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I want to know how to use linear and bilinear interpolation in 2D. Specifically the pairs $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$, and $(x_4,y_4)$ are given in a quadrilateral. In this case how to interpolate any unknown $(x,y)$ ? Do i need a weight for each point to find the points ?

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  • $\begingroup$ You have to use a function in the form of $y=f(x)$ $\endgroup$ – AnilB Jun 29 '15 at 20:19
  • $\begingroup$ Occupy Gezi - if im using RSSI readings $(RS1,RS2,RS3)$ for $f(x)$ how to find the location x y ? more like inverse bi-linear $\endgroup$ – Harry1234 Jun 29 '15 at 20:32
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You can define a bilinear surface from 4 points as

$S(u,v)=$$\begin{pmatrix} 1-u & u\end{pmatrix}$ $\begin{bmatrix} P_{00} & P_{01} \\ P_{10} & P_{11} \end{bmatrix}$ $\begin{Bmatrix} 1-v \\ v\end{Bmatrix}$

where $0 \le u \le 1, 0 \le v \le 1$, $P_{00}=(x_1,y_1)$, $P_{10}=(x_2,y_2)$,$P_{01}=(x_3,y_3)$ and $P_{11}=(x_4,y_4)$.

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  • $\begingroup$ Thank you fang. if theres three sensor readings how to use all three? or using one is enough ? $\endgroup$ – Harry1234 Jun 30 '15 at 8:23

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