Lecture 7: Intro to Geometry, Splines, and Bezier Curves (38)
phoebeli23
I'm a bit confused here. What do these basis functions have in common and how are they combined to get the final solution?
Staffajayjain
@phoebeli23 the inputs to cubic hermite interpolation, h0,h1,h2,h3, are coefficients for the Hermite basis functions. So, given hi, the interpolating polynomial is P(t)=h0H0(t)+h1H1(t)+h2H2(t)+h3H3(t). That's really convenient!
phoebeli23
That makes a lot of sense, thank you
nobugnohair
Representation of a polynomial with several base functions reminds me of Fourier Transforms. Are these bases functions reused in all cases like sines and cosines in Fourier Transforms? Are there exceptions?
I'm a bit confused here. What do these basis functions have in common and how are they combined to get the final solution?
@phoebeli23 the inputs to cubic hermite interpolation, h0,h1,h2,h3, are coefficients for the Hermite basis functions. So, given hi, the interpolating polynomial is P(t)=h0H0(t)+h1H1(t)+h2H2(t)+h3H3(t). That's really convenient!
That makes a lot of sense, thank you
Representation of a polynomial with several base functions reminds me of Fourier Transforms. Are these bases functions reused in all cases like sines and cosines in Fourier Transforms? Are there exceptions?