Calculating bezier curve smoothness?

thomthom · 5 Mar 2011, 14:07

Anyone got an idea on how to calculate the number of segments a bezier curve needs in other to ensure a given smoothness? (Max angle between each edge segment.)

mitcorb · 5 Mar 2011, 17:14

Hi, thomthom:
I have returned to this post several times trying to start a reply. I am not qualified to even provide the beginning of an answer. But I can see several questions that might need to be considered. And I think I am pathologically inclined to try to help.
Would the degree depend on the final view? I mean how far "away" will you view the object?
Or, how smooth is smooth enough?
Or, 130 degrees?
If a Bezier curve, let alone a Bezier surface, is adjustable/editable, couldn't this action remove the smoothness you have already established?

thomthom · 5 Mar 2011, 17:46

@mitcorb said:

Or, how smooth is smooth enough?

User spesified. The user defines what the maximum angle between edges are which can be considered smooth.

@mitcorb said:

If a Bezier curve, let alone a Bezier surface, is adjustable/editable, couldn't this action remove the smoothness you have already established?

I'm trying to contemplate an automatic segment adjustment based on how smooth the user wants the curve. An alternative to manually setting the segment count.

@mitcorb said:

I mean how far "away" will you view the object?

Unknown.

@mitcorb said:

Would the degree depend on the final view?

Not in this case. It is something I've also considered, adjustment according to the view, but right now I'd just like to work out how many segments a bezier curve need in order to ensure a minimum smoothness based on the angles between the line segments.

mitcorb · 5 Mar 2011, 18:38

The first person that comes to mind regarding this is Fredo6. -but there may be others.

Pixero · 6 Mar 2011, 07:26

Not sure if this is what your after. Still it might be useful info:
http://www.antigrain.com/research/adaptive_bezier/index.html

thomthom · 6 Mar 2011, 16:27

@pixero said:

Not sure if this is what your after. Still it might be useful info:
http://www.antigrain.com/research/adaptive_bezier/index.html

That looks very interesting. I quickly scanned it and it seems to be what I'm looking for. He describe the issues with bezier curves I wanted to deal with.

mitcorb · 6 Mar 2011, 16:29

Check his updates at the end of the article also.