  This paper concerns an analytical stratification question of real algebraic
and semi-algebraic sets. For Whitney's stratification in 1957, it partitions a
real algebraic set into partial algebraic manifolds\cite{W}. In 1975 Hironaka
reproved that a real algebraic set is triangulable and also generalized it to
semi-algebraic sets, following the idea of Lojasiewicz's triangulation of
semi-analytic sets in 1964. Following their examples and wondering how geometry
looks like locally. this paper tries to come up with a stratification, in
particular a cell decomposition, such that it satisfies the following
analytical property. Given any shortest curve between two points in a real
algebraic or semi-algebraic set, it interacts each cell (or simplex) at most
finitely many times.
