In the aforementioned 5-axes aerospace contouring, if A and B are the orientation axes, and if you want to interpolate in 5-space, the FGROUP command would be FGROUP(X, Y, Z, A, B).
The algorithm acts on the geometric data of the part program to interpolate a curve that is rendered as a sequence of parametric polynomial interpolation functions that blend smoothly with one another.
Spline algorithms are software engines that interpolate curves.
This third meaning is probably what most CNC workers have in mind when they point to the CNC and say, "That thing interpolates.
We wish to prove that the space F of the first 4k - 1 harmonic polynomials interpolate the values of the function and all of its partial derivatives at an arbitrary k points.
k] [member of] R, we will say that the space F interpolates the functionals [[PHI].
d] such that F interpolates [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], .
MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]}, find the space F that interpolates [[PHI].
This is a practical concern where a wavelength offset may be present in measurements, although in general it is a better practice to retain the wavelength values of the measured points and interpolate
weighting functions such as the illuminant or the colorimetric response functions as these carry no uncertainty.
We also demonstrated MRI imagery using our patented 'Supercine' process that interpolates
imagery resulting in greater clarity.