# Beizer Curves : Questrion

Hey guys,

any idea what the smallest n.o of control points that can create a 2D Bezier curve with a loop in it would be?

I think it’s four. But I would not put my hand in the fire for this one. In the NURBS book by Les Piegl and Wayne Tiller there is a figure with a 2d Bézier curve with a loop that have 4 control points.

thats also what I was thinking, but I wasn’t too sure. I mean 2 is for a straight line, 3 for a curve, so 4… seems like it for the loop, thanks for your help.

If start and end point aren’t count as single point, a minimum of 5 points are required, because the points 0;1,n-1;n have to be placed on a straight line.

A good replacement are 3 parabolic Bezier segments. With a non uniform modification, it’s also possible to use them as circle.

If start and end point aren’t count as single point, a minimum of 5 points are required, because the points 0;1,n-1;n have to be placed on a straight line.
With this you describe a smooth closed Bézier curve I think. The answer I give is for the kind of curve described in the middle of this page.