This paper presents a shape-based approach to compute, in an optimal sense, the control of a single degree-of-freedom point absorber wave energy converter. In this study, it is assumed that a prediction for the wave is available. The control is computed so as to maximize the energy extraction over a future time horizon. In the shape-base approach, one of the system states is represented by a series expansion. The optimization variables are selected to be the coefficients in the series expansion instead of the history of the control variable. A gradient-based optimizer is used to optimize the series coefficients. The available wave prediction is used to compute an initial guess for the unknown series coefficients. This concept is tested on two different dynamic models: a simplified reduced-order model and a dynamic model with radiation dynamic states necessary to compute the radiation force. Several test cases are presented that cover a range of different sea states. The results show that the shape-based approach finds efficient solutions in terms of the extracted energy. The results also show that the obtained solutions are suitable for real-time implementation in terms of the smoothness of the obtained control and the speed of computations. Comparisons between the results of the shape-based approach and other techniques are presented and discussed.