Methods, and apparatus are disclosed for performing corneal ablation procedures of the eye (12) in a manner which does not interfere with the natural shape of the cornea or its orientation relative to the remainder of the eye, but which changes its surface curvature appropriately to achieve the required correction of vision. Three preferred embodiments are described, which model the cornea to different degrees of accuracy. Once the model of the cornea is obtained (610, 620, 630), surface curvature is modified (650) to achieve the degree of correction in refraction that is necessary, as determined by an eye test of the patient. The modified model of the cornea is then utilized to control the removal of material from the surface of the cornea in a corneal ablation operation.