A computer-implemented method, apparatus, and system for discretizing lane markings and for generating a lane reference line is disclosed. A polynomial defined over an (x,y) coordinate system is received, the polynomial being representative of at least a portion of a lane boundary line. A length of the polynomial is determined. The polynomial is discretized, comprising determining a plurality of discretization points on the polynomial to represent the polynomial, wherein a first discretization point is a first end of the polynomial, wherein subsequent discretization points are determined successively until the polynomial is completely discretized, and wherein each discretization point other than the first discretization point is determined based at least in part on a slope of the polynomial at a previous discretization point. Thereafter, a lane reference line comprising a plurality of points is generated based on the discretized polynomial.