Problem 42762. Is 3D point set Co-Planar?
This Challenge is to determine if four 3D integer points are co-planar. Given a 4x3 matrix representing four x,y,z integer points, output True if the set is co-planar and False otherwise.
m = [0 0 0;1 0 0;0 1 0;0 0 1] Output: False, this point set is non-coplanar.
m = [0 0 0;0 0 1;1 1 0;1 1 1] Output: True, this point set is co-planar.
Reference: The March 2016 Al Zimmermann Non-Coplanar contest is to maximize the number of points in an NxNxN cube with no 4 points in a common plane. Future challenge will be to find N=2 and N=3 solutions.
Theory: Plane is defined as Ax+By+cZ=D. [A,B,C] can be found using cross of 3 points. D can be found by substitution using any of these 3 points. Co-Planarity of the fourth point is True if Ax4+By4+Cz4==D
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