Abstract:

A new kind of cubic algebraic trigonometric interpolation splines with a shape parameter over space Ω=span {1, t, sint, cost, sint2t, cos2t} was presented. The interpolation splines have many similar properties with cubic B-splines. The curves and surfaces can interpolate directly some control points without solving system of equations or inserting some additional control points. The curves can be used to exactly represent straight line segment, circular arc, elliptic arc, parabola and some transcendental curves such as circular helix. The corresponding tensor product surfaces can also precisely represent some quadratic surfaces and transcendental surfaces, such as sphere, cylindrical surfaces and helix tube. The shape of the curves and surfaces can be modified globally through changing the values of the parameters. Furthermore, the local parameters are introduced in the splines using the singular blending technique. Examples are given to illustrate that the splines can be used as a novel efficient model for geometric design in the fields of CAGD.

Key words: cubic B-splines;algebraictrigonometric spline;interpolation;shape parameter;singular blending