## Reduced Mathemaical Form ## LaTeX Formula

 w_i=\max\left\{\left\|\ell_j-I\right\|^{-p}\cos\left(s_i,\ell_j-I\right):j\in\left\{1,2,3,\dots,N\right\}\right\} \\ \\ m_i=\mbox{any }v_j:\left[\left(\left\|\ell_j-I\right\|^{-p}\cos\left(s_i,\ell_j-I\right)=w_i\right)\land j\in\left\{1,2,3,\dots,N\right\}\right] \\ \\ f(I)=\begin{cases} v_i\mbox{ if }\exists{i}\in\left\{1,2,3,\dots,N\right\}\left(I=\ell_i\right)\\ \displaystyle\frac{\displaystyle\sum_{i=1}^{P}m_iw_i} {\displaystyle\sum_{i=1}^{P}w_i}\mbox{ otherwise } \end{cases} \\ \\ \\ I = \mbox{Location of interpolation} \\ p = \mbox{Propagation of influence power, } p>0 \\ v_i = \mbox{Value of sample }i,~i\in\left\{1,2,3,\dots,N\right\} \\ \ell_i = \mbox{Location of sample }i,~i\in\left\{1,2,3,\dots,N\right\} \\ N = \mbox{Number of samples} \\ s_i = \mbox{Evenly spaced unit vector on surface of sphere,}~i\in\left\{1,2,3,\dots,P\right\} \\ P = \mbox{Precision (number of unit vectors on sphere),}~P\gg2d \\ d = \mbox{Dimensionality of data (}d=2\mbox{ is planar)}