A sound zone control method is proposed, based on the frequency domain variable span trade-off filter (VAST). Existing VAST methods optimizes the sound field at a set of discrete points, while the proposed method uses kernel interpolation to instead optimize the sound field over a continuous region. When the loudspeaker positions are known, the performance can be improved further by applying a directional weighting to the interpolation procedure. The proposed method is evaluated by simulating broadband sound in a reverberant environment, focusing on the case when microphone placement is restricted. The proposed method with directional weighting outperforms the pointwise VAST over the full bandwidth of the signal, and the proposed method without directional weighting outperforms the pointwise VAST at low frequencies.