How to draw normal line at given points ?

Hello everyone,

I have a red curve that fit 4 bleu points. I want to draw normal at these points.

Here attached my curve.

and the x, y coordinates of the bleu points are :

x=[142;127;181;234];
y=[251;251;261;255];

So, please, how to get the normal line ?

I will be very grateful if anyone could help me.

[Ameer Hamza]

How did you create this curved line fitting through these points?

[MMSAAH]

Hello Ameer,

Here is my code:

x=[142;127;181;234]
y=[251;251;261;255]
p = polyfit(x, y, 1);
v = polyval(p, x);
xint = linspace(127,300,50)';
spl = spline(x,y);
figure
t=plot(y,x,'.',ppval(spl,xint),xint,'r-')
xlim([200 300])
ylim([50 234])

Answer 1

[Ameer Hamza]

Try this:

x=[142;127;181;234];
y=[251;251;261;255];

[x, idx] = sort(x);
y = y(idx);

points = [x y];

xint = linspace(127,234,50)';
spl = spline(x,y);

tangent_vector = zeros(4,2);
for i=1:4
    if i==4 % last polynomial need to evalauted at endpoint
        deri_coef = polyder(spl.coefs(i-1,:));
        tangent_vector(i, :) = [1 polyval(deri_coef, x(end)-x(end-1))];
    else
        deri_coef = polyder(spl.coefs(i,:));
        tangent_vector(i, :) = [1 polyval(deri_coef, 0)];
    end
end

normal_vec = [-tangent_vector(:,2) tangent_vector(:,1)];

start_points = points;
end_points = 10*normal_vec + points;

fig = figure;
ax = axes();
hold(ax);
t = plot(y,x,'.',ppval(spl,xint),xint,'r-');
for i=1:4
    p1 = start_points(i,:);
    p2 = end_points(i,:);
    plot([p1(2) p2(2)], [p1(1) p2(1)], 'r', 'LineWidth', 2);
end

daspect([1 1 1]);

xlim([180 340])
ylim([100 250])

[MMSAAH]

Thank you very much for the answer.It worked perfectly.

However, could you explain me more the for loop ? and why did you evaluated the polynome at endpoint ?

Thank you though!

[Ameer Hamza]

For loop is just calculating the tangent vector at each point, since we can calculate the normal vectors from tangent vectors. The spline function output 3 polynomials for 4 data points. So to compute tangent at 4 data points, we need to do it like this

datapoint # 1 -> polynomial # 1 (start point)

datapoint # 2 -> polynomial # 2 (start point) or polynomial # 1 (end point)

datapoint # 3 -> polynomial # 3 (start point) or polynomial # 2 (end point)

datapoint # 4 -> polynomial # 3 (end point)

Which shows where I evaluated the derivative of each polynomial

Answer 2

[michael scheinfeild]

https://michaelsheinfeild.medium.com/unit-normal-vector-to-curve-d63ef0124acd