# tem_intp_trilinear_vec Function

## private function tem_intp_trilinear_vec(srcVal, targetCoord, nVals) result(phi)

This function returns the tri-linearly interpolated values from the eight source points to the target position located at targetCoord. The source points are arranged in a square from (0,0,0)x(1,1,1) The order of the source points are according to the morton curve 1 2 3 4 (0,0,0); (1,0,0); (0,1,0); (1,1,0) 5 6 7 8 (0,0,1); (1,0,1); (0,1,1); (1,1,1)

### Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(in) :: srcVal(nVals,8)

source values of the square corners

real(kind=rk), intent(in) :: targetCoord(3)

interpolation location within the square

integer, intent(in) :: nVals

number of values

### Return Value real(kind=rk), (nVals)

interpolated value

## Source Code

  function tem_intp_trilinear_vec( srcVal, targetCoord, nVals ) result( phi )
! -------------------------------------------------------------------- !
!> number of values
integer, intent(in) :: nVals
!> source values of the square corners
real(kind=rk), intent(in) :: srcVal(nVals,8)
!> interpolation location within the square
real(kind=rk), intent(in) :: targetCoord(3)
!> interpolated value
real(kind=rk) :: phi(nVals)
! -------------------------------------------------------------------- !
real(kind=rk) :: phi_northFront, phi_southFront
real(kind=rk) :: phi_northBack,  phi_southBack
real(kind=rk) :: phi_front, phi_back
integer :: iVal
! -------------------------------------------------------------------- !
do iVal = 1, nVals
! Linear interpolation on the north nodes
phi_northFront = (1._rk - targetCoord(1)) * srcVal(iVal,3) &
&              + targetCoord(1) * srcVal(iVal,4)
phi_southFront = (1._rk - targetCoord(1)) * srcVal(iVal,1) &
&              + targetCoord(1) * srcVal(iVal,2)
! Linear interpolation on the cube back side (z = 1 )
phi_northBack = (1._rk - targetCoord(1)) * srcVal(iVal,7) &
&             + targetCoord(1) * srcVal(iVal,8)
phi_southBack = (1._rk - targetCoord(1)) * srcVal(iVal,5) &
&             + targetCoord(1) * srcVal(iVal,6)
! Linear interpolation on the cube front side (z = 0 )
phi_front = (1._rk - targetCoord(2)) * phi_southFront &
&         + targetCoord(2) * phi_northFront
! Linear interpolation on the cube back side (z = 1 )
phi_back  = (1._rk - targetCoord(2)) * phi_southBack &
&         + targetCoord(2) * phi_northBack
phi(iVal) = (1._rk - targetCoord(3)) * phi_front &
&         + targetCoord(3)*phi_back
enddo

end function tem_intp_trilinear_vec