<p>I have a problem of linear interpolation of <a href="https://books.google.fr/books?id=94HtCAAAQBAJ&amp;pg=PA9&amp;dq=Rigid+and+Flexible+Mechanisms+A+Finite+Element+Approach+Based+on+the+Conformal+Rotation+Vector&amp;hl=en&amp;sa=X&amp;redir_esc=y#v=onepage&amp;q=Rigid%20and%20Flexible%20Mechanisms%20A%20Finite%20Element%20Approach%20Based%20on%20the%20Conformal%20Rotation%20Vector&amp;f=false" rel="nofollow noreferrer">CRV (Conformal Rotation Vector)</a> in which CRVs are used to parameterize the orientations. </p>

<p>In my knowledge, in order to derive a linear interpolation of orientations, we could apply a conversion from CRV into the corresponding unit quaternion, and then a SLERP (<a href="https://en.wikipedia.org/wiki/Slerp" rel="nofollow noreferrer">Spherical Linear Interpolation</a>) could be performed to interpolate linearly the orientation parametrized by CRVs. </p>

<p>My question is: Could we derive an interpolation of quality directly using CRVs (in linear scope)? </p>

CC BY-SA 3.0
2017-06-07T13:41:56.787Z
You can slerp a quaternion by repeatedly nlerping to 0.5 and binary searching. So if you can expand out the math of conversion to quaternion, the nlerp and the conversion back, then it should be possible
ratchet freak
CC BY-SA 3.0
2017-06-09T09:16:09.300Z
Thank you for your valuable comments, Ratchet Freak and Rahul! I will take your advice and answer this question.
Zihan Shen
<3d>
Interpolation of orientations
Zihan Shen
# Interpolation of orientations

(Asked by: username_0 on 2017-06-07)

I have a problem of linear interpolation of [CRV (Conformal Rotation Vector)](https://books.google.fr/books?id=94HtCAAAQBAJ&pg=PA9&dq=Rigid+and+Flexible+Mechanisms+A+Finite+Element+Approach+Based+on+the+Conformal+Rotation+Vector&hl=en&sa=X&redir_esc=y#v=onepage&q=Rigid%20and%20Flexible%20Mechanisms%20A%20Finite%20Element%20Approach%20Based%20on%20the%20Conformal%20Rotation%20Vector&f=false) in which CRVs are used to parameterize the orientations.

In my knowledge, in order to derive a linear interpolation of orientations, we could apply a conversion from CRV into the corresponding unit quaternion, and then a SLERP ([Spherical Linear Interpolation](https://en.wikipedia.org/wiki/Slerp)) could be performed to interpolate linearly the orientation parametrized by CRVs.

My question is: Could we derive an interpolation of quality directly using CRVs (in linear scope)?

**Tags:** 3d

> **Comments:**
> **username_1**: You can slerp a quaternion by repeatedly nlerping to 0.5 and binary searching. So if you can expand out the math of conversion to quaternion, the nlerp and the conversion back, then it should be possible  
> **username_0**: Thank you for your valuable comments, username_1 username_1 and Rahul! I will take your advice and answer this question.  

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## 0 answers

