Unit normal vector to curve

Sometime we need to draw normal to curve, so we need to remember math from school…

Based on nice link https://www.khanacademy.org/math/multivariable-calculus/integrating-multivariable-functions/line-integrals-in-vector-fields-articles/a/constructing-a-unit-normal-vector-to-curve

i decided to write small Matlab program to implement this.

The Program

figure,imshow(ones(400));

x =[ 229.0000
253.0000
242.0000
231.0000
154.0000
105.0000
69.0000
66.0000
77.0000
138.0000];

y =[ 283.0000
269.0000
222.0000
204.0000
185.0000
167.0000
130.0000
80.0000
45.0000
27.0000];

hold on;
plot(x,y,’r’)
plot(x,y,’ro’)

for(k=2:length(x)-1)
plot(x(k),y(k),’bo’)

%% step 1 dv/dt
dx = (x(k+1)-x(k-1));
dy =(y(k+1)-y(k-1));

dvdt = [dx;dy];

%% step2 rotate 90%
dvdtRot = [-dy ;dx];

%% Step 3: Scale it to magnitude 1
% unit vector
% sqrt(0.2818*0.2818 + -0.9595*(-0.9595))=1
dvdtRotNorm = dvdtRot/norm(dvdtRot);

scale=50;
pNorm = [x(k);y(k)]+scale*dvdtRotNorm;
plot(pNorm(1),pNorm(2),’gs’)
line([x(k);pNorm(1)],[y(k);pNorm(2)])
end

Curve red and normal's