Yes. A spline is a mechanical device which is used to draw a curve which passes thru several known points.What is the meaning of "cubic" term in a cubic spline?
Is it mean a spline with a degree of 3?
In theory, you could produce higher order splines, but the math becomes more complex with increasing order. Higher order splines tend to oscillate as well, and sometimes fail to produce a smooth curve which passes thru the data points.Does this mean a quadratic spline is a spline with degree 2?
Is there availabe a quartic, quintic, and so on, of a spline?
What is the difference between quadratic and cubic spline?
What kind of numerical error it is?Yes, the differences between all those curves are really a matter of polynomial degree. Quadratic splines can interpolate the same data points that cubic splines can, but it doesn't have quite the same shape. You can imagine a quadratic spline being a series of parabolas that you're trying to string together to run through the data points and maintain a certain continuity. Cubic splines are like that in much the same way, and quartic, quintic, etc.
Splines are interesting because they form the math basis of computer-aided design. Because of numerical errors, generally lower-degree splines are nicer to work with, but you can't really go too low without getting some interesting effects. For example, cubic splines are usually used because you can achieve what's called C2 continuity. The math is kinda cool, but this has effects in the real world. For example, car bodies are usually C2 because if they weren't they wouldn't look smooth in a showroom because it wouldn't have smooth reflection lines.