epiparametric

Epiparametric refers to a specific type of parameterization used in mathematics, particularly in the context of describing curves, surfaces, or other geometric objects. It involves defining a set of parameters that depend on another parameter, or a set of parameters that are themselves dependent on a global parameter. Essentially, it's a nested or hierarchical parameterization.

This concept is often encountered when dealing with complex shapes or motion. For instance, imagine describing the path of a point on a rotating wheel that is also moving along a straight line. The position of the point on the wheel can be parameterized by an angle relative to the wheel's center (an inner parameter), while the position of the wheel's center itself can be parameterized by time or distance along the line (an outer parameter). The combination of these parameterizations creates an epiparametric description of the point's overall motion.

In a more abstract sense, epiparametric functions are functions where the parameters themselves are functions of other variables. This allows for a flexible and dynamic way to represent and manipulate complex mathematical objects. The term is not as widely used as simpler parameterization methods but is useful for describing situations where multiple levels of control or dependence are present in the definition of a geometric entity or its evolution. It signifies a layered approach to defining variables.