Degree reduction of SG‐Bézier surfaces based on grey wolf optimizer

Abstract

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.