Control points
One possible way of defining parametric curves:
Define points near which the curve should pass:
p1 = (x1,y1), p2 = (x2,y2)...
For each point pi choose a parameter value ti.
Simplest choice: 1,2,3,... (uniform parameterization).
For each point specify a blending function Bi(t),
which defines how much it contributes to the value