A Class of Variable Degree Trigonometric Polynomial Spline and Its Applications

A class of variable degree trigonometric polynomial spline is presented for geometric modeling and industrial design. The corresponding generalized Hermite-like interpolating base functions provide bias and tension control facilities for constructing continuous interpolating curves and surfaces. The constructed curves and surfaces by the new spline can represent some conic and conicoid segments very approximately. The new interpolation spline, which need not solve m-system of equations, provides higher approximation order for data fitting than normal cubic Hermite interpolation spline for proper parameters. The idea is extended to produce Coons-like surfaces. Moreover, the new spline can be used for trajectory planning of manipulators in industrial design, which provides a continuity of position, velocity and acceleration, in order to ensure that the resulting trajectory is smooth enough. The variable degree trigonometric polynomial spline can be used to fit the sequence of joint positions for N joints. This new method approve to be practicable by the experimental results, and can meet the requirements of smooth motion of the manipulator.