How to plot curvature comb for discrete data

Hello,

everyone! I want to plot the curvature comb from some discrete data, which lie in circle. I only get a graph of curvature curve, actually to better observe I want to get a graph of curvature comb, like Fig(a). So could you give me some suggestions? Thank you very much!

(a)

 clc;clear all;  
 i=1:45;
 x0=sin(pi*i/20);
 y0=cos(pi*i/20);

  h1 = abs(diff([x0])) ;
  h = [h1 h1(end)];
  ht = h;
  yapp1 = gradient(y0)./ht; 
  yapp2 = del2(y0)./ht; 
  k2 = abs(yapp2)./(1+yapp1.^2).^(3/2);
  figure
  plot(k2,'color','r')
  title('Curvature curve')

  figure
  plot(x0,y0,'.-');

[lei]

Thanks for all your help! I think I may solve my problem. Thank you again.

A “curvature comb” is a type of graphical diagram added to the plot of a curve which shows a number of “teeth” segments with their bases along the curve, oriented perpendicular to the curve and proportional in length to its curvature. I think you can better understand curvature comb through the following figure.

• The length of each curvature line is proportional to the inverse of the radius of the curve at that point.
• The direction of each curvature line is at 90 degrees (normal) to the curve at each point.
• The red outline shows the smoothness and character of the curve.

http://www.bluesmith.co.uk/evaluateComb.htm

    
 clc;clear all;  
 i=0:360;
 theta = 2*pi/360 * i;
 x0 = cos(theta);
 y0 = sin(theta);
 
%Curvature
%k2: curvature（k2=y''/[(1+(y')^2)^(3/2)]）, where y' and y'' are the first
%and second derivatives
 h1 = abs(diff([x0])) ;
 h = [h1 h1(end)];
 ht = h;
 yapp1 = gradient(y0)./ht; 
 yapp2 = del2(y0)./ht; 
 k2 = abs(yapp2)./(1+yapp1.^2).^(3/2);

%normal vector of points
%dy=y2-y1;dx=x2-x1;
%normal vector: (-dy,dx) and (dy,-dx)
%Source:https://stackoverflow.com/questions/1243614/how-do-i-calculate-the-normal-vector-of-a-line-segment
 dy = gradient(y0);
 dx = gradient(x0);

quiver(x0,y0,-k2.*dy,k2.*dx,'g','ShowArrowHead','off','LineWidth',1);
hold on; 
plot(x0,y0,'color','blue','LineWidth',1.5);

[Star Strider]

O.K. I’m still not sure I understand what you want to do, however at least this solves the mystery of a ‘curvature comb’.

I moved this because it belongs here.