# Compute quantity in terms of N.x and N.y on boundary

**URL:** <https://community.freefem.org/t/compute-quantity-in-terms-of-n-x-and-n-y-on-boundary/190>\
**Category:** General Discussion\
**Created:** [December 3, 2019, 2:40pm UTC](https://community.freefem.org/t/compute-quantity-in-terms-of-n-x-and-n-y-on-boundary/190 "2019-12-03T14:40:57Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![BeniaminBogosel](https://avatars.discourse-cdn.com/v4/letter/b/3ec8ea/32.png) [@BeniaminBogosel](https://community.freefem.org/u/BeniaminBogosel)\
**Post date:** [December 3, 2019, 2:40pm UTC](https://community.freefem.org/t/compute-quantity-in-terms-of-n-x-and-n-y-on-boundary/190/1 "2019-12-03T14:40:57Z")

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Hello,  
I would like to compute a quantity of the form atan2(N.y,N.x) on the boundary. I need to store this and use it multiple times in my code. (It allows me to find a reverse parametrization…)

Can you suggest a way to do this? Is it possible to recover the normal vector at a point of the boundary (without recomputing it)?

Thank you.  
Best regards,  
Beniamin

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**Author:** ![frederichecht](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/frederichecht/32/15_2.png) [@frederichecht](https://community.freefem.org/u/frederichecht)\
**Post date:** [December 5, 2019, 2:51pm UTC](https://community.freefem.org/t/compute-quantity-in-terms-of-n-x-and-n-y-on-boundary/190/2 "2019-12-05T14:51:13Z")

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just build a interpolation of

var vtheta(Uvarov) = on(1,2,u=atan2(N.y,N.x) o);  
fespace Wh(Th,P0edge);

Wh theta= vtheta(0,Wh,tgv=1);

now you avec a store the value in finite element function.

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<div class="post-metadata">

**Author:** ![BeniaminBogosel](https://avatars.discourse-cdn.com/v4/letter/b/3ec8ea/32.png) [@BeniaminBogosel](https://community.freefem.org/u/BeniaminBogosel)\
**Post date:** [December 6, 2019, 10:39pm UTC](https://community.freefem.org/t/compute-quantity-in-terms-of-n-x-and-n-y-on-boundary/190/3 "2019-12-06T22:39:56Z")

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Thank you for your answer. I will try it!