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derivation of b spline equations

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I found this tutorial on b-spline curves At the end of tutorial, it shows how to solve for some parametric knots that will create a b spline curve to go through some geometric knots via a system of linear equations. I don't quite understand how they derived the matrix they used, specifically the first and last row which is designed to satisfy the user set gradient values for the curve at the start and the end. Why N / 2 for the entries and is the gradient suppose to be normalised? thanks for any help.

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