In piecewise interpolation,....
points are called knots.
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Knots are something which is particular to the way splines are constructed. For a sequence of knots, (t1,…,tm), a spline is a function which is polynomial when restricted to each nonempty knot span (ti,ti+1) and satisfies some additional continuity assumptions in the knots. So knots and nodes are not the same.
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