# Mapping from mesh.coordinates() to u.vector()

**URL:** <https://fenicsproject.discourse.group/t/mapping-from-mesh-coordinates-to-u-vector/5067>\
**Category:** Uncategorized\
**Created:** [February 10, 2021, 12:17pm UTC](https://fenicsproject.discourse.group/t/mapping-from-mesh-coordinates-to-u-vector/5067 "2021-02-10T12:17:38Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![VKTR](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/vktr/32/2119_2.png) [@VKTR](https://fenicsproject.discourse.group/u/VKTR)\
**Post date:** [February 10, 2021, 12:17pm UTC](https://fenicsproject.discourse.group/t/mapping-from-mesh-coordinates-to-u-vector/5067/1 "2021-02-10T12:17:38Z")

</div>

Hello there,

Given some index i that I use to get the position on a mesh: x = mesh.coordinates()[i],  
is there a way to find out the index j (indices for non-scalar functions) such that u.vector()[j] = u(x)?

```
from dolfin import *

f = Expression('sin(x[0])*cos(x[1])', degree=2)
mesh = UnitSquareMesh(10, 10)
V = FunctionSpace(mesh, 'CG', 1)
u = interpolate(f, V)
i = 21
x = mesh.coordinates()[i]

# j = some_mapping(i)
# print(u(x) == u.vector()[j]) # check if mapping works
```

---

<div class="post-metadata">

**Author:** ![dokken](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/dokken/32/1560_2.png) [@dokken](https://fenicsproject.discourse.group/u/dokken)\
**Post date:** [February 10, 2021, 12:26pm UTC](https://fenicsproject.discourse.group/t/mapping-from-mesh-coordinates-to-u-vector/5067/2 "2021-02-10T12:26:18Z")

</div>

You can use the `vertex_to_dof_map` function, as used here: [Bitbucket](https://bitbucket.org/fenics-project/dolfin/src/b495043d6b3914383eb939ea6c6794442080a3a5/python/test/unit/fem/test_dofmap.py?at=master#test_dofmap.py-245,269)

---

<div class="post-metadata">

**Author:** ![VKTR](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/vktr/32/2119_2.png) [@VKTR](https://fenicsproject.discourse.group/u/VKTR)\
**Post date:** [February 10, 2021, 12:29pm UTC](https://fenicsproject.discourse.group/t/mapping-from-mesh-coordinates-to-u-vector/5067/3 "2021-02-10T12:29:53Z")

</div>

Awesome! Thank you very much!