:orphan:
# Compute_Lagrange_Basis_3D_Internal
Evaluate bases and derivatives at quadrature points for a HEX8 or TET4 element. 
## Synopsis
```
#include "petscdt.h" 
#include "petscdmmoab.h"   
PetscErrorCode Compute_Lagrange_Basis_3D_Internal(const PetscInt nverts, const PetscReal *coords, const PetscInt npts, const PetscReal *quad, PetscReal *phypts, PetscReal *jxw, PetscReal *phi, PetscReal *dphidx, PetscReal *dphidy, PetscReal *dphidz, PetscReal *jacobian, PetscReal *ijacobian, PetscReal *volume)
```
The routine is given the coordinates of the vertices of a hexahedra or tetrahedra.

The routine evaluates the basis functions associated with each quadrature point provided,
and their derivatives with respect to X, Y and Z.


## Notes

Example Physical Element (HEX8)
```none
      8------7
     /|     /|        t  s
    5------6 |        | /
    | |    | |        |/
    | 4----|-3        0-------r
    |/     |/
    1------2
```



## Input Parameters

- ***PetscInt  nverts -*** the number of element vertices
- ***PetscReal coords[3*nverts] -*** the physical coordinates of the vertices (in canonical numbering)
- ***PetscInt  npts -*** the number of evaluation points (quadrature points)
- ***PetscReal quad[3*npts] -*** the evaluation points (quadrature points) in the reference space



## Output Parameters

- ***PetscReal phypts[3*npts] -*** the evaluation points (quadrature points) transformed to the physical space
- ***PetscReal jxw[npts] -*** the jacobian determinant * quadrature weight necessary for assembling discrete contributions
- ***PetscReal phi[npts] -*** the bases evaluated at the specified quadrature points
- ***PetscReal dphidx[npts] -*** the derivative of the bases wrt X-direction evaluated at the specified quadrature points
- ***PetscReal dphidy[npts] -*** the derivative of the bases wrt Y-direction evaluated at the specified quadrature points
- ***PetscReal dphidz[npts] -*** the derivative of the bases wrt Z-direction evaluated at the specified quadrature points
- ***jacobian -*** jacobian
- ***ijacobian -*** ijacobian
- ***volume -*** volume





## Level
advanced

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/dm/impls/moab/dmmbfem.cxx.html#Compute_Lagrange_Basis_3D_Internal">src/dm/impls/moab/dmmbfem.cxx</A>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/dm/impls/moab/dmmbfem.cxx)


[Index of all DMMOAB routines](index.md)  
[Table of Contents for all manual pages](/manualpages/index.md)  
[Index of all manual pages](/manualpages/singleindex.md)