In mathematics a Curve is "a line that does not need to be straight". With that definition a large number of different curves exist each of which can be described by a mathematical formula.
Different mathematical curves
In computer graphics we're most interested in curves that can be described by mathematical formulas that are called polynomial functions. In order to be able to draw arbitrarily curved lines often multiple such curve-segments are combined to a Spline. The term "Spline" originates from an old draftsmen tool called a Flat Spline.
Curves that are piecewise defined by polynomial functions are called Splines
There are many different types of splines (hermite, bézier, catmull-rom, b-spline,..). but they all share the following key properties:
- they are continuous at the Knots
- Control Points influence their shape
Splines with their segments, control points and knots