Primary liver cancer and oligometastatic liver disease are one of the major causes of mortality worldwide and its treatment ranges from surgery to more minimally invasive ablative procedures. With the increasing availability of minimally invasive hepatic approaches, a real-time method of determining the 3D structure of the liver and its location during the respiratory cycle is clinically important. However, during treatment, it is difficult to acquire images spanning the entire 3D volume rapidly. In this paper, a dynamic 3D shape instantiation scheme is developed for providing subject-specific optimal scan planning. Using only limited planar information, it is possible to instantiate the entire 3D geometry of the organ of interest. The efficacy of the proposed method is demonstrated with both detailed numerical simulation and a liver phantom with known ground-truth data. Preliminary clinical application of the technique is evaluated on a patient group with metastatic liver tumours.