Algorithm 1 Generating Binary Encoding for the $n\times n$ Hilbert Curve

1:Input: Area size $n\times n$ (assumed $n=2^m$), Point coordinates $(x,y)\in {\{0,...,n-1\}}^2$ 2:Output: Binary encoding of each point on the Hilbert curve 3:For each point $(x,y)$ do 4:$index\leftarrow 0$ 5:$scale\leftarrow n/2$ 6:$x_{temp}\leftarrow x$, $y_{temp}\leftarrow y$ 7:while $scale>0$ do 8:      $rx\leftarrow \mathrm{bit}(x_{temp},scale)$ 9:      $ry\leftarrow \mathrm{bit}(y_{temp},scale)$ 10:    $index\leftarrow index+scale\times scale\left(\right(3\times rx)\oplus ry)$ 11:    if $ry=0$ then 12:        if $rx=1$ then 13:             $(x_{temp},y_{temp})\leftarrow (n-1-x_{temp},n-1-y_{temp})$ 14:        end if 15:        $(x_{temp},y_{temp})\leftarrow (y_{temp},x_{temp})$ 16:    end if 17:    $scale\leftarrow scale/2$ 18:end while 19:Output binary representation of $index$