Pidgonacci

clear all;

% Pidgeon locations in pixels
x = [39, 48, 60, 77, 93, 116, 140, 172, 209, 256, 312, 418, 629].'
n = size(x)

% Fibonacci, variable a is for shifting all the locations
cvx_begin
    variables x_fib(n) a
    minimize norm(x_fib - (x - a))
    subject to
        x_fib(1:n-2) + x_fib(2:n-1) == x_fib(3:n)
        2 * x_fib(1) == x_fib(2)
cvx_end

% Quadratic
p = polyfit([1:n].', x, 2)
p_objective = norm(polyval(p, [1:n].') - x)