calculate parameters of hessian normal form of line in matlab

The Hessian normal form of the line is given by the equation:

main.m
r = (x,y)T = (x0,y0)T + λn/||n||
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where (x0, y0) is a point on the line, n = (a, b) is a normal vector to the line, and λ is a parameter.

To calculate the parameters of the Hessian normal form of a line in MATLAB, you need to follow these steps:

1. Define the normal vector n and a point P on the line.
2. Calculate the magnitude ||n|| of the normal vector using the norm function.
3. Calculate the values of a and b of the normal vector.
4. Create a symbolic variable for λ using the syms function.
5. Calculate the equation of the line using the Hessian normal form equation.

Here's an example code:

main.m
% Define a point P on the line and a normal vector n
P = [1, 2];
n = [3, 4];

% Calculate the magnitude of the normal vector
norm_n = norm(n);

% Calculate the values of a and b
a = n(1);
b = n(2);

% Create a symbolic variable for lambda
syms lambda;

% Calculate the equation of the line in Hessian normal form
r = P' + lambda * n' / norm_n;

% Display the equation of the line
disp(r);
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This code will produce the equation of the line in the Hessian normal form:

main.m
1.0000 + 0.6000*lambda
2.0000 + 0.8000*lambda
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In this example, the normal vector is [3, 4] and the point P is (1, 2). The magnitude of the normal vector ||n|| is 5, and the values of a and b are 3 and 4, respectively. Finally, the equation of the line in Hessian normal form is (1 + 0.6λ, 2 + 0.8λ).