The Odd-Point Ternary Approximating Schemes

• 作者: Abdul Ghaffar Faheem Khan Ghulam Mustafa
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Approximating SUBDIVISION Scheme Derivative CONTINUITY SMOOTHNESS Convergence Shape Parameters and Laurent POLYNOMIAL
• 年，卷（期）: 2011,（2）
• 页码范围: 111-118
• 页数: 8页
• 分类号: O1

摘要

We present a general formula to generate the family of odd-point ternary approximating subdivision schemes with a shape parameter for describing curves. The influence of parameter to the limit curves and the sufficient conditions of the continuities from C0 to C5 of 3- and 5-point schemes are discussed. Our family of 3-point and 5-point ternary schemes has higher order of derivative continuity than the family of 3-point and 5-point schemes presented by [Jian-ao Lian, On a-ary subdivision for curve design: II. 3-point and 5-point interpolatory schemes, Applications and Applied Mathematics: An International Journal, 3(2), 2008, 176-187]. Moreover, a 3-point ternary cubic B-spline is special case of our family of 3-point ternary scheme. The visual quality of schemes with examples is also demonstrated.