MedicalVisualization
Interpolation
← Data Representation | ● | Discrete Data →
The discrete representation requires the interpolation of function values $f(x_i)=y_i$ at the data grid points $x_i$.
Interpolation can be (from worst to best)
- linear
- cubic
- spline
- sinc
Linearily interpolated function f(x) between function values $y_1$ und $y_2$ of two data points $x_1$ und $x_2$ with interpolation weight (factor) $w\in[0..1], w=\frac{x-x_1}{x_2-x_1}$:
$ f(x) = (1-w) \cdot y_1 + w \cdot y_2 $
Cubically interpolated function:
$ f(x) = ax^3 + bx^2 + cx + d $
$ f(x_i) = y_i, i=0..3 $
for $x_i = i-1$, the cubic coefficients a, b, c and d are:
$ a = (y_3 - y_2) - (y_0 - y_1) $
$ b = (y_0 - y_1) - a $
$ c = y_2 - y_0 $
$ d = y_1 $
faster evaluation of f(x):
$ f(x) = d+(c+(b+ax)x)x $
← Data Representation | ● | Discrete Data →