I may be interpreting this incorrectly, but immediately I'm drawing parallels between the Fourier Transform and the Bernstein Polynomials. From what we've learned, the Fourier transform can break down a signal into its basis components (just a bunch of cos waves of differing frequency), and then just every signal is a linear combination of those basis components. This method seem to be a way of breaking down the Bezier curve into the Bernstein polynomials (essentially the basis components of the curve) and then creating a linear combination of them to get the final Bezier curve. To me I can see a lot of parallels between how we can use the inverse Fourier Transform to construct a polynomial out of component parts, and this method of constructing a curve out of the Bernstein polynomials. Is this analysis correct?
cornrow-kenny
I think you're correct. From my understanding both processes (Fourier transform and transforming to Bernstein polynomials) are just change of bases from a linear algebra perspective.
I may be interpreting this incorrectly, but immediately I'm drawing parallels between the Fourier Transform and the Bernstein Polynomials. From what we've learned, the Fourier transform can break down a signal into its basis components (just a bunch of cos waves of differing frequency), and then just every signal is a linear combination of those basis components. This method seem to be a way of breaking down the Bezier curve into the Bernstein polynomials (essentially the basis components of the curve) and then creating a linear combination of them to get the final Bezier curve. To me I can see a lot of parallels between how we can use the inverse Fourier Transform to construct a polynomial out of component parts, and this method of constructing a curve out of the Bernstein polynomials. Is this analysis correct?
I think you're correct. From my understanding both processes (Fourier transform and transforming to Bernstein polynomials) are just change of bases from a linear algebra perspective.