Indirect Pythagorean hodographs(IPH)spline curves are a set of curves which have rational Pythagorean hodographs after reparameterization by a fractional quadratic transformation.In this paper,the authors provide an a...Indirect Pythagorean hodographs(IPH)spline curves are a set of curves which have rational Pythagorean hodographs after reparameterization by a fractional quadratic transformation.In this paper,the authors provide an algorithm to interactively design a cubic IPH spline curve from any given control polygon.The method has the same friendly interface and properties as those for B-splines,meanwhile facilitates intuitive and efficient construction of open and closed IPH spline curves.The key idea is to solve the ratios of a set of auxiliary points associated with the edges and then construct a piecewise cubic IPH spline curve which has as high as possible continuity,i.e.,the absolute curvature value of the adjacent curve segments are the same.A very interesting observation is that for any open control polygon,a quadratic B-spline curve can have continuous absolute curvature by carefully choosing the knots as the function of the control points.展开更多
基金supported by the National Science Foundation of China under Grant No.11801126.
文摘Indirect Pythagorean hodographs(IPH)spline curves are a set of curves which have rational Pythagorean hodographs after reparameterization by a fractional quadratic transformation.In this paper,the authors provide an algorithm to interactively design a cubic IPH spline curve from any given control polygon.The method has the same friendly interface and properties as those for B-splines,meanwhile facilitates intuitive and efficient construction of open and closed IPH spline curves.The key idea is to solve the ratios of a set of auxiliary points associated with the edges and then construct a piecewise cubic IPH spline curve which has as high as possible continuity,i.e.,the absolute curvature value of the adjacent curve segments are the same.A very interesting observation is that for any open control polygon,a quadratic B-spline curve can have continuous absolute curvature by carefully choosing the knots as the function of the control points.
