Subdivision of point-normal pairs with application to smoothing feasible robot path

Lipovetsky, Evgeny

doi:10.1007/s00371-021-02110-9

Cited by 2 publications

(1 citation statement)

References 15 publications

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“…The starting point of this theory was Rahm's article (see [1]); a few years later several schemes were developed to extend the field of application to more complicated curves and surfaces. This theory has found huge success in many fields of application such as curve and surface reconstruction (see [2][3][4][5]), computer animation and graphics (see [6][7][8]), robotics (see [9]), medical science processing (see [10][11][12]), wavelet and frame construction (see [13][14][15][16]), etc. Subdivision schemes have a very strong link with splines, so they are widely used to describe various properties of splines such as shape reproduction and approximation order calculation [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

A Reverse Non-Stationary Generalized B-Splines Subdivision Scheme

Lamnii

Nour

Zidna³

2021

Mathematics

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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.

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