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baconbeastnz
10-28-2008, 02:12 PM
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?

trinitrotoluene
10-28-2008, 02:49 PM
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.

baconbeastnz
10-28-2008, 02:51 PM
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.

oc2k1
10-29-2008, 09:14 AM
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.

trinitrotoluene
10-29-2008, 11:11 AM
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 (http://freespace.virgin.net/hugo.elias/graphics/x_bezier.htm).