how to plot a line given hessian normal form in matlab

To plot a line given in Hessian normal form using Matlab, we need to perform the following steps:

1. Define the parameters of the line
2. Generate a set of points along the line
3. Plot the line using the generated points

Here is the code (with detailed comments) for the implementation:

main.m
% Define the parameters of the line in Hessian normal form
normal_vector = [2, -1];  % the normal vector of the line
d = 5;  % the perpendicular distance from the line to the origin

% Generate a set of points along the line
t = linspace(-10, 10, 100);  % parameter values for the line
x = t*normal_vector(1) + d*cos(atan2(normal_vector(2), normal_vector(1)));  % x-coordinate of the points
y = t*normal_vector(2) + d*sin(atan2(normal_vector(2), normal_vector(1)));  % y-coordinate of the points

% Plot the line using the generated points
plot(x, y);
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We first define the normal vector and the perpendicular distance in Hessian normal form. We then use a set of parameter values to generate a set of points along the line. Finally, we plot the line using the plot() function.

Note that we used atan2() to compute the angle of the normal vector, which is used to determine the initial position of the line. Also, vectorization is used to perform the computations for all points along the line, resulting in faster and cleaner code.