28 lines
585 B
Matlab
28 lines
585 B
Matlab
%*** CHAPTER 3: RIGID-BODY MOTIONS ***
|
|
|
|
function d = DistanceToSO3(R)
|
|
% Takes mat: A 3x3 matrix.
|
|
% Returns d, a quantity describing the distance of R from the SO(3)
|
|
% manifold.
|
|
% Computes the distance from R to the SO(3) manifold using the following
|
|
% method:
|
|
% If det(R) <= 0, return a large number.
|
|
% If det(R) > 0, return norm(R' * R - I).
|
|
% Example Inputs:
|
|
%{
|
|
clear; clc;
|
|
R = [1.0, 0.0, 0.0;
|
|
0.0, 0.1, -0.95;
|
|
0.0, 1.0, 0.1];
|
|
d = DistanceToSO3(R)
|
|
%}
|
|
% Output:
|
|
% d =
|
|
% 0.0884
|
|
|
|
if det(R) > 0
|
|
d = norm(R' * R - eye(3), 'fro');
|
|
else
|
|
d = 1e+9;
|
|
end
|
|
end |