Problem with curves Normal and Orientation

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Hello guys!

First time here opening a new topic.
I've been struggling so far with some Curve issues as I wanted to recreate an arena's seats system for some personal stuff.

My main goal right now is that I have multiple curves which I want to scatter the signle seat onto. I've generated the standings pretty easily and everything went good until I had to deal directly with the Normals on the single points of the curves (generated with edgegroup_to_curve lab tool) as they have the same up vector but the tangent of it needed to orient the seats toward the court are pointing differently one curve each other. Since I can't understand a proper way to reorient all the curve together, would someone of you share at least a way to overcome this unespectedly stopping problem?

Since I've approached to houdini lately and I'm still getting my head around it, I've tried with different approaches with no result.

Many thanks in advance!
You'll find some screenshot down below

Attachments:
hou_04.PNG (1.0 MB)
hou_03.PNG (1.9 MB)
hou_02.PNG (1.1 MB)
hou_01.PNG (1.6 MB)
standings01_v003.hiplc (476.3 KB)

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since your stadium is centered around 0, you can for example append Point Wrangle SOP after your polyframe1 node:
vector center = {0,0,0};
vector up = {0,1,0};

vector z = v@N;
vector x = center - v@P;
vector y = cross(x, z);

if ( dot(y, up) < 0.0) v@N *= -1;
Tomas Slancik
FX Supervisor
Method Studios, NY
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