Abstract: A system, method, and computer program for a finding an intersection for geometrically coincident curves, comprising selecting a curve pair where at least one curve in said curve pair is a parametric curve; determining a curve parameter for each curve in said curve pair; splitting each of said curves into a plurality of candidate segments; recursively subdividing each of said candidate segments into a pair of finalized segments that are sufficiently straight; intersecting an approximation for each of said finalized segments; obtaining a plurality of next parameter values from said intersecting step; and testing for a terminating condition and appropriate means and computer-readable instructions.