Methods and apparatus are provided for developing a complete set of all admissible Type I and Type II fixture designs for a workpiece. The fixture processor generates the set of all admissible designs based on geometric access constraints and expected applied forces on the workpiece. For instance, the fixture processor may generate a set of admissible fixture designs for first, second and third locators placed in an array of holes on a fixture plate and a translating clamp attached to the fixture plate for contacting the workpiece. In another instance, a fixture vise is used in which first, second, third and fourth locators are used and first and second fixture jaws are tightened to secure the workpiece. The fixture process also ranks the set of admissible fixture designs according to a predetermined quality metric so that the optimal fixture design for the desired purpose may be identified from the set of all admissible fixture designs.