Abstract: A computer control system in a paving machine determines a location, long slope (pitch), cross-slope (roll), and elevation (with respect to reference surface) of the machine with reference to a plurality of sensors. The long slope, cross slope and elevation are compared to values from a design surface (horizontal alignment, vertical profile, and cross sections) using the location of the machine to query the design data. Deviations from measured orientation and elevation to the design (desired values) are determined for each elevation cylinder of the paving machine based on the sensor data using constrained geometric control algorithms that predict future deviations. Corrections are applied to bring the actual location, long slope, cross-slope and elevation to within acceptable tolerances of the desired values. Sensors are associated with specific legs, with some sensors associated with more than one leg, such that sensor values may be averaged to reduce error.