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