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2D Line Curvature and Normals

version (8.97 KB) by Dirk-Jan Kroon
Accurate Curvature and Normals of a line/contour consisting of 2D points


Updated 17 Oct 2011

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Editor's Note: This file was selected as MATLAB Central Pick of the Week

LineCurvature2D, This function calculates the curvature of a 2D line. It first fits polygons to the points. Then calculates the analytical curvature from the polygons.

K = LineCurvature2D(Vertices,Lines)

Vertices : A M x 2 list of line points.
Lines : A N x 2 list of line pieces, by indices of the vertices
(if not set assume Lines=[1 2; 3 4 ; ... ; M-1 M])

K : M x 1 Curvature values

LineNormals2D, This function calculates the normals, of the line. Using the neighbouring points of each line/contour point, and forward an backward differences on the end points


V : List of points/vertices 2 x M
Lines : A N x 2 list of line pieces, by indices of the vertices
(if not set assume Lines=[1 2; 3 4 ; ... ; M-1 M])

N : The normals of the Vertices 2 x M

Cite As

Dirk-Jan Kroon (2021). 2D Line Curvature and Normals (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (35)

Jim Dunlop

Giuseppe Pontrelli

Does the algorithm work also for concave 2D surface? how can I recognize the points where the surface is convex and where it is concave?
Thank you

James L

Pavel Kolesnichenko

Luxiao Cui


Dear all, the curvature is calculated simply by the formula in the following link, which is a result of planar differential geometry.


Dear Dirk,
Could you refer as to the math behind the last step of the calculation?Is there any literature? That is, how you get the curvature from the fitted polynomial?

jian fu

Dear Dirk-Jan Kroon,
thanks for this great function! Is there any chance for me to get the related papers explaining this method?
Thanks a lot!


Aitor Arana

Liliana Valencia

It's a very nice code but I would like to know the mathematical foundation. Does anybody know it??

iman memarzade

Mandeep Dhanda


Felix Oberle

Adrian Szatmari

Yaoshen Yuan

Arash Shahirpour

linfeng yang

Ilya Belevich


Anwer khan

Ben King

Sleh Eddine Brika


Hi . Can this code be used to break the curved line into small line segments of appropriate size with their ends overlapped to some small extent and then take hough transform?

GOPEE Ajit Kumar

can the code be used to find singular points in fingerprint? if yes how plz? thx. Ajit

Benjamin Miller

Robbin van Hoek

From what i understand the algorithm only uses the direct neighbors of the point to be evaluated correct? is it possible to include multiple nearby points to get a more accurate result?

Khalid Ali

What is meant by lines?


very useful code. i would also like to know the mathematical model used. does it use the freeman chain code Dirk?


Thank you, good code to find in my case finger tips on a hand scan



Is there any literature to back this up??
Also, the grammar in the comments needs serious work....


Thank you! Very usefull code! I would like to understand the maths behind the code better. Is this code based on some literature?

Ravikiran Janardhana

I would like to point out a small typo:-
L=[(1:(size(V,1)-1))' (2:size(V,1))'];
In the code I saw,the above was :-
Lines=[(1:(size(Vertices,1)-1))' (2:size(Vertices,1))'];

MATLAB Release Compatibility
Created with R2011a
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired: thick_line(x,y,thickness)

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