Research On The Artificial Intelligence Algorithm For Degree Reduction Of NURBS Curves

Degree reduction of curves has been one of the research hotspots in CAGD. Currently the study is mainly about the degree reduction approximation of Bézier curves, and it formed a set of mature theories and methods. NURBS curves can not only express general B-spline curves and Bézier curves, but also accurately describe the quadratic curves. And NURBS is the only mathematical method of defining the geometry of industrial products. So the degree reduction of NURBS curves has important theoretical value and immediate demand of application. This thesis studies how to use artificial intelligence algorithms to solve the problem of degree reduction combining artificial intelligence algorithms with the degree reduction of curves.Firstly, some common artificial intelligence algorithms are introduced, and the degree reduction of NURBS curves is described in several ways: (1) the method of using curves in explicit matrix presentation and the theory of the best polynomial consensus approach. (2) the method of degree reduction of NURBS curves based on genetic algorithm.Secondly, based on Particle Swarm Optimization algorithm, this thesis gives a new method of the degree reduction of NURBS curves.Finally, an example is given to verify the feasibility of the algorithm.