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Degree reduction of SG‐Bézier surfaces based on grey wolf optimizer
Author(s) -
Qin Xinqiang,
Qiao Yu,
Hu Gang
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6382
Subject(s) - degree (music) , bézier curve , reduction (mathematics) , mathematics , interpolation (computer graphics) , mathematical optimization , good reduction , mathematical analysis , geometry , computer science , image (mathematics) , artificial intelligence , medicine , physics , surgery , acoustics
Aiming at the problem of approximate degree reduction of SG‐Bézier surfaces, a method is proposed to achieve the degree reduction from ( n × n) to ( m × m) ( m < n ). Starting from the idea of grey wolf optimizer (GWO) algorithm and combining the geometric properties of SG‐Bézier surfaces, this method transforms the degree reduction problem of SG‐Bézier surfaces into an optimization problem. By choosing the fitness function, the degree reduction approximation of shape‐adjustable SG‐Bézier surfaces under unconstrained and angular interpolation constraints is realized. At the same time, some concrete examples of degree reduction and its errors are given. The results show that this method not only achieves good degree reduction effect but also is easy to implement and has high precision.