Borrar filtros
Borrar filtros

Calculate the 3D angle between two vectors

121 visualizaciones (últimos 30 días)
Paul Huter
Paul Huter el 5 de Mzo. de 2017
Editada: Bruno Luong el 31 de Jul. de 2020
How do you calculate the angles between two vectors in order to generate a direction cosine matrix? I have MATLAB, Simulink, and Aerospace Toolkit/Toolbox. For reference, I am trying to use MATLAB to calculate a rotation matrix between the body frame of an object and (preferably) a fixed-frame or (not so preferably) an inertial-frame.

Respuestas (3)

Roger Stafford
Roger Stafford el 5 de Mzo. de 2017
Editada: Roger Stafford el 5 de Mzo. de 2017
The angle between two three-element vectors, P1 and P2, can be calculated using matlab in the following way:
a = atan2(norm(cross(P1,P2)),dot(P1,P2)); % Angle in radians
The angle will lie between 0 and pi radians. To get degrees use ‘atan2d’.
Note: However, the cosine of such an angle can be calculated as:
cosine of the angle = dot(P1,P2)/(norm(P1)*norm(P2))
No need to compute the angle itself.
  4 comentarios
Zhafirah Ariana
Zhafirah Ariana el 31 de Jul. de 2020
I tried this and it worked! But when i use this for array it didn't work. Do you have any idea why this happened?
Bruno Luong
Bruno Luong el 31 de Jul. de 2020
Editada: Bruno Luong el 31 de Jul. de 2020
For array of size 3 x N where 3 rows are x-y-z coordinates you might replace the
  • CROSS with CROSS_DIM1
  • DOT with DOT_DIM1
  • NORM(X) with vecnorm(x, 2, 1) or sqrt(sum(x.^2,1)).
  • "^" with ".^"
CROSS_DIM1
function c = cross_dim1(a,b)
% c = cross_dim1(a,b)
% Calculate cross product along the first dimension
% NOTE: auto expansion allowed
c = zeros(max(size(a),size(b)));
c(1,:) = a(2,:).*b(3,:)-a(3,:).*b(2,:);
c(2,:) = a(3,:).*b(1,:)-a(1,:).*b(3,:);
c(3,:) = a(1,:).*b(2,:)-a(2,:).*b(1,:);
end % cross_dim1
and DOT_DIM1
function d = dot_dim1(a,b)
% d = dot_dim1(a,b)
% Calculate dot product along the first dimension
% NOTE: auto expansion allowed
d = sum(a.*b,1);
end % dot_dim1

Iniciar sesión para comentar.


Image Analyst
Image Analyst el 5 de Mzo. de 2017

Bingo
Bingo el 25 de Mayo de 2020
function r = vrrotvec(a, b, options)
%VRROTVEC Calculate a rotation between two vectors.
% R = VRROTVEC(A, B) calculates a rotation needed to transform
% a 3d vector A to a 3d vector B.
  4 comentarios
John D'Errico
John D'Errico el 25 de Mayo de 2020
Not really. It is only there IF you just happen to have the correct toolbox.
help vrrotvec
'vrrotvec' requires Simulink 3D Animation.
Otherwise, you need to use the alteriatives.
Image Analyst
Image Analyst el 25 de Mayo de 2020
Editada: Image Analyst el 25 de Mayo de 2020
I don't have that toolbox. Simulink 3D Animation is not on the Products list on the right. I will add it.

Iniciar sesión para comentar.

Productos

Community Treasure Hunt

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

Start Hunting!

Translated by