# Curvature, torsion, tortuosity computation algorithms in VMTK

**URL:** <https://discourse.slicer.org/t/curvature-torsion-tortuosity-computation-algorithms-in-vmtk/29186>\
**Category:** VMTK\
**Created:** [April 28, 2023, 2:42pm UTC](https://discourse.slicer.org/t/curvature-torsion-tortuosity-computation-algorithms-in-vmtk/29186 "2023-04-28T14:42:12Z")\
**Posts on this page:** 3\
**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:** [April 28, 2023, 2:42pm UTC](https://discourse.slicer.org/t/curvature-torsion-tortuosity-computation-algorithms-in-vmtk/29186/1 "2023-04-28T14:42:12Z")

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Hello!

I am trying to calculate the geometric indices such as curvature, torsion and tortuosity from the extracted centrelines in 3D slicer by using VMTK extension. Can anyone please tell me what are the mathematical definitions used over here for calculations?

Thanks!

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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:** [April 28, 2023, 2:44pm UTC](https://discourse.slicer.org/t/curvature-torsion-tortuosity-computation-algorithms-in-vmtk/29186/2 "2023-04-28T14:44:00Z")

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You can find it in Luca Antiga’s [PhD thesis](https://lantiga.github.io/media/AntigaPhDThesis.pdf) and/or papers. If the definitions are not clear enough then you can always take a look at the [source code](https://github.com/vmtk/vmtk).

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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 28, 2023, 2:55pm UTC](https://discourse.slicer.org/t/curvature-torsion-tortuosity-computation-algorithms-in-vmtk/29186/3 "2023-04-28T14:55:34Z")

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Thanks for the help! I found it in papers! 🙂