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On Tue, 23 Mar 1999 14:52:36 -0500, david sharp <dsh### [at] interport net> wrote:
>Ron Parker wrote:
>[ ... ]
>> If you're trying to create a twisted-ribbon type of thing, perhaps you
>> would find more success and realism with bicubic patches.
>
>oh thats probably true, but then I would have to figure them out.
>Aren't bicubic patches those things you specify with huge arrays of
>numbers that don't make any sense?
No, those are those things you specify with 4x4 arrays of numbers that
make perfect sense once you understand them. :) The best understanding
I've been able to formulate for a bicubic patch is that the four corners
of a patch are always on the surface of the patch. The other eight edge
points are "control points" analogous to the "handles" on Bezier curves
in programs like Corel Draw, Freehand, or Illustrator in that they define
the beginning and ending direction of the curves that define the edges of
the patch, as well as the "tension" at the corners. These eight points
also specify the surface normals at the four corners, sorta indirectly.
The four points in the middle of the patch are the hardest to understand,
but I tend to visualize them as the same sort of "control points," except
that the "anchors" they are associated with are not actually on the
surface of the patch. In a sense, they control how the surface slopes
away from the edge curves, though their exact effect might not be
immediately or intuitively obvious.
An alternate view (less precise, more "artsy") is to just visualize the
sixteen points as a simple mesh of quadrilaterals, like a wire screen.
Bend it and stretch it however you will, and the resultant patch will do
its best to approximate that shape while remaining smooth (though it will
only actually touch any of the grid points at the corners, in most cases.)
If you want to play, grab the source to my IRTC entry for the latest
round and check out the source to the bedsheet. Some of the commented-out
code in that file allows you to visualize the control mesh that governs
the final shape of the sheet.
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