# Regarding definition of mean curvature

**URL:** <https://discourse.slicer.org/t/regarding-definition-of-mean-curvature/32326>\
**Category:** VMTK\
**Tags:** vmtk-centerline\
**Created:** [October 19, 2023, 1:36pm UTC](https://discourse.slicer.org/t/regarding-definition-of-mean-curvature/32326 "2023-10-19T13:36:22Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Mudrika](https://avatars.discourse-cdn.com/v4/letter/m/c57346/32.png) [@Mudrika](https://discourse.slicer.org/u/Mudrika)\
**Post date:** [October 19, 2023, 1:36pm UTC](https://discourse.slicer.org/t/regarding-definition-of-mean-curvature/32326/1 "2023-10-19T13:36:22Z")

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Hello everyone!

I am extracting a centerline model for a geometry. By using the ‘markups’, I am drawing curves on the selected arteries and calculating geometric parameters like length and mean curvature. As we know, the curvature changes at every point and for drawing a curve, few control points are defined. So, for the calculation of the mean curvature, is it the mean curvature of the defined control points or is it something else?

Thank you!

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**Author:** ![Slogish](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/slogish/32/69830_2.png) [@Slogish](https://discourse.slicer.org/u/Slogish)\
**Post date:** [March 31, 2024, 4:10pm UTC](https://discourse.slicer.org/t/regarding-definition-of-mean-curvature/32326/2 "2024-03-31T16:10:22Z")

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I have the same question,and i also would like to know how to define the maximum curvature?What is the radius of the Osculating circle?

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**Author:** ![lassoan](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/lassoan/32/13_2.png) [@lassoan](https://discourse.slicer.org/u/lassoan)\
**Post date:** [March 31, 2024, 7:22pm UTC](https://discourse.slicer.org/t/regarding-definition-of-mean-curvature/32326/3 "2024-03-31T19:22:29Z")

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The control points are only used for computing the curve. Radius is computed on the curve that you see, which has many more (by default 10x more) points than control points. Mean curvature is the average curvature value along the entire curve that you see (not just at the control points).

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**Author:** ![Mudrika](https://avatars.discourse-cdn.com/v4/letter/m/c57346/32.png) [@Mudrika](https://discourse.slicer.org/u/Mudrika)\
**Post date:** [April 3, 2024, 5:50am UTC](https://discourse.slicer.org/t/regarding-definition-of-mean-curvature/32326/4 "2024-04-03T05:50:22Z")

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Thanks a lot for the clarification!

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<div class="post-metadata">

**Author:** ![Slogish](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/slogish/32/69830_2.png) [@Slogish](https://discourse.slicer.org/u/Slogish)\
**Post date:** [April 3, 2024, 10:35pm UTC](https://discourse.slicer.org/t/regarding-definition-of-mean-curvature/32326/5 "2024-04-03T22:35:20Z")

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Thanks！！！！

---- Replied Message ----

> From | [Andras Lasso via 3D Slicer Community](mailto:notifications@slicer.discoursemail.com)[notifications@slicer.discoursemail.com](mailto:notifications@slicer.discoursemail.com) |
> 
> - | - |  
> Date | 04/01/2024 03:22 |  
> To | [up\_wyp](mailto:up_wyp@163.com)[up\_wyp@163.com](mailto:up_wyp@163.com) |  
> Subject | [Slicer] Regarding definition of mean curvature |

The control points are only used for computing the curve. Radius is computed on the curve that you see, which has many more (by default 10x more) points than control points. Mean curvature is the average curvature value along the entire curve that you see (not just at the control points).

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_Previous Replies_  
I have the same question,and i also would like to know how to define the maximum curvature?What is the radius of the Osculating circle?