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Volume graphics is a key technology in fields such as fluid dynamics and medical science. The visualization of volume data requires the creation of a continuous scalar field to exactly or approximately interpolate scalar values assigned to the discrete voxels. In the present paper, we propose a method that we refer to as the volumic version of the multi-level partition of unity (volumic MPU). The method approximately interpolates the scalar values with good precision to generate a scalar field that is continuous up to second-order differentiation. The volumic MPU, being independent of grid structures of input volume data, is applicable to both irregular-grid data and regular grid data. The volumic MPU can also be used as an effective data-compression technique. The speed to evaluate the created scalar field is almost as high as that of trilinear interpolation.