The Bj{\o}ntegaard Delta rate (BD-rate) objectively assesses the coding efficiency of video codecs using the rate-distortion (R-D) performance but overlooks encoding energy, which is crucial in practical applications, especially for those on handheld devices. Although R-D analysis can be extended to incorporate encoding energy as energy-distortion (E-D), it fails to integrate all three parameters seamlessly. This work proposes a novel approach to address this limitation by introducing a 3D representation of rate, encoding energy, and distortion through surface fitting. In addition, we evaluate various surface fitting techniques based on their accuracy and investigate the proposed 3D representation and its projections. The overlapping areas in projections help in encoder selection and recommend avoiding the slow presets of the older encoders (x264, x265), as the recent encoders (x265, VVenC) offer higher quality for the same bitrate-energy performance and provide a lower rate for the same energy-distortion performance.