A method for the automatic, discrete rezoning of two-dimensional Lagrangian codes for inertial confinement fusion (ICF) implosions has been developed. The method, which applies to matrix-ordered, quadrilateral zone meshes, allows the preservation of the interface tracking property of the Lagrangian approach. Total mass and momentum are conserved exactly, total energy is approximately conserved, and numerical diffusion is kept to tolerable levels. The mesh generator, the mapping scheme, and the actual implementation in a two-temperature laser fusion code are described. The performance of the method is illustrated by several sample applications.