# how to project trajectories on a plane which is made from normal vector?

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Sierra on 11 Jun 2022
Commented: Sierra on 12 Jun 2022
Hello Everyone, I have trouble projecting trajectories on a plane.
First, there are a lot of trajectories which is consist of data(longitude, latitude, altitude) and I calculated the mean of longitude data, latitude data and altitude data.
This is aircraft's data.
This is mean trajectory's data.
And Using this data, I want to project trajectories on a plane.
The blue lines are aircraft's trajectories and the black line is a mena trajectory. (I intentionally made this image 2D to explain this easily.)
The red line is a normal vector made on mean trajectory's line and from this vector, I want to make a plane like the image below.
this is an example plane which is projected.(this plane is 3D (longitude, latitude, altitude))
Please let me know how to project a trajectory on a plane using normal vector.
Thanks and Have a Good Day!
Sierra on 12 Jun 2022
This image is what i did before.
If i can project trajectories on a plane like this, I will make a boundary using 'percentile'.
But for this image, I didn't use the normal vector. So final result doesn't look good when viewing from top.
As you can see, since the y value is fixed, the boundary is not perpendicular to mean trajectory.(In this image, I didn't plot trajectories to see boundaries well)
To solve this problem, i thought i have to use 'normal vector'.
I think if i can use 'normal vector', it will be good. But I don't know how to do now.
And for clarification, I will explain about the boundary again.
The boundary is made using 'percentile'. That's why the boundary doesn't contain every trajectory. In my case, percentile was 97.5
Ex) if percentile is 100, the boundary will be bigger and contains every trajectory.