This paper describes a novel phase error compensation method for reducing the measurement error caused by non-sinusoidal waveforms in the phase-shifting method. For 3D shape measurement systems using commercial video projectors, the non-sinusoidal nature of the projected fringe patterns as a result of the nonlinear gamma curve of the projectors causes significant phase measurement error and therefore shape measurement error. The proposed phase error compensation method is based on our finding that the phase error due to the non-sinusoidal waveform of the fringe patterns depends only on the nonlinearity of the projector's gamma curve. Therefore, if the projector's gamma curve is calibrated and the phase error due to the nonlinearity of the gamma curve is calculated, a look-up-table (LUT) that stores the phase error can be constructed for error compensation. Our experimental results demonstrate that by using the proposed method, the measurement error can be reduced by 10 times. In addition to phase error compensation, a similar method is also proposed to correct the nonsinusoidality of the fringe patterns for the purpose of generating a more accurate flat image of the object for texture mapping. While not relevant to applications in metrology, texture mapping is important for applications in computer vision and computer graphics.