<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1602" altimg="si351.svg"><mml:mi>α</mml:mi></mml:math>-B-splines non-stationary subdivision schemes for grids of arbitrary topology design

Barrera, D.; Lamnii, A.; Nour, M. Y.; Zidna, Ahmed

doi:10.1016/j.cag.2022.09.004

Cited by 4 publications

(2 citation statements)

References 43 publications

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“…From Theorem 5, it can be seen that when v 0 = 0, the corresponding limit position in (9) actually reduces to the one in (8).…”

Section: Limit Positions Of Initial Pointsmentioning

confidence: 95%

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A Symmetric Non-Stationary Loop Subdivision with Applications in Initial Point Interpolation

Zhang,

Zheng

2024

Symmetry

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Loop subdivision is a significant surface scheme with wide applications in fields like computer graphics and wavelet. As a type of stationary scheme, Loop subdivision cannot adjust the limit surface directly. In this paper, we present a new way to solve this problem by proposing a symmetric non-stationary Loop subdivision based on a suitable iteration. This new scheme can be used to adjust the limit surfaces freely and thus can generate surfaces with different shapes. For this new scheme, we show that it is C2 convergent in the regular part of mesh and is at least tangent plane continuous at the limit positions of the extraordinary points. Additionally, we present a non-uniform generalization of this new symmetric non-stationary subdivision so as to locally control the shape of the limit surfaces. More interestingly, we present the limit positions of the initial points, both for the symmetric non-stationary Loop subdivision and its non-uniform generalization. Such limit positions can be used to interpolate the initial points with different valences, generalizing the existing result. Several numerical examples are given to illustrate the performance of the new schemes.

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“…From Theorem 5, it can be seen that when v 0 = 0, the corresponding limit position in (9) actually reduces to the one in (8).…”

Section: Limit Positions Of Initial Pointsmentioning

confidence: 95%

“…Badoual et al [7] constructed a non-stationary generalized Loop subdivision for chemical imaging. For other non-stationary surface subdivisions, see also [8][9][10][11] and references therein.…”

Section: Introductionmentioning

confidence: 99%