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I was reading a article about about Hermite interpolation on this link. In cardinal spline curve section they give a formula to calculate tangents at end point given as
$$T_i = a ( P_{i+1} - P_{i-1} ) . $$

Doubt:if i have two point $P_1$ AND $P_2$ then to find $T_1$
$T_1=a(P_2-P_0)$..i need to calculate this but what should be my $P_0$ point?
similarly to find $T_2$ i will need to KNOW $P_3$

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    For the endpoints in splines, it is customary to either estimate slopes from the data points given (through polynomial extrapolation for instance) or to supply them. From that, the slopes at the inner points are computed. I would suggest getting a better reference for Hermite interpolation/splines than that web page; any decent CG book should give the proper formulae.2011-05-09

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