A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined...A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.展开更多
This paper analyzes the principle of spline interpolation, pointed out the reasons for the feed rate fluctuations and proposed interpolation algorithm based on the secant iteration method NURBS curve. The algorithm of...This paper analyzes the principle of spline interpolation, pointed out the reasons for the feed rate fluctuations and proposed interpolation algorithm based on the secant iteration method NURBS curve. The algorithm of the speed the planning section uses cubic polynomial acceleration and deceleration control methods to ensure the acceleration of the process of continuous high-speed operation, so that the machine runs smoothly, avoiding the machine have a big impact; while parameter calculation part using the Secant iterative interpolation method to calculate parameter, reducing the speed fluctuation, the machine is further reduced tremor. Simulation results show that the algorithm can obtain a continuous velocity and acceleration curves, and can be controlled in real time interpolation velocity fluctuations in the ideal range, the machine achieve the smooth running ,and meet the high-speed, high quality processing requirements.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10171026 and 60473114), the Research Funds forYoung Innovation Group, Education Department of Anhui Prov-ince (No. 2005TD03) and the Natural Science Foundation of An-hui Provincial Education Department (No. 2006KJ252B), China
文摘A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.
文摘This paper analyzes the principle of spline interpolation, pointed out the reasons for the feed rate fluctuations and proposed interpolation algorithm based on the secant iteration method NURBS curve. The algorithm of the speed the planning section uses cubic polynomial acceleration and deceleration control methods to ensure the acceleration of the process of continuous high-speed operation, so that the machine runs smoothly, avoiding the machine have a big impact; while parameter calculation part using the Secant iterative interpolation method to calculate parameter, reducing the speed fluctuation, the machine is further reduced tremor. Simulation results show that the algorithm can obtain a continuous velocity and acceleration curves, and can be controlled in real time interpolation velocity fluctuations in the ideal range, the machine achieve the smooth running ,and meet the high-speed, high quality processing requirements.
