摘要
A new method is presented to determine parameter values(knot)for data points for curve and surface generation.With four adjacent data points,a quadratic polynomial curve can be determined uniquely if the four points form a convex polygon.When the four data points do not form a convex polygon,a cubic polynomial curve with one degree of freedom is used to interpolate the four points,so that the interpolant has better shape,approximating the polygon formed by the four data points.The degree of freedom is determined by minimizing the cubic coefficient of the cubic polynomial curve.The advantages of the new method are,firstly,the knots computed have quadratic polynomial precision,i.e.,if the data points are sampled from a quadratic polynomial curve,and the knots are used to construct a quadratic polynomial,it reproduces the original quadratic curve.Secondly,the new method is affine invariant,which is significant,as most parameterization methods do not have this property.Thirdly,it computes knots using a local method.Experiments show that curves constructed using knots computed by the new method have better interpolation precision than for existing methods.
基金
the followingNational Natural Science Foundation of China under Grant Nos.61602277 , 61772319
Natural Science Foundation of Shandong Province under Grant Nos.ZR2016FQ12 , ZR2018BF009
Key Research and Development Program of Yantai City under Grant No.2017ZH065
CERNET Innovation Project under Grant No.NGII20161204
Science and Technology Innovation Program for Distributed Young Talents of Shandong Province Higher Education Institutions under Grant No.2019KJN042。