# Vector Directions

Hi all,

maybe a quick answer for a quick question. When I do an average of the red vectors I got that green one. But what I want to have is that blue vector. I think i have a mathematical misunderstanding of how I can get there. 200113_Vectorlines.gh (9.6 KB)
Any help? Thanks!

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Looks like it makes sense to me. The 4 vectors tending left cancel the 4 tending right leaving a small almost vertical component.

i think i have to specify my problem: I have a bunch of vectors and points. The result should be that the lines are in harmonic grid. Here you can see that some Lines are unharmonic due to the earlier problem:
200113_Vectorlines_Var2.gh (19.8 KB)

Hendrik

Try thisâ€¦
200113_Vectorlines_Var2.gh (23.7 KB)

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Are you looking for something like Principal Component Analysis? (good explanation of PCA here)
One easy way to approximate this in GH is to take the vector for each line and its negative and plot it as a point, then fit a line through these points.
fitline.gh (17.0 KB)

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Thanks David,
that seems to me a good solution, but it refer all lines to one â€śguideâ€ť line.
In some cases that could cause errors.
Hendrik

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Thanks Daniel,
Iâ€™m not sure if i understand how fitline solves that problem. But it does it pretty good!
And that forum about PCA looks interesting. Thanks for sharing.
Hendrik

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Quick fix. You can have a general direction as an input to eliminate the issue. Or try DanielÂ´s solution which is free from that BS

Yes, I have to figure out Daniels solution.

Btw, between all these experts here I feel like Doofus Rick, but without the uncommon eating habits

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DonÂ´t worry. On this forum the learning curve is like a rollercoaster. Just keep playing.

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To try and clarify why I used FitLine here-
If you have the 3 red vectors and take their average, you get the result in green, because one of the inputs points is almost the opposite direction to the other two, so they partially cancel out:

If instead for each of the input vectors, you place a point at its end, and also at the end of the reversed vector, you can fit a line like this:

The advantage of this over choosing one of the vectors or a global direction and flipping the input vectors based on their sign relative to this is that there thereâ€™s always a chance you get unlucky and the flipping reference vector ends up being nearly perpendicular to the other inputs so the original problem still occurs.

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