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In this paper, we present an information entropy-based viewpoint-planning approach for reconstruction of freeform surfaces of three-dimensional objects. To achieve the reconstruction, the object is first sliced into a series of cross section curves, with each curve to be reconstructed by a closed B-spline curve. In the framework of Bayesian statistics, we propose an improved Bayesian information criterion (BIC) for determining the B-spline model complexity. Then, we analyze the uncertainty of the model using entropy as the measurement. Based on this analysis, we predict the information gain for each cross section curve for the next measurement. After predicting the information gain of each curve, we obtain the information change for all the B-spline models. This information gain is then mapped into the view space. The viewpoint that contains maximal information gain about the object is selected as the next best view. Experimental results show successful implementation of our view planning method for digitization and reconstruction of freeform objects.