Fourier volume rendering (FVR) is a volume rendering method based on the Fourier slice theorem. With an n n n volume data, the FVR algorithm requires O(n2 log n) time to generate a result. Because it requires time less than O(n3) does, FVR is preferred for designing a real-time rendering algorithm with a preprocessing step. We improve upon our previous work. We demonstrate that a B-spline is significantly more useful when designing a transfer function. To design an appropriate transfer function with a spline function, additional control points are required. However, the memory space required for the proposed method increases in linear proportion to the number of control points. We show that the set of control points can be clustered into groups, ensuring the memory required is linearly proportional to the number of groups. The proposed technique supports real-time rendering after adjusting the transfer function for FVR.