A 2D point projection on a 3D segment.

IhorV

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Feb 28, 2019
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Hello everyone. So, there is a point in 2D space with known coordinates. Also, there is a segment in 3D space with known coordinates (both beginning and end). The point overlaps the segment. Is there a way to find 3D coordinates of the point's projection onto this segment?
 

Dr.Peterson

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Nov 12, 2017
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Huh? A 2D space and a 3D space are separate things. You seem to be assuming the former is in the latter.

Maybe you mean this: You are given a point P, say on the x-y plane, and a segment with known endpoints \(\displaystyle A(x_0, y_0, z_0)\) and \(\displaystyle B(x_1, y_1, z_1)\), and you want to project the point perpendicularly onto the line, and find the (x, y, z) coordinates of the projection.

It doesn't matter where the point is; it doesn't have to be on some particular plane in order to project it. Have you searched for information on projection onto a line?

I might do a vector projection of AP onto AB, and add the resulting vector to the location vector OA.
 

HallsofIvy

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Jan 27, 2012
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When you say "2D space" do you mean, say, the xy-plane in an xyz coordinate system?
 
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