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Calculation of tangents for cardinal splines curves

I am reading an article on cubic interpolation of Hermite. In the section of the cardinal spline curve, they give a formula for calculating the tangents at the end points defined by the formula:

Ti = a * ( Pi+1 - Pi-1 )

However, if I have two points P1and P2then findT1

T1 = a*(P2-P0).

I need to calculate this, but what should be my point P0? Similarly find T2I need to know P3. Can this explain this?

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You are right, this formula makes sense only for the internal points of your spline, which have neighbors on both sides. For endpoints, you should get tangent from other constraints. General solutions:

, , , .

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