We wish to model similar kinds of curves using a set of mathematical equations. Assume we have a sequence of n + 1 knots, (x_0, y_0) through (x_n, y_n). There will be a cubic polynomial q_i(x)=y between each successive pair of knots (x_{i-1}, y_{i-1}) and (x_i, y_i) connecting to both of them, where i = 1, 2, \dots, n. So there will be n polynomials, with the first polynomial starting at (x_0, y_0), and the last polynomial ending at (x_n, y_n).
