Bezier control points question

I was wondering about the structure of bezier control points, I have had problems with this sometimes in the past that near the corners of a surface the curvature seems to like to go flat. This could be explained by the notion that control points on a bezier surface are clamped to the surface.

I made a quick picture of how I would naturally assume the control points to look, floating away from the surface just like all the other midside nodes of a bezier net.

Obviously, it doesn’t. So why do you think this is?
surface degree 2x3 bezier.jpg
surface degree 2x3 alternative.jpg

I’m not 100% sure I understand but I’ll take a stab:

Forget about 3D surfaces for a second and consider a single 2D bezier curve.

If you consider how the curve is constructed, the curvature approaching the beginning and the end of the curve will always flatten towards tangency with the control points.

Once you consider that your surface is created from those 4 boundary equations, yes, it will always approach being “flat” (Tangent to the hull) at the corners. What you drew in the sketch would simply represent a surface that has been trimmed back past it’s true boundaries to eliminate the flat section.

Does that help?

Yes that makes sense, no way anybody in their right mind would trim every patch just to get rid of those flat corners.
But I still think it’s just one additional thing in traditional surfacing designed to piss people off, ha ha

Not sure it should be pissing you off - the fact that the surface does that is precisely what enables a surface to generate G0, G1, G2+ Continuity. There is a lot of math behind it, but understanding the differences mathmatically and not just visually helps to make sense of why CV hulls are aligned to control the flow and continuity between surface boundaries.

The corner is not “flat”, it simply matches the tangency of the control point. Turning on things like Curvature combs will also help you understand the relationship between the edges and the adjoining surfaces.

If you have a specific design intent you are trying to get but having problems with you could post a screen shot, may be easier to suggest surfacing techniques for a specific form vs the general concept.

Nah I’m cool, I’ve just noticed flatness near corners before but I can’t find exactly a good example of it right now. Perhaps you’re right and this “problem” exists only in my own imagination :slight_smile:

Nope you will get flatness in corners due to the way that the software interpolates the curves to create the surface so