Forums Technical Discussion up/N orient info to quaternion

up/N orient info to quaternion

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element33
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I have a point. animated in space, whose orientation is defined by its N and up vectors (perpendicular). I need to interpolate between some of its positions, so likely I'll have to use a quaternion. What's the best way to convert up/N orient info into a quaternion? I suppose I can pass a matrix into the quaternion(m) declaration, but how do I get a matrix from up and N?
Edited by element33 - 2022年3月24日 06:03:40
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animatrix_
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Hi,

You can do something like this:

matrix3 m = maketransform ( v@N, v@up );
vector4 q = quaternion ( m );
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mestela
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  @orient = quaternion(maketransform(@N, @up));
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mestela
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Ha, damnit, beat me again!
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element33
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Cool, thanks.
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tamte
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make sure both @N and @up are normalized to get expected result
Tomas Slancik
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element33
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A quick follow-up: can I extract the third axis (not @up, not @N) from a matrix (or quat) defined this way? Yes, I can do cross(@up,@N) myself, but I wonder if I can get the 3rd axis "for free":
matrix3 m = maketransform ( v@N, v@up );
vector4 q = quaternion ( m );
v@sideways = ? ... // some kind of a get_3rd_axis(m) :)
Edited by element33 - 2022年3月29日 13:13:43
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tamte
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v@x = qrotate(q, {1,0,0});
or 
v@x = {1,0,0} * m;
or
v@x = set(m.xx, m.xy, m.xz);

but again, make sure your N and up are normalized and also up is not gonna necessarily be exact y axis so you may want to extract that one also if you want all 3 orthogonal vectors
Tomas Slancik
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Method Studios, NY
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element33
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Sounds good, thanks. Yes, @up and @N are normalized.
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element33
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One more follow-up I may have to do the @N/@up-to-quaternion conversion in Python (in Houdini), not vex. I assume the relevant Python package is numpy, it seems to have quaternions. Has anyone done this in Python? If so what would be the equivalent of the vex code below, so that the result can be assigned as a Houdini quaternion attribute? What's the appropriate Python variable? A tuple? np.array?

Vex:
matrix3 m = maketransform ( v@N, v@up );
vector4 q = quaternion ( m );

Python:
up = (0,1,0)# tuple
N = (0,0,1)# tuple
orient = np.quaternion ( up?  N? )
pt.setAttribValue('orient',orient)
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element33
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I just realized I can compile that little snippet of vex, then do hou.runVex()
https://www.sidefx.com/docs/houdini/hom/hou/runVex.html [www.sidefx.com]
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