Quasi-Euclidean Norm

Returns the quasi-euclidean norm of an array in 1, 2 or 3 dimensions.
Updated 20 Mar 2022

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Calling [x, e] = qnorm(X, dim) returns the quasi-euclidean norm of X along its rows or columns for dim = 1 or 2, respectively, and the calculation error compared to the Euclidean norm. The values are derived from the information of neighbourhoods using 1, 2 or 3D distance transforms in (1), (2 2) or (3 3 3) voxel models.
The coefficients or weights are calculated seeking to maximise the norm of the vector X (approaching the L2 norm value within a small error). This makes this function a good approximation for the euclidean distance without the need for square roots or powers.
An example of the use of this function is:
n = 200;
[x, y, z] = meshgrid(-1 : 2 / (n - 1) : 1);
d = zeros(size(x));
for i = 1 : n
for j = 1 : n
for k = 1 : n
d(i, j, k) = qnorm([x(i, j, k) y(i, j, k) z(i, j, k)]);
s = isosurface(x, y, z, d, 0.5);
p = patch(s);
isonormals(x, y, z, d, p)
set(p, 'FaceColor', [0.85 0.85 0.85])
set(p, 'EdgeColor', 'none')
axis equal
lighting gouraud

Cite As

Moreno, M. (2024). Quasi-Euclidean Norm (https://www.mathworks.com/matlabcentral/fileexchange/108209-quasi-euclidean-norm), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2022a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes

Trivial case residual update


Specified a dimension for the norm calculation, and added as an output the error compared to the Euclidean norm.