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.