  In this paper we study Lipschitz contact equivalence of continuous function
germs in the plane definable in a polynomially bounded o-minimal structure,
such as semialgebraic and subanalytic functions. We partition the germ of the
plane at the origin into zones where the function has explicit asymptotic
behavior. Such a partition is called a pizza. We show that each function germ
admits a minimal pizza, unique up to combinatorial equivalence. We show then
that two definable continuous function germs are definably Lipschitz contact
equivalent if and only if their corresponding minimal pizzas are equivalent.
