SLAM on the Hexagonal Grid

. 2022 Aug 19;22(16):6221. doi: 10.3390/s22166221

Algorithm 1 Discretization of Hexagonal Coordinates

{\hat{x}}_{d} + {\hat{y}}_{d} + {\hat{ζ}}_{d} = 0

then

x_{d} \leftarrow {\hat{x}}_{d}

y_{d} \leftarrow {\hat{y}}_{d}

ζ_{d} \leftarrow {\hat{ζ}}_{d}

else
if

{x_{c} / w} \geq {y_{c} / w}

and

{x_{c} / w} \geq {ζ_{c} / w}

then

x_{d} \leftarrow - {\hat{y}}_{d} - {\hat{z}}_{d}

y_{d} \leftarrow {\hat{y}}_{d}

ζ_{d} \leftarrow {\hat{ζ}}_{d}

else if

{y_{c} / w} \geq {x_{c} / w}

and

{y_{c} / w} \geq {ζ_{c} / w}

then

x_{d} \leftarrow {\hat{x}}_{d}

y_{d} \leftarrow - {\hat{x}}_{d} - {\hat{ζ}}_{d}

ζ_{d} \leftarrow {\hat{ζ}}_{d}

else

x_{d} \leftarrow {\hat{x}}_{d}

y_{d} \leftarrow {\hat{y}}_{d}

ζ_{d} \leftarrow - {\hat{x}}_{d} - {\hat{y}}_{d}

end if
end if