1. A computer implemented method for determining at least some coordinates of at least some points on an implicit curve resulting from an intersection of a plurality of graphical objects, the method comprising: receiving a sparse parameterized representation of at least a portion of the implicit curve, the representation comprising: sparse convergence region descriptor data for describing one or more convergence regions of the implicit curve and sparse starting point descriptor data for deriving starting points associated with the one or more convergence regions; at runtime, based at least on the sparse starting point descriptor data of the starting points associated with the one or more convergence regions, deriving the coordinates of at least some of the starting points associated with the one or more convergence regions; and applying Newton iteration starting from the derived coordinates of the at least some of the starting points to determine at least some coordinates of one or more points on the implicit curve.