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

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 :

$y = \sqrt{x}\,p(x) + \sqrt{1-x}\,q(x)$

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,