Abstract
In this paper, two new families of non-stationary subdivision schemes are introduced. The schemes are constructed from uniform generalized B-splines with multiple knots of orders 3 and 4, respectively. Then, we construct a third-order reverse subdivision framework. For that, we derive a generalized multi-resolution mask based on their third-order subdivision filters. For the reverse of the fourth-order scheme, two methods are used; the first one is based on least-squares formulation and the second one is based on solving a linear optimization problem. Numerical examples are given to show the performance of the new schemes in reproducing different shapes of initial control polygons.
Highlights
The usage of subdivision schemes played a crucial role in developing computer graphics and creating smooth curves and surfaces
Recent proposals of efficient non-stationary subdivision schemes have been presented by Ghaffar et al [21], Fakhar et al [22,23], Siddiqi et al [24,25], where the authors have built elegant methods capable of reproducing complex curves or surfaces
We introduce generalized B-splines of order 3 and 4 with multiple knots
Summary
The usage of subdivision schemes played a crucial role in developing computer graphics and creating smooth curves and surfaces. From these B-splines, we have constructed two non-stationary subdivision schemes called generalized subdivision schemes of order 3 and 4 These subdivision schemes can exactly reproduce trigonometric and hyperbolic limit curves. To calculate the reverse generalized scheme of order 4 we use two methods: the first is similar to the one presented by Olsen in [32] which is based on multiresolution. It starts by finding the approximate reverse scheme and finding the error between the control polygonal and the one constructed by using this approximate reverse scheme.
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