Drawing and intuition are often useful, but sometimes they are an obstacle in seeing the truth. I suggest to write the general equation of a surface Bézier patch and follows the advices we have already given. When you fix one of the two coordinates, the corresponding Bernstein polynomials becomes constants and you can rewrite the terms of the sums to get the equation of a Bézier curve. The control points of this new curve are simply obtained evaluating the curves I have written in my last post. C(P(1,0), P(1,1), P(1,2), 0.7) is not contained in the surface.

Drawing and intuition are often useful, but sometimes they are an obstacle in seeing the truth. I suggest to write the general equation of a surface Bézier patch and follows the advices we have already given. When you fix one of the two coordinates, the corresponding Bernstein polynomials becomes constants and you can rewrite the terms of the sums to get the equation of a Bézier curve. The control points of this new curve are simply obtained evaluating the curves I have written in my last post. C(P(1,0), P(1,1), P(1,2), 0.7) is not contained in the surface.

Isnt the C a set of points belonging to a curve? If so this point is belonging to the curve/surface.

I will try munch the formulas later but I am not to much accustomed to it.(now I am not able to do it just need a

rest)

I would like tu understand it, thats why I am asking

It is a point on a curve, but that curve does not belongs to the surface.. The blue curve in cadjunkie post is not contained in the surface. It is the set of the middle control points of the isoparametric curves.

Sorry for my misleading picture. The blue curve is a curve generated by the middle control points. As apatriarca said, it is NOT on the Bezier surface, however, the middle control point for any v-isoparameter curve will be on that blue curve. This is analogous to the first and last control points being on the edge curves of the Bezier surface, and these edge curves are generated by the left and right control points at the edge of the control net.

The idea is that you can treat the columns of the control grid as separate Bezier curves and evaluate them at a specific v. Then, those evaluated points can become another Bezier curve (a v-isoparameter curve) that you can evaluate at a specific u. Then, that evaluated point is on the surface. You can do the same thing with the rows of the control grid to get a u-isoparameter curve, and then evaluate that at a specific v to get the point on the surface.

HTH

allright, much tnx, those are good answers probably answers the thing, (though i will need to think abit about this yet, if something will be unclear maybe i will yet ask something, tnx)