الگوریتم فورچون

let ${\displaystyle \ast (z)}$
 be the transformation ${\displaystyle \ast (z)=(z_x,z_y+d(z))}$
,
  where ${\displaystyle d(z)}$
 is the Euclidean distance between ${\displaystyle z}$
 and the nearest site
let ${\displaystyle T}$
 be the "beach line"
let ${\displaystyle R_p}$
 be the region covered by site ${\displaystyle p}$
.
let ${\displaystyle C_{pq}}$
 be the boundary ray between sites ${\displaystyle p}$
 and ${\displaystyle q}$
.
let ${\displaystyle p_1,p_2,...,p_m}$
 be the sites with minimal ${\displaystyle y}$
-coordinate, ordered by ${\displaystyle x}$
-coordinate
${\displaystyle Q\leftarrow S-p_1,p_2,...,p_m}$

create initial vertical boundary rays ${\displaystyle C_{p_1,p_2}^0,C_{p_2,p_3}^0,...C_{p_{m-1},p_m}^0}$

${\displaystyle T\leftarrow \ast (R_{p_1}),C_{p_1,p_2}^0,\ast (R_{p_2}),C_{p_2,p_3}^0,...,\ast (R_{p_{m-1}}),C_{p_{m-1},p_m}^0,\ast (R_{p_m})}$

while not IsEmpty(${\displaystyle Q}$
) do
    ${\displaystyle p}$
 ← DeleteMin(${\displaystyle Q}$
)
    case ${\displaystyle p}$
 of
    ${\displaystyle p}$
 is a site in ${\displaystyle \ast (V)}$
:
        find the occurrence of a region ${\displaystyle \ast (R_q)}$
 in ${\displaystyle T}$
 containing ${\displaystyle p}$
,
          bracketed by ${\displaystyle C_{rq}}$
 on the left and ${\displaystyle C_{qs}}$
 on the right
        create new boundary rays ${\displaystyle C_{pq}^{-}}$
 and ${\displaystyle C_{pq}^{+}}$
 with bases ${\displaystyle p}$

        replace ${\displaystyle \ast (R_q)}$
 with ${\displaystyle \ast (R_q),C_{pq}^{-},\ast (R_p),C_{pq}^{+},\ast (R_q)}$
 in ${\displaystyle T}$

        delete from ${\displaystyle Q}$
 any intersection between ${\displaystyle C_{rq}}$
 and ${\displaystyle C_{qs}}$

        insert into ${\displaystyle Q}$
 any intersection between ${\displaystyle C_{rq}}$
 and ${\displaystyle C_{pq}^{-}}$

        insert into ${\displaystyle Q}$
 any intersection between ${\displaystyle C_{pq}^{+}}$
 and ${\displaystyle C_{qs}}$

    ${\displaystyle p}$
 is a Voronoi vertex in ${\displaystyle \ast (V)}$
:
        let ${\displaystyle p}$
 be the intersection of ${\displaystyle C_{qr}}$
 on the left and ${\displaystyle C_{rs}}$
 on the right
        let ${\displaystyle C_{uq}}$
 be the left neighbor of ${\displaystyle C_{qr}}$
 and
          let ${\displaystyle C_{sv}}$
 be the right neighbor of ${\displaystyle C_{rs}}$
 in ${\displaystyle T}$

        create a new boundary ray ${\displaystyle C_{qs}^0}$
 if ${\displaystyle q_y=s_y}$
,
          or create ${\displaystyle C_{qs}^{+}}$
 if ${\displaystyle p}$
 is right of the higher of ${\displaystyle q}$
 and ${\displaystyle s}$
,
          otherwise create ${\displaystyle C_{qs}^{-}}$

        replace ${\displaystyle C_{qr},\ast (R_r),C_{rs}}$
 with newly created ${\displaystyle C_{qs}}$
 in ${\displaystyle T}$

        delete from ${\displaystyle Q}$
 any intersection between ${\displaystyle C_{uq}}$
 and ${\displaystyle C_{qr}}$

        delete from ${\displaystyle Q}$
 any intersection between ${\displaystyle C_{rs}}$
 and ${\displaystyle C_{sv}}$

        insert into ${\displaystyle Q}$
 any intersection between ${\displaystyle C_{uq}}$
 and ${\displaystyle C_{qs}}$

        insert into ${\displaystyle Q}$
 any intersection between ${\displaystyle C_{qs}}$
 and ${\displaystyle C_{sv}}$

        record ${\displaystyle p}$
 as the summit of ${\displaystyle C_{qr}}$
 and ${\displaystyle C_{rs}}$
 and the base of ${\displaystyle C_{qs}}$

        output the boundary segments ${\displaystyle C_{qr}}$
 and ${\displaystyle C_{rs}}$

    endcase
endwhile
output the remaining boundary rays in ${\displaystyle T}$