So basically as we can see directly from the graph, the h_0 function of Catmull-Rom algorithm might as well be the exact negative of h_2 of Hermite interpolation? Are these set of four functions used for other linear interpolation algorithms as well? Or is there any other linear interpolation scheme?
frankieeder
I am struggling to get an intuition for how two of our basis functions are now negative, in contrast to the cubic hermite functions derived earlier where just one was negative. Considering that our x,y,z, etc. components are independent, shouldn't our interpolation functions be identical to those proposed earlier? Is this because Catmull-Rom has multiplied our last two basis functions by 1/2 and -1/2 respectively?
So basically as we can see directly from the graph, the h_0 function of Catmull-Rom algorithm might as well be the exact negative of h_2 of Hermite interpolation? Are these set of four functions used for other linear interpolation algorithms as well? Or is there any other linear interpolation scheme?
I am struggling to get an intuition for how two of our basis functions are now negative, in contrast to the cubic hermite functions derived earlier where just one was negative. Considering that our x,y,z, etc. components are independent, shouldn't our interpolation functions be identical to those proposed earlier? Is this because Catmull-Rom has multiplied our last two basis functions by 1/2 and -1/2 respectively?