A method and apparatus for precisely controlling and determining the location of the interaction point of a surgical laser beam, and for controlling the shape of the cornea during ophthalmic surgery. A transparent applanator plate is placed in contact with the cornea of a patient's eye. The applanator plate creates a fixed positional frame of reference from which a laser beam control system can determine the desired point or points at which to focus the surgical laser beam. A surgical tip at the distal end of an articulated arm having flexible joints is placed in contact with the applanator plate and follows any motion of the patient's eye and directs the laser beam to the surgical tip. The applanator plate also provides a means to control the contour of the index of refraction boundary between the corneal epithelium of the patient's eye and the air.