Study On Multiresolution Approximation Of Curves Using Normal Trichotomized Subdivision Scheme

In this paper we give a new normal triadic subdivision scheme if the multiresolution analysis of a curve is normal, and study normal triadic subdivision scheme properties, such as regularity, convergence, and stability. In particular we show that these wavelets coefficient critically depend on the normal triadic subdivision scheme.In the Chapter Ⅱ, we give a new definition of 3-band normal subdivision scheme, And give the prove of the subdivision scheme. In the § 2.2 we give some lemmas' prove which be used in the main result's prove. In the § 2.3 we give the main prove:let{x_j},α,a,v,S₃ be given as in above sections, Suppose those j,k,such thatt_j,k= k3^-j ∈I , where I is a (possibly infinite) interval, . let φ be a piecewise linear function, φ_j (t) is the point (x_j.k) at t_{j,k o} If |xo|_∞ < ∞ , then there exists a functionφ∈C^1- (I) , such that φ_j —> φ uniformly exponentially. And φ satisfies the inequality:In the § 2.4 we give the wavelets coefficient theorem, and prove the convergence of wavelets coefficient equal to the convergence of basic subdivision scheme.In the Chapter Ⅲ, we give the definition of the derived subdivision schemes with studying the 3-band mask. 3-band normal derived subdivision scheme can let the curve get high lubricity. In the § 3.2 we give the prove of convergence of the derived subdivision schemes. And in the § 3.3 we give some examples of the derived subdivision schemes...