Containing The Parameters Of The Six Subdivision Method

Subdivision is an important modeling method in CAGD. Subdivisio-n schemes abandon the pattern "discrete-continuous-discrete" geometrical construction. It is a kind of method to generate curve, surface or other geometrical graphics straightly in computer according original dates. It is a kind of fast iterative arithmetic from sequence to sequence virtually. Subdivision schemes can greatly improve the speed of calculation, generation and display of curve and surface in computer. So lots of people research subdivision and it has been applied widely in geometrical construction.In this paper, a class of six-point subdivision schemes with two parametersμ,ωis presented. Using the presented scheme one can not only model smooth interpolating subdivision curves but also can model approximating subdivision curves. By adjusting these two parametersμ,ωappropriately, the subdivision curve can satisfy the uniform convergence property, C~1 or C~2 continuity property. Based on the six-point subdivision schemes with two parameters, a class of six-point subdivision schemes with three parametersλ,μ,ωis presented. Four-point subdivision schemes with two parameters and six-point subdivision schemes with two parameters are included in the six-point subdivision schemes with three parameters as special cases. Whenλ∈(-1/36,1/44), the range ofμ,ωcan be gained, where the subdivision curve can satisfy the uniform convergence property or C~k (0≤k≤4) continuity properties.