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How to check that these points formulate flat plane(on the same plane)?

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M
M 2023-2-8
编辑： Jan 2023-2-9
In hyperplanes (4d and more),How to check that these points formulate flat plane(on the same plane)?
for example these points (6d plane)?
P1 =[396326796.725069,-205153846.153846,0,0,0,0];
P2 =[-205153846.153846,396326796.725069,-205153846.153846,0,0,0];
P3= [0,-205153846.153846,396326796.725069,-205153846.153846,0,0];
P4 = [0 0 -205153846.153846 396326796.725069 -205153846.153846 0];
P5=[0 0 0 -205153846.153846 396326796.725069 -205153846.153846];
P6=[0 0 0 0 -205153846.153846 198163398.362534];

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回答（1 个）

Jan
Jan 2023-2-8
编辑：Jan 2023-2-9
Ran in:
P1 = [396326796.725069,-205153846.153846,0,0,0,0];
P2 = [-205153846.153846,396326796.725069,-205153846.153846,0,0,0];
P3 = [0,-205153846.153846,396326796.725069,-205153846.153846,0,0];
P4 = [0 0 -205153846.153846 396326796.725069 -205153846.153846 0];
P5 = [0 0 0 -205153846.153846 396326796.725069 -205153846.153846];
P6 = [0 0 0 0 -205153846.153846 198163398.362534];
P = [P1; P2; P3; P4; P5; P6];
RankP = rank(P - P(1, :))
RankP = 5
isHyperplane = RankP < 6 % [EDITED] "coplanar" was a clumsy term
isCoplanar = logical
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Torsten
Torsten 2023-2-8
编辑：Torsten 2023-2-8
Yes, but it's superfluous to test it for the example given because the rank could not come out to be >= 6.
The first row of P - P(1, :) is a zero row.
Jan
Jan 2023-2-9
The term "isCoplanar" in my answer was a bad choice. Then rank tells us the dimensions of the spanned subspace (or "affine hyperplane"). "Planar" and in consequence "coplanar" are less useful in 6D.
I'm not sure if the meaning of the original question has been defined clearly yet: What do you call a "flat plane"?

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