Splatting-based rendering techniques are currently the best choice for efficient high-quality rendering of point-based geometries. However, such techniques are not suitable for large magnification, especially when the object is undersampled. This paper improves the rendering quality of pure splatting techniques using a fast dynamic up-sampling algorithm for point-based geometry. Our algorithm is inspired by interpolatory subdivision surfaces where the geometry is refined iteratively. At each step the refined geometry is that from the previous step enriched by a new set of points. The point insertion procedure uses three operators: a local neighborhood selection operator, a refinement operator (adding new points) and a smoothing operator. Even though our insertion procedure makes the analysis of the limit surface complicated and it does not guarantee its G1 continuity, it remains very efficient for high-quality real-time point rendering. Indeed, while providing an increased rendering q...