A Family of Binary Approximating Subdivision Schemes basedon Binomial Distribution

Abstract

A simplest way is introduced to generate a generalized algorithm of univariate and bivariate subdivisionschemes. This generalized algorithm is based on the symbol of uniform B-splines subdivision schemesand probability generating function of Binomial distribution. We present a family of binary approximatingsubdivision schemes which has maximum continuity and less support size. Our proposed family membersP4, P5, P6, and P7, have C7, C9, C11 and C13 continuities respectively. In fact, we use Binomial probabilitydistribution to increase the continuity of uniform B-splines subdivision schemes up to more than double.We present the complete analysis of one family member of proposed schemes and give a visual performanceto check smoothness graphically. In our analysis, we present continuity, Holder regularity, degree ofgeneration, degree of reproduction and limit stencils analysis of proposed family of subdivision schemes.We also present a survey of high continuity subdivision schemes. Comparison shows that our proposedfamily of subdivision schemes gives high continuity of subdivision schemes comparative to existingsubdivision schemes. We have found that as complexity increases the continuity also increases. In thelast, we give the general formula for tensor product surface subdivision schemes and also present thevisual performance of proposed tensor product surface subdivision schemes.