And here is the circle created with four rational bezier3 curves. Again, we get a perfect circle.

If you play with the weights of some points (the w of the 4D vector) you will pull or push away the curve segment at that point. Try it.

What I did to create the circles is called piecewise curve (linking curve segments to create a bigger curve). Try to create a rounded square.....

Hint! You will need four bezier2 (linear interpolation between two points) for the straight line segments!

Cheers!

Dan

Thanks for adding the screenshots.
Now at least I can see at a glance what I don't get...
(but that's just MY ignorance, I hasten to add)

Here I am showing the effect of changing the weight at the corner's control points using the four segments circle previously illustrated.

Top right: w = 0.7071. The curve describe a perfect arc circle. (note the with a value of 1, the curve is pulled slightly toward the point, this is why the non-rational bezier3 cannot represent a circle exactly).

Top left: w = 0. This result in eliminating the influence of that point on the curve and therefore we get a line.

Bottom left, w = 10. This result in pulling the curve toward the point creating sort of a rounded corner.

Bottom right: w = -0.5. This result in pushing the curve away from the point creating an inside arc.

Now imagine you have an object with all the points represented with the x,y,z,w you could use the w to influence the object points and sculpt details using say ...... a weight map!

Now is this a novel idea ....

Using the points created by the bezier nodes, I was able to create a polymesh topology driven by two curve bezier3 nodes.

Here is a screen of the results so far.

And by changing one of the curve description to another type of curve (Rational Bezier4), I easily changed the shape of the topology.

Finally, after some hard work, and some hits and misses on the way, I finally got the bezier patch working. It is not a "surface" by Softimage definition but a polymesh, the end result is very similar.

Below is the bezier patch result and the ICE tree. It is controlled by 16 nulls and just for fun I cranked up the subdivision to 30 in U and V.

The bezier definition does work, although with very high subdivisions, I get weird results, probably because of the precision of some of the calculation.

Attached is the compound as well. Enjoy!

The next screen shows the patch with nulls moved to create the curved surface. I then selected some points on the patch and pull/push them at will without affecting the rest of the patch.

I also simplified the ICE tree.

The end result is quite flexible. Each bezier node can be modified easily with an other surface representation just by changing the matrices inside each nodes to say, a cubic hermite or catmull-rom.

Like curves, the patch can be connected to one another in piecewise fashion to get larger surfaces. The possibilities are endless.

Cheers!

Dan

And a quick render of the surface.

Little update.

I was able to correct the quad description error and was able to pass subdivision 50 on the bezier patch. Now I crash Softimage because I run out of memory (I am still working on a very low spec machine by today standards).

Here is a screen grab of the bezier patch at 500 x 500 subdivisions. Useful for some terrain modeling. The picture shows the wireframe so tightly pack it's showing white! I have to zoom in to see the texture!

In the thread Modulo and variant, i provided the screen grab of the quad description compound for those interested!

Now moving to rational bezier surface!