Canonical piecewise-linear representation

Every continuous piecewise-linear function of one variable f:R/sup 1/ to R/sup 1/ has a unique canonical piecewise-linear representation. However, only a subclass of higher-dimensional piecewise-linear functions f:R/sup n/ to R/sup n/, n>1, has a canonical piecewise-linear representation. It is proved that the necessary and sufficient conditions for the existence of a canonical piecewise-linear representation is that fpossess a consistent variation property. The geometrical constraints imposed by this property are analyzed and discussed in detail along with many examples.<
>