Is a cubic Lagrange interpolation tensor product the same as bicubic interpolation? I just implemented some interpolated texture sampling by sampling the 4x4 nearest pixels then doing Lagrange interpolation across the x axis to get four values to use Lagrange interpolation on across the y axis.

Is this the same as bicubic interpolation or is it different?

Webgl implementation here:
https://www.shadertoy.com/view/MllSzX
i don't need the points, but the Community keeps resurrecting unanswered questions (or answered questions that have no accepted answer) until i go batty seeing them on the list, time and time-again.

:-\

i think the bicubic interpolation is more likely 3rd-order Hermite polynomial than 3rd-order Lagrange polynomial interpolation. the former guarantees continuity of both the zeroeth and first derivative. the latter only guarantees continuity of the zeroeth derivative (the interpolated function itself).  

this previous answer deals pretty completely with the necessary math of it.