2D Line Curvature and Normals

Accurate Curvature and Normals of a line/contour consisting of 2D points

Description

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)
  
  inputs,
    Vertices : A M x 2 list of line points.
    (optional)
    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])
 
  outputs,
    K : M x 1 Curvature values

.
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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

  N=LineNormals2D(V,L)
 
  inputs,
    V : List of points/vertices 2 x M
  (optional)
    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])
 
  outputs,
    N : The normals of the Vertices 2 x M
 

• MATLAB release: MATLAB 7.12 (2011a)

[Ravikiran Janardhana]

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