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CUBIC SPLINES
The objective in cubic plotters is to obtain a third degree polynomial for each Interval between the nodes:
Thus, for n + 1 data (i = 0, 1, 2, ..., n), there are n intervals and, consequently, 4n unknowns to be evaluated. As with quadratic tracers, 4n conditions are required to evaluate the unknowns. These are:
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1. The values ​​of the function must be the same in the inner nodes (2n - 2 conditions).
2. The first and last function must pass through the endpoints (2 conditions).
3. The first derivatives in the interior nodes must be equal (n - 1 conditions).
4. The second derivatives in the interior nodes must be equal (n - 1 conditions).
5. The second derivatives in the extreme nodes are zero (2 conditions)
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