This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control poin...This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control points without solving a system of equations or inserting additional control points. They have the local properties like the cubic B spline. Besides, the quintic curve would be able globally to tend the control polygon.展开更多
By using the geometric constraints on the control polygon of a Pythagorean hodo- graph （PH） quartic curve, we propose a sufficient condition for this curve to have monotone curvature and provide the detailed proof. ...By using the geometric constraints on the control polygon of a Pythagorean hodo- graph （PH） quartic curve, we propose a sufficient condition for this curve to have monotone curvature and provide the detailed proof. Based on the results, we discuss the construction of spiral PH quartic curves between two given points and formulate the transition curve of a G2 contact between two circles with one circle inside another circle. In particular, we deduce an attainable range of the distance between the centers of the two circles and summarize the algorithm for implementation. Compared with the construction of a PH quintic curve, the complexity of the solution of the equation for obtaining the transition curves is reduced.展开更多
A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape paramet...A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape parameters. Comput. Aided Geom. Design, 28：151-163 （2011）], is proposed. Without solving a linear system, the spline curves can be used to interpolate sets of points with C2 continuity partly or entirely. The shape parameters have a predictable adjusting role on the sp[ine curves.展开更多
文摘This paper presents a method for creating modificable quartic and quintic curves with shape parameters. The curves can achieve C 2 even C 3 continuity and unify both interpolation and approximation to the control points without solving a system of equations or inserting additional control points. They have the local properties like the cubic B spline. Besides, the quintic curve would be able globally to tend the control polygon.
基金Supported by the National Natural Science Foundation of China(61272300)
文摘By using the geometric constraints on the control polygon of a Pythagorean hodo- graph （PH） quartic curve, we propose a sufficient condition for this curve to have monotone curvature and provide the detailed proof. Based on the results, we discuss the construction of spiral PH quartic curves between two given points and formulate the transition curve of a G2 contact between two circles with one circle inside another circle. In particular, we deduce an attainable range of the distance between the centers of the two circles and summarize the algorithm for implementation. Compared with the construction of a PH quintic curve, the complexity of the solution of the equation for obtaining the transition curves is reduced.
基金Supported by the National Natural Science Foundation of China(No.10871208,No.60970097)Graduate Students Scientific Research Innovation Project of Hunan Province(No.CX2012B111)+1 种基金the Postdoctoral Science Foundation of China(No.2015M571931)the Fundamental Research Funds for the Central Universities(No.2017MS121)
文摘A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape parameters. Comput. Aided Geom. Design, 28：151-163 （2011）], is proposed. Without solving a linear system, the spline curves can be used to interpolate sets of points with C2 continuity partly or entirely. The shape parameters have a predictable adjusting role on the sp[ine curves.
