B.3.2 Hexagon

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u( $\displaystyle \xi$ , $\displaystyle \eta$ , $\displaystyle \zeta$ ) = $\displaystyle \alpha_{1}^{}$ + $\displaystyle \alpha_{2}^{}$ $\displaystyle \xi$ + $\displaystyle \alpha_{3}^{}$ $\displaystyle \eta$ + $\displaystyle \alpha_{4}^{}$ $\displaystyle \zeta$ +
$\displaystyle \alpha_{5}^{}$ $\displaystyle \xi$ $\displaystyle \eta$ + $\displaystyle \alpha_{6}^{}$ $\displaystyle \xi$ $\displaystyle \zeta$ + $\displaystyle \alpha_{7}^{}$ $\displaystyle \eta$ $\displaystyle \zeta$ + $\displaystyle \alpha_{8}^{}$ $\displaystyle \xi$ $\displaystyle \eta$ $\displaystyle \zeta$

N₁( $\displaystyle \xi$ , $\displaystyle \eta$ , $\displaystyle \zeta$ )	=	(1 - $\displaystyle \xi$ )(1 - $\displaystyle \eta$ )(1 - $\displaystyle \zeta$ )
N₂( $\displaystyle \xi$ , $\displaystyle \eta$ , $\displaystyle \zeta$ )	=	$\displaystyle \xi$ (1 - $\displaystyle \eta$ )(1 - $\displaystyle \zeta$ )
N₃( $\displaystyle \xi$ , $\displaystyle \eta$ , $\displaystyle \zeta$ )	=	$\displaystyle \xi$ $\displaystyle \eta$ (1 - $\displaystyle \zeta$ )
N₄( $\displaystyle \xi$ , $\displaystyle \eta$ , $\displaystyle \zeta$ )	=	$\displaystyle \eta$ (1 - $\displaystyle \xi$ )(1 - $\displaystyle \zeta$ )
N₅( $\displaystyle \xi$ , $\displaystyle \eta$ , $\displaystyle \zeta$ )	=	(1 - $\displaystyle \xi$ )(1 - $\displaystyle \eta$ ) $\displaystyle \zeta$
N₆( $\displaystyle \xi$ , $\displaystyle \eta$ , $\displaystyle \zeta$ )	=	$\displaystyle \xi$ (1 - $\displaystyle \eta$ ) $\displaystyle \zeta$
N₇( $\displaystyle \xi$ , $\displaystyle \eta$ , $\displaystyle \zeta$ )	=	$\displaystyle \xi$ $\displaystyle \eta$ $\displaystyle \zeta$
N₈( $\displaystyle \xi$ , $\displaystyle \eta$ , $\displaystyle \zeta$ )	=	$\displaystyle \eta$ (1 - $\displaystyle \xi$ ) $\displaystyle \zeta$