Position of points relative to a plane

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Harold on 16 May 2013
Commented: Diego Hens on 21 Aug 2020
I'm looking for a way to decide whether a point is on, to the left, or to the right of a plane. I have it to work for a selected point. For example, given a number of (x,y,z) coordinates, I'm able to determine what points are on, or across the a line drawn from a point say x = 3. The code I developed works perfect. However, I want to expand on this so that any plane can be used not just the yz plane (x = 3). I want to do a batch check on all the points in a variable called vertices. There will always be three point coordinates in this variable.

Accepted Answer

Yao Li
Yao Li on 16 May 2013
  1. Obtain the equation of the plane
  2. If the point (x,y,z) satisfy the equation, the point is on the plane. I don't think you can use the word 'left' and 'right' to describe the position before you have specified the reference axis.
Diego Hens
Diego Hens on 21 Aug 2020
Did you find a solution to this? I have the same problem. I want to erase all points under a plane from an stl

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More Answers (1)

Jan on 16 May 2013
If the plane is defined by one point P and the normal vector N, is is easy to decide on which side (defined by the orientation of N) the point Q is: check the sign of:
v = dot(Q - P, N);


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