Modified form of binary and ternary 3-point subdivision schemes
A modification of both a binary 3-point approximating subdivision scheme and a ternary 3-point approximating subdivision scheme is presented. The modification lies in an introduction of a tension parameter which generates a family of \(C^1\) limiting curves in case of the binary 3-point scheme and \(C^1\) and \(C^2\) limiting curves in case of the ternary 3-point scheme. After the introduction, the analysis of the modified binary and ternary 3-point approximating subdivision scheme is presented. Then, many examples of subdivision results for both open and closed curves are given to show the usefulness of the suggested modification and the role of the introduced tension parameter. The obtained results can be used in many areas of computer aided geometric design when generating smooth shapes of curves or surfaces through subdivision techniques.
scientific article; zbMATH DE number 5707077