FEATool  v1.9Finite Element Analysis Toolbox
sf_hex_Q3.m File Reference

## Description

SF_HEX_Q3 Tricubic conforming shape function for hexahedrons (Q3).

[ VBASE, NLDOF, XLDOF, SFUN ] = SF_HEX_Q3( I_EVAL, N_SDIM, N_VERT, I_DOF, XI, AINVJAC, VBASE ) Evaluates conforming tricubic Q3 shape functions on hexahedrons with values defined in the nodes, edges, faces, and cell center. XI is [-1..1]^3 reference coordinates.

```Input       Value/[Size]           Description
-----------------------------------------------------------------------------------
i_eval      scalar:  1             Evaluate function values
>1             Evaluate values of derivatives
n_sdim      scalar:  3             Number of space dimensions
n_vert      scalar:  8             Number of vertices per cell
i_dof       scalar: 1-n_ldof       Local basis function to evaluate
xi          [n_sdim]               Local coordinates of evaluation point
aInvJac     [n,n_sdim*n_sdim]      Inverse of transformation Jacobian
vBase       [n]                    Preallocated output vector
.
Output      Value/[Size]           Description
-----------------------------------------------------------------------------------
vBase       [n]                    Evaluated function values
nLDof       [4]                    Number of local degrees of freedom on
vertices, edges, faces, and cell interiors
xLDof       [n_sdim,n_ldof]        Local coordinates of local dofs
sfun        string                 Function name of called shape function
```
sflag3, sf_hex_Q1

# Code listing

``` nLDof = [8 24 24 8];
xLDof = [ -1  1  1 -1 -1  1  1 -1  -1/3 1   1/3 -1   -1    1    1   -1  -1/3 1   1/3 -1    1/3 1   -1/3 -1   -1   1   1  -1   1/3 1  -1/3 -1   -1/3 -1/3  1    1/3 -1   -1/3  1/3  1/3  1   -1/3 -1    1/3  1/3  1/3 1   -1/3 -1   1/3 -1/3 -1/3  1   1/3 -1  -1/3   -1/3  1/3  1/3 -1/3 -1/3  1/3  1/3 -1/3 ;
-1 -1  1  1 -1 -1  1  1  -1  -1/3 1    1/3 -1   -1    1    1  -1  -1/3 1    1/3 -1   1/3  1   -1/3 -1  -1   1   1  -1   1/3 1   -1/3 -1/3 -1   -1/3  1    1/3 -1/3 -1/3 -1    1/3  1   -1/3 -1/3  1/3 -1   1/3  1   -1/3 1/3  1/3 -1   -1/3 1    1/3 1/3   -1/3 -1/3  1/3  1/3 -1/3 -1/3  1/3  1/3 ;
-1 -1 -1 -1  1  1  1  1  -1  -1  -1   -1   -1/3 -1/3 -1/3 -1/3 1   1   1    1   -1  -1   -1   -1    1/3 1/3 1/3 1/3 1   1   1    1   -1   -1/3 -1/3 -1/3 -1/3  1   -1   -1/3 -1/3 -1/3 -1/3  1   -1    1/3 1/3  1/3  1/3 1   -1    1/3  1/3 1/3  1/3 1     -1/3 -1/3 -1/3 -1/3  1/3  1/3  1/3  1/3 ];
sfun  = 'sf_hex_Q3';

switch i_eval

case 1

switch i_dof
case 1
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 2
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 3
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 4
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 5
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 6
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 7
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) + 1)*(xi(3) + 1)/4096;
case 8
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) + 1)/4096;
case 9
vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 10
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 11
vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 12
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 13
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 14
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 15
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 16
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 17
vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 18
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 19
vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) + 1)/4096;
case 20
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 21
vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 22
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 23
vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 24
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 25
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 26
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 27
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 28
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 29
vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 30
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 31
vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) + 1)/4096;
case 32
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 33
vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 34
vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 35
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 36
vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 37
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 38
vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 39
vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 40
vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 41
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 42
vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 43
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 44
vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 45
vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 46
vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 47
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 48
vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 49
vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 50
vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 51
vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 52
vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 53
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 54
vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
case 55
vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 56
vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
case 57
vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 58
vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 59
vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 60
vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 61
vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 62
vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 63
vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
case 64
vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
end

case {2,3,4}

switch i_dof
case 1
dNdxi1 = ((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 2
dNdxi1 = ((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 3
dNdxi1 = -((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 4
dNdxi1 = -((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 5
dNdxi1 = -((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 6
dNdxi1 = -((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 7
dNdxi1 = ((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 8
dNdxi1 = ((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 9
dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 10
dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 11
dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = (9*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = -(9*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 12
dNdxi1 = (9*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 13
dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 14
dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 15
dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 16
dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 17
dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 18
dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 19
dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = -(9*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = -(9*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 20
dNdxi1 = -(9*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 21
dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = (9*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = (9*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 22
dNdxi1 = (9*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 23
dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 24
dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 25
dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 26
dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 27
dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 28
dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 29
dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = -(9*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = (9*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 30
dNdxi1 = -(9*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 31
dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 32
dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 33
dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 34
dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 35
dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 36
dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = -(81*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = (81*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 37
dNdxi1 = -(81*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 38
dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 39
dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = -(81*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = -(81*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 40
dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = -(81*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = -(81*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 41
dNdxi1 = -(81*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 42
dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 43
dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 44
dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = (81*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = -(81*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 45
dNdxi1 = -(81*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = -(81*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = (81*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 46
dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = (81*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = -(81*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 47
dNdxi1 = (81*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 48
dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 49
dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 50
dNdxi1 = (81*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = (81*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = (81*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 51
dNdxi1 = -(81*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
case 52
dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 53
dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 54
dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = (81*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
dNdxi3 = (81*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 55
dNdxi1 = (81*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 56
dNdxi1 = (81*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
case 57
dNdxi1 = -(729*(3*xi(2) - 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = -(729*(3*xi(1) - 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = -(729*(3*xi(1) - 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 58
dNdxi1 = -(729*(3*xi(2) - 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = (729*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = (729*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 59
dNdxi1 = (729*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = (729*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = -(729*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 60
dNdxi1 = (729*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = -(729*(3*xi(1) - 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = (729*(3*xi(1) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
case 61
dNdxi1 = (729*(3*xi(2) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = (729*(3*xi(1) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = -(729*(3*xi(1) - 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 62
dNdxi1 = (729*(3*xi(2) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = -(729*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
dNdxi3 = (729*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 63
dNdxi1 = -(729*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
dNdxi2 = -(729*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = -(729*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
case 64
dNdxi1 = -(729*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
dNdxi2 = (729*(3*xi(1) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
dNdxi3 = (729*(3*xi(1) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
end

if     ( i_eval==2 )   % x-derivative.

vBase = aInvJac(:,1)*dNdxi1 + aInvJac(:,2)*dNdxi2 + aInvJac(:,3)*dNdxi3;

elseif ( i_eval==3 )   % y-derivative.

vBase = aInvJac(:,4)*dNdxi1 + aInvJac(:,5)*dNdxi2 + aInvJac(:,6)*dNdxi3;

elseif ( i_eval==4 )   % z-derivative.

vBase = aInvJac(:,7)*dNdxi1 + aInvJac(:,8)*dNdxi2 + aInvJac(:,9)*dNdxi3;
end

case {22,23,24,32,33,34,42,43,44}   % Evaluation of second order derivatives.
error('sf_hex_Q3: second order derivative evaluation not supported.')

otherwise
vBase = 0;

end```