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Proper way to blend between a polynomial with two sets of coefficients

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If you have two sets of coefficients that feed into a polynomial and you want to blend between them for whatever reason, is it typically okay to blend them linearly? Or is there some other ways to consider depending on application? This probably sounds like an odd question, but I've actually never had to do this.

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It's a fairly standard approximation to use a linear representation between points on a curve.

If precision is important, then just make sure you do it on a small enough step.

If you remember early on in calculus, this is the method they use to arrive at the derivative in the first place.

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Blending linearly all coefficients by a given factor also blends the outputs at any point by the same factor. This is often what one refers to by "blending two polynomials together".

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