Rotate Basis Vectors Programmatically
1 vue (au cours des 30 derniers jours)
Afficher commentaires plus anciens
I have six 6-dimensional basis vectors, i.e., that are orthogonal. I wonder how I can rotate these 6 vectors programatically in the 6D space to build new basis vectors. In other words, is there a way to parameterize these basis vectors so that I can change them without losing orthogonality?
A = [a1,a2,...,a6];
B = [b1,b2,...,b6];
C = [c1,c2,...,c6];
D = [d1,d2,...,d6];
E = [e1,e2,...,e6];
F = [f1,f2,...,f6];
Thank you.
0 commentaires
Réponse acceptée
Plus de réponses (2)
Chunru
le 30 Sep 2022
Modifié(e) : Chunru
le 30 Sep 2022
V1 = orth(randn(6)) % your original orthonormal basis
% Then you can apply any other orthonormal basis to it
% For example,
V2 = orth(randn(6)); % get another orthonormal basis
Vnew = V2*V1; % this is the transform of the original orthonormal basis
Vnew*Vnew' % to demonstrate the oorthonormal property
% If you want to control the rotation with angle in N-D space
% Rotate on hyperplane i-j by theta
i=2; j=4; % for example
theta = 5; % deg
R = eye(6); % 6D
R([i j], [i j]) = [cosd(theta) -sind(theta); sind(theta) cosd(theta)]
% Then you can have a series of rotation matrices and you can put them
% together as one rotation matrices
5 commentaires
Mohammad MSBR
le 30 Sep 2022
4 commentaires
Jan
le 1 Oct 2022
Sorry, there are only 15 hyperplanes in 6D: 6 choices for the first vector, 5 possible choices for the 2nd one, but the order does not matter, so divide by 2.
nchoosek(1:6, 2)
Voir également
Catégories
En savoir plus sur Graphics Object Properties dans Help Center et File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!