For every segment, there are four values that should be determined(the coefficients of a cubic polynomial or identically four control points(p0, p1, p2, p3), where the dimension of control points or coefficients depend on the situation). Therefore, there are 4n degrees of freedom for n segments.
In Adobe Illustrator, four control points are manually given for each segment, so there are also 4n constraints. Therefore, the curve can be uniquely determined.
Without manually assigning values, I believe there are 2n - 2 equations for the whole curve since there are n - 1 linking nodes and we have two constraints for each node ("equal positions" and "equal tangents").
For every segment, there are four values that should be determined(the coefficients of a cubic polynomial or identically four control points(p0, p1, p2, p3), where the dimension of control points or coefficients depend on the situation). Therefore, there are 4n degrees of freedom for n segments.
In Adobe Illustrator, four control points are manually given for each segment, so there are also 4n constraints. Therefore, the curve can be uniquely determined.
Without manually assigning values, I believe there are 2n - 2 equations for the whole curve since there are n - 1 linking nodes and we have two constraints for each node ("equal positions" and "equal tangents").