Declaration

TInvertedDistanceWeightingSampler = class(TCustomArbitrarySparsePointGradientSampler)

Description

TInvertedDistanceWeightingSampler samples smooth multivariate color gradients across scattered points using Shepard's Inverse Distance Weighting (IDW).

Power=1	Power=2	Power=4	Power=8

Mathematics & Algorithm

Given $N$ scattered control points $P_i$ with colors $C_i$, the interpolated color $C(P)$ at point $P=(X,Y)$ is computed using Shepard's method with power parameter $p$ (Power):

$$w_i(P)=\frac{1}{d(P,P_i{)}^p}=\frac{1}{\parallel (X,Y)-(X_i,Y_i){\parallel }^p}$$$$C(P)=\frac{\sum _{i=1}^N{w}_i(P)C_i}{\sum _{i=1}^N{w}_i(P)}$$

If $P=P_i$, then $C(P)=C_i$.

References

• Inverse Distance Weighting - Wikipedia