This is actually a problem of interpolation function in mathematics. You can imagine a straight line, and two points can define a straight line. The definition of a straight line can be written as: y=kx+b, which is linear, that is to say, the first-order curve (straight line) is defined by two points. Similarly, the second-order parabola y = ax 2+bx+c is defined by three points. Spline curve in UG is represented or approximated by polynomial interpolation, so we can see the expression y = anxn+ an-1x (n-1)+...+a1x+A0 = 0, and there are n+ 1 unknowns, so we need to solve this one.

If you want to know more about this knowledge, you can look at the definition of spline curve in the numerical analysis textbook.