There are many ways to replicate a curve. Some methods are more accurate than others and some are faster than others. In general, the most common method is to use a spline or NURBS curve.
A spline is a mathematical function that interpolates between points. There are many different types of splines, but the most common type is the cubic spline. A cubic spline has four control points: two endpoints and two middle points. The middle points control the shape of the curve and the endpoints control the slope of the curve at each endpoint.
NURBS (Non-Uniform Rational B-Splines) curves are similar to splines, but they have additional control over the shape of the curve. NURBS curves have weights associated with each control point that control how much influence that point has on the shape of the curve. NURBS curves also have knots which define how the curve wraps around each control point.
Both Splines and NURBS can be used to create very accurate representations of curves, however NURBS usually require more computational resources than Splines.