A new technique based on digital shearography for determining the transient curvature and twist of a continuously deforming object from a series of speckle patterns is presented. The intensity variation of each pixel is analyzed along the time axis by using a complex Morlet wavelet transform. The absolute sign of the phase variation is determined by introduction of a temporal carrier when the speckle patterns are captured by a high-speed camera. A high-quality spatial distribution of the deflection derivative is extracted at any instant without the need for temporal or spatial phase unwrapping. The continuous Haar wavelet transform is subsequently processed as a differentiation operator to reconstruct the instantaneous curvature and twist of a continuously deforming object.