Intuitively, think of a curve as something you can draw with a pen. The curve is the set of points that the pen traces over an interval of time. While we usually think of a pen writing on paper (e.g., a curve that is in a 2D space), the pen could move in 3D to generate a space curve, or you could imagine the pen moving in some other kind of space.
Mathematically, definitions of curve can be seen in at least two ways:
- the continuous image of some interval in an n-dimensional space;
- a continuous map from a one-dimensional space to an n-dimensional space.
Both of these definitions start with the idea of an interval range (the time over which the pen traces the curve). However, there is a significant ...