Correct terminology for polylines, their segments, knots, etc.

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Background: piecewise-linear continuous functions $f(x_k)=y_k$ with fixed set of knots $x_k$ with restrictions on the angles between adjacent segments.

The translator who dealt with my paper, introduced terminology that I don't like, i.e. (my variants are on the left):

  • knots -> nodes
  • adjacent segments -> neighboring links
  • segment -> link
  • polylines -> broken lines

Which one is better? How would you call piecewise-linear function, its segments, its knots? What are the most common namings for these?

NB: That's more about piecewise-linear functions than about polylines in the geometrical sense.