|March 12th, 2017, 11:10 PM||#1|
Joined: Nov 2016
Can anyone tell how to convert this polynomial to a bezier curve = 1/(4x^2 +1). I have to take 5 knots i.e from -1 to 1 with a 0.5 increment.
|March 13th, 2017, 09:01 AM||#2|
Joined: Jan 2016
From: Athens, OH
I'm not sure what your mean. Perhaps this?
Let $f(x)=1/(x^2+4)$, $x_i=-1+(1/2)i$ and $P_i=(x_i,f(x_i)),\,i=0\cdots 4$
Now form a Bezier curve with the 5 control points $P_i$. The obvious choice of degree of the Bezier curve is 4. Just use the standard formula for the curve. Here's a drawing with f(x) dotted and the Bezier curve in red:
Another option is to paste together Bezier curves of smaller degree, say quadratic curves. As you know 3 control points are needed for a quadratic Bezier. To paste these together so that the resultant curve is $C^1$ continuous at the joints (points where the curves are pasted together), you can add control points to make this happen. In the following, the red circles indicate the added control points:
As you know, Bezier curves do not interpolate the control points. But the technique of pasting together Bezier curves can be used to approximate a curve. In this last drawing there were 31 "equally spaced" control points with the pieces quartic Bezier curves:
Last edited by johng40; March 13th, 2017 at 09:15 AM.
|bezier, curve, numerical analysis, numerical method|
|Thread||Thread Starter||Forum||Replies||Last Post|
|Arc length of cubic bezier curve||ghafarimahsa||Number Theory||3||February 26th, 2014 12:00 PM|
|draw a quad bezier having curve length||appollosputnik||Algebra||0||November 24th, 2013 10:00 PM|
|Bezier Approximation||resurector||Applied Math||0||October 27th, 2009 07:38 AM|
|Bezier curves..||repstosw||Linear Algebra||1||March 12th, 2008 06:30 AM|
|Bezier curves||roadnottaken||Applied Math||2||August 15th, 2007 03:11 PM|