how to get x and y components of normal vector of curve like this??

I am trying to get the x and y components of the normal vector in the curve similar to the one attached here, any idea how to implement this ??

Answer 1

[Satwik]

Hi @Turbulence Analysis,

I understand that the goal is to compute the the X and Y components of the normal vector to a given curve. This can be achieved by following the steps given below:

1. Parameterize the curve as ( (x(t), y(t)) ) or as discrete points ((x_i, y_i)).
2. Compute the tangent vector at each point.
3. Find the normal vector by rotating the tangent vector by 90°.

Here is an exmaple script you may refer to implement the above steps:

x = linspace(-2, 2, 100);
y = x.^2; % Example: parabola

dy_dx = gradient(y, x); % Numerical derivative

% Tangent vector: (1, dy_dx)
% Normal vector: (-dy_dx, 1)
norms = sqrt(dy_dx.^2 + 1);
nx = -dy_dx ./ norms;
ny = 1 ./ norms;

figure;
plot(x, y, 'b-', 'LineWidth', 2); hold on;
quiver(x, y, nx, ny, 0.3, 'r');
axis equal; grid on;
title('Parabola with normal vectors');
legend('Curve', 'Normals');

Here is an image of the resulting plot:

I hope this helps!