Improved Four Points Subdivision Scheme and its Applications
改进四点细分法及其应用

This paper extends the classical 4 point interpolating subdivision scheme, and brings forward a new 4-point subdivision scheme with four parameters for curve design, which can be controlled by choosing these four parameters appropriately. At the same time, we expand it to surface design. The sufficient conditions of the uniform convergence property and continuity properties of the subdivision scheme are proved. It can generate expectable terrain shapes using 4 point subdivision scheme with four parameters in terrain simulation. Through selecting four parameters flexibly, we can adjust generating terrain shape suitably and produce ample physiognomy shape. We can describe physiognomy de tail because subdivision scheme has multi-scale character. The method can generate terrain simulation preferably and of fer an effective scheme for terrain simulation.