ron.
I was seeing black and white stripes in one view which had 3 levels of height as a
group, might this be a direct cause and effect due to the pixel sized checkers and
something inherent to the way a HF is calculated as well? Makes me wonder....
The person originally wondering about "smoothing" a HF further would seem correct then
about possibly interpolating via spline between the intitial triangle creation and
producing a further tessalation. I could also see where this would also produce more
work for the parser and yet still amount to just making yet smaller triangles still
visible when viewed up close.
Not an idea to totally throw out I guess none the less.


Ron Parker wrote:
> 
> Each 'cell' in a heightfield is a pair of triangles
> whose vertices are the values of the four pixels surrounding the cell.
> The simplest case is when you have an image of 2x2 pixels.  In that
> case, you get a heightfield of a single cell, composed of two triangles.
> 
> If you look at the heightfield from the +y direction with a sky of +z,
> it will be constructed like this:
> 
>    z=1,x=0  x=z=1
>     +------+
>     |\     |
>     | \    |
>     |  \   |
>     |   \  |
>     |    \ |
>     |     \|
>     +------+
>    0        x=1,z=0
> 
> Here's what you get with a 3x3 source image:
> 
>    +---+---+
>    |\  |\  |
>    | \ | \ |
>    |  \|  \|
>    +---+---+
>    |\  |\  |
>    | \ | \ |
>    |  \|  \|
>    +---+---+
> 
> In the absence of interference effects, a checkerboard like the one
> you're using will always be rendered as a series of diagonal ridges
> and valleys.

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