Generalized Subdivision Surface Scheme Based on 2D Lagrange Interpolating Polynomial and its Error Estimation - Omar, Muhammad; Khan, Faheem (Communications in Mathematics and Applications, 2018)
This work gives the idea for constructing subdivision rules for surface based on 2D Lagrange interpolating polynomial [13]. In this method, subdivision rules for quad mesh has been obtained directly from the Lagrange interpolating polynomial. We also see that the simple interpolatory subdivision scheme for quadrilateral nets with arbitrary topology is presented by L. Kobbelt [5], can be directly calculated from the proposed generalized formula for subdivision surface refinement rules. Furthermore, some characteristics, applications and error bounds of the proposed work are also discussed.