The invention provides for a system and method for minimizing space requirements and increasing speed in a geometry accelerator for a computer graphics system. In architecture, the system is implemented as follows. The geometry accelerator includes a plurality of processing elements (e.g., an arithmetic logic unit, a multiplier, a divider, a compare mechanism, a clamp mechanism, etc.) and a plurality of control units (e.g., a transform mechanism, a decomposition mechanism, a clip mechanism, a bow-tie mechanism, a light mechanism, a classify mechanism, a plane equation mechanism, a fog mechanism, etc.) that utilize the processing elements for performing data manipulations upon image data. In accordance with the invention, the control units are implemented in a read-only memory (ROM) via microcode. A next address field is associated with each of the microcode instructions and defines a location in the ROM of a next instruction to be executed. A plurality of control unit logic elements correspond respectively with the control units and control instruction branching within their respective control unit by defining the next address field. A branch central intelligence mechanism controls branching between the control units by defining the next address field.