Providing interactive, precise and intuitive control of shapes is now a fundamental issue in the development of new three dimensional modelling techniques. Volume models are rapidly becoming a practical solution , due to the increase in computing power and storage capacity of recent workstations combined with the latest developments of graphics hardware. Interactive modelling for general volume objects is a difficult task due to the expensive computation necessary to visualize the surface. For this reason, we believe that providing an adaptive multiresolution discrete data structure is essential. It allows us to accurately store the values of the potential after each operation, which consequently decreases the computation time when the potential function is evaluated. We also focus on the C1 continuous reconstruction of the discrete data because it is the minimal continuity necessary to define smooth objects.