A Pachner move is any of a set of ways of replacing a triangulation of a piecewise linear manifold by a different triangulation of a homoeomorphic manifold.

A bistellar flip is another term for a Pachner move, any of a set of ways of replacing a triangulation of a piecewise linear manifold by a different triangulation of a homeomorphic manifold.

J. F. P. Hudson has written:

'Piecewise linear topology' -- subject(s): Piecewise linear topology

The form of the piecewise functions can be arbitrarily complex, but higher degrees of specification require considerably more user input.

Interpolation in general is a way to determine intermediate values from a set of coordinates. Linear interpolation would be to fit a single linear function to the entire set of coordinates. Piecewise linear interpolation would then be to determine intermediate values from the set of coordinates by fitting linear functions between each set of coordinates. Connect-the-dots so to speak.