Research On The Problem Of The Curves Interpolation In The CAGD

This paper summaries the researches on interpolantion curves of three types which includes Ferguson curves many-knot splines and algebraic curves.Putting forward to two new Ferguson curves--the HP-Ferguson curve and H-Ferguson curve ,two types of many-knot splines-triangle polynomial many-kont and hyperbolic polynomial many-knot, three types take parameter of many-knot splines, paper gives algebraic curves interpolation with geometric constraints finally, and giving an application which constructs the polygon tangent fasten.First, this paper introduces two types of shape mathematics description curve—approach curve and interpolation curve,the latter includes polynomial interpolants, subsection three hermite interpolants, three parameter curves, many-knot splines, algebra curves,singular blending splines, arc splines etc...By analyzing the characters of interpolation curves namely the curves should to pass every node, respectively construct in triangle function space and hyperbolic function space, similar characteristic of traditional Ferguson and many-kont interpolation curves. Generalized Ferguson and many-kont splines inherited characteristics of Ferguson curve and many-knot splines, the curve means in brief and keeps a view. In addition, they have the advantage of triangle function and hyperbolic function. As taking parameter in two types of generalized curves in particular, so the curve can also adjust curve shape. Finally, because of constitutes to from triangle function and hyperbolic function, so they convert into the rational polynomial curves more easily. Integrate several existing shape system.With the illuminating of the variety upon the curves shape follow with shape parameter in recent years, this paper constructed further three types many-kont interpolation curve which take shape parameter, studying the influence of the change upon the parameter.later, giving the method of mant-knot splines which is according to a rank, two ranks differentia-vector constraints.At last, introducing cubic algebraic curves interpolation with geometric constrains, and giving an application which constructs the polygon tangent fasten ,,give solid example, and draw a sketch.