A model of a simple geometric processor which geometric computation packages for solid modeling and computer graphics can be based on is introduced. An exact integer representation and an adaptive determinant sign detection method is built into a geometric library to give a solution to the problem of accuracy and efficiency in three dimensional geometric programs. The computational core of this geometric library is designed so that it can be readily replaced with a simple hardware processor. The geometric computations are based on signed Pluecker coordinates and the 4 x 4 determinant method. A method for classifying degenerate configurations of points using parallel sign detections of the Pluecker coordinates of points, lines and planes using the processor is developed. A geometric computation library designed in this way has many advantages when compared to conventional geometric approaches.