Abstract
In this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to three displacement vectors containing two shape parameters. We first study the characteristics of the new subdivision scheme analytically and then present numerical experiments to justify these analytical characteristics geometrically. We also extend the new derived scheme into its bivariate/tensor product version. This bivariate scheme is applicable on quadrilateral meshes to produce smooth limiting surfaces up to C 3 continuity.
Highlights
CAGD is considered as an emerging research field of computational mathematics, which has been fast growing in the last two decades due to a vast range of applications in a number of scientific fields and in real life
In CAGD, subdivision schemes have become one of the most important, efficient, and emerging modeling tools for designing and modeling of objects. It defines a smooth curve after applying a sequence of successive refinements. e subdivision schemes are main approaches used to create a curve from an initial control polygon or a surface from an initial control mesh by subdividing them according to the refining rules. ese refining rules take the initial control polygon or mesh to produce a sequence of finer polygons or meshes converging to a smooth limiting curve or surface
Interpolatory subdivision schemes produce the limit curves that pass through all the initial points, whereas the approximating subdivision schemes generate the limit curves that do not pass through the initial control points. e combined subdivision schemes produce the limit curves that may or may not pass through the initial control points
Summary
CAGD is considered as an emerging research field of computational mathematics, which has been fast growing in the last two decades due to a vast range of applications in a number of scientific fields and in real life It has been extended into new directions owing to several generalizations and applications. In CAGD, subdivision schemes have become one of the most important, efficient, and emerging modeling tools for designing and modeling of objects It defines a smooth curve after applying a sequence of successive refinements. E combined subdivision schemes produce the limit curves that may or may not pass through the initial control points. Their construction has become a new and important trend in CAGD.
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