AnsweredAssumed Answered

How to sketch the sum of two Bézier curves w.r.t an axis

Question asked by Adil Amezouak on Jan 9, 2018
Latest reply on Jan 9, 2018 by Elmar Klammer

Short version of the question:

Suppose that I have two "style splines" in a 2D sketch with different control points as shown below

How to sketch the sum of these two style splines w.r.t the vertical direction ? i.e. h(x) = f(x) + g(x)

 

Detailed version of the question:

I need to sketch exactly in SolidWorks a curve of the form :

where p(x) and q(x) are polynomials of the same degree.

 

Indeed the first term of the sum can be converted to a Bézier curve using the change of variable x = t²

which leads to a set of Bézier control points distributed quadratically in the x axis from 0 to 1.

The second term can be converted  again to Bézier curve using the change of variable x = 1-t² leading

to the same number of Bézier control points distributed quadratically in the x axis but now from 1 to 0.

 

The sum of the two curves is not a parametric polynomial curve, thus it cannot be sketched using style splines. However I suppose that it can be exactly represented in SolidWorks using NURBS (or B-splines). But how ?

 

I know that the equation driven curve can be used for this situation, but the resulting curve is then just an approximate B-spline.

 

 

Many thanks,

Outcomes