Abstract: To obtain the maximum interspace of Euclidean-space with obstacles——MAXG(Ω),a new method of map algebra is used to analysis. With distance-transforming and constructing the Voronoi diagram of holomorphism,the maxdistance point is got to resolve MAXG(Ω).The arithmetic and some experiment results are also given.It may be spreaded in the interest of three dimensions and power distance without remarkable difficultly.