> I have a collection of Bezier curves that forms a network of patches, I'd

> like to find out the technique(s) used to generate the patches from those

> Bezier curves network.

[snip]

Quote:> Having tried out various modelling/animation software, they all seems

> happy to allow a user to just move the end points and the software uses some

> form of blending/blending-fuction to find the "inner/interior" four vertices

> of each Bezier patch base of the 4 boundary curve and if necessary, the

> neighbouring patches. It is this blending/interpolation algorithm/technique

> I am keen to find out.

I have recently done some work using cubic bezier patches (triangle and

quadratic). When i built the editor for the system I found out that for

ensuring C1 continuity across the borders of two patches (the borders

have no whole and are smooth) I actually have to restrict handling of

the controlpoints to the corners. The other points are then calculated

to fit the continuity.

I have found the following code to work pretty good for triangle patches:

define the three corner points and the normal at that point (they may be

modified by the user at will)

All control poitns with distance "1" (i.e: next neighbors) have to lie

on a plane which goes through the controlpoint on the corner and has the

defined normal. the excet position on the plane is not so important and

could be chose by the user (i just project them from their original

position onto the plane so that they stay more or less where they would

be if the patch is flat.

The center point in a trinagle patch is a little problematic, as it

requires to solve some complex eqations, but just using an average of

all controlpoints excet the corner works quite fine. (if anyone has a

good way to calculate the center point please let me know)

For quadratic patches this should work the same way, except that you

have no center point but the interior controls are assigned to the next

corner. In this case the mathematics should actually be exact.

Mucki