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August 20, 2015 22:09
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Given two vectors, create a rotation matrix to rotate from A to B, in matlab
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function R=fcn_RotationFromTwoVectors(A, B) | |
% http://math.stackexchange.com/questions/180418/calculate-rotation-matrix-to-align-vector-a-to-vector-b-in-3d | |
% R*v1=v2 | |
% v1 and v2 should be column vectors and 3x1 | |
%% Method 1 | |
% % 1. rotation vector | |
% w=cross(v1,v2); | |
% w=w/norm(w); | |
% w_hat=fcn_GetSkew(w); | |
% % 2. rotation angle | |
% cos_tht=v1'*v2/norm(v1)/norm(v2); | |
% tht=acos(cos_tht); | |
% % 3. rotation matrix, using Rodrigues' formula | |
% R=eye(size(v1,1))+w_hat*sin(tht)+w_hat^2*(1-cos(tht)); | |
% | |
% function x_skew=fcn_GetSkew(x) | |
% x_skew=[0 -x(3) x(2); | |
% x(3) 0 -x(1); | |
% -x(2) x(1) 0]; | |
%% Method 2 | |
% g = [ dot(A,B) -norm(cross(A,B)) 0; | |
% norm(cross(A,B)) dot(A,B) 0; | |
% 0 0 1]; | |
% | |
% f = [ A (B-dot(A,B)*A)/norm(B-dot(A,B)*A) cross(B,A) ]; | |
% | |
% R = f*g/f; | |
%% Method 3 | |
v = cross(A,B); | |
ssc = [0 -v(3) v(2); v(3) 0 -v(1); -v(2) v(1) 0]; | |
R = eye(3) + ssc + ssc^2*(1-dot(A,B))/(norm(v))^2; |
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Thanks ! just what I was looking for. One minor improvement would be to offer an option to return normalised matrix.