From what I've read, you cannot construct an elliptical or circular arc with a single bezier curve (though I read maybe you can if the arc is less than 1/4 of a circle or something small like that, or maybe it approximates it close enough).
I would like to know in detail how to think about curves in the general sense, whether the curve be bezier curves or elliptical or circular arcs. I would like to apply this to computer formulas.
- The first part of my question is, why you can't use (cubic) bezier curves to model circular/elliptical arcs.
- The second part is, if you can combine multiple (cubic) bezier curves to define an elliptical/circular arc, and if so, if there is a pattern or formula to it.
- If there are any classes of arcs or curves that are outside of these two that these two cannot model. That would at least introduce me to the idea of what is not possible with these in terms of modeling curves.
The reason for asking is because I was initially under the assumption that all curves were about the same and that they could be modeled by bezier curves, which turns out to be incorrect.
I also just read this:
Maybe you already know this, but it's impossible to convert nurbs to bezier splines exactly because nurbs are rational functions, and bezier splines are polynomials.
I would like to know as part of this if there is any way to transform a NURBS curve into a cubic bezier curve, similar to the other above points. Not necessarily how exactly to do it, but just to know if it is possible to get started.