Declaration

TMitchellKernel = class(TCustomKernel)

Description

TMitchellKernel implements the Mitchell-Netravali cubic filter optimized for visual quality with parameters $B=\frac{1}{3}$ and $C=\frac{1}{3}$. It strikes an optimal visual balance between blurring, ringing, and aliasing artifacts.

Mathematics

With $B=\frac{1}{3}$ and $C=\frac{1}{3}$, the Mitchell-Netravali piecewise cubic function $f(x)$ is defined as:

$$f(x)=\{\begin{array}{ll}\frac{1}{18}(21|x{|}^3-36|x{|}^2+16),& \text{if }|x|<1\\ \frac{1}{18}(-7|x{|}^3+36|x{|}^2-60|x|+32),& \text{if }1\le |x|<2\\ 0,& \text{otherwise}\end{array}$$

INFO

Many other variants of this filter, with various other values for B&C, exist. Often people come up with some variation of B&C and then put their own name on the filter. For example Robidoux (B:0.3782, C:0.3109), etc.

References

• Don P. Mitchell & Arun N. Netravali, "Reconstruction Filters in Computer Graphics", ACM SIGGRAPH Computer Graphics, Volume 22, Number 4, August 1988.