Interactive Design of cubic IPH spline curves with Control Polygon
*Jingjing Zhang (安徽大学)
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, we 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 and meanwhile facilitates intuitive and efficient construction of open
and closed PH 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 higher as possible continuity,
i.e., the absolute curvature value of the adjacent curve segments are same. A very interesting observation is
that for any open control polygon, a quadratic B-spline curve can have continuity absolute curvature by
carefully choosing the knots as the function of the control points.