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

5 次查看（过去 30 天）
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];

请先登录，再回答此问题。

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
1
  19 个评论
显示 17更早的评论
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"?

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Resizing and Reshaping Matrices 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by