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 f...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.展开更多
基金the followingNational Natural Science Foundation of China under Grant Nos.61602277 , 61772319Natural Science Foundation of Shandong Province under Grant Nos.ZR2016FQ12 , ZR2018BF009+2 种基金Key Research and Development Program of Yantai City under Grant No.2017ZH065CERNET Innovation Project under Grant No.NGII20161204Science and Technology Innovation Program for Distributed Young Talents of Shandong Province Higher Education Institutions under Grant No.2019KJN042。
文摘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.
