1. A computer executed method for regulating the number of active faces rendered for an adaptively refined mesh used to approximate a graphical object, the method comprising the following steps: determining a desired number of active faces-F to render from the adaptively refined mesh at a time-t; iteratively repeating the steps of: modifying a value of a screen space tolerance-.tau..sub.t to maintain the desired number of active faces-F rendered at a substantially constant level; and adaptively refining and coarsening the mesh constrained at least partially based on the regulated screen space tolerance-.tau..sub.t.