Abstract
This work presents the new cubic trigonometric Bézier-type functions with shape parameter. Basis functions and the curve satisfy all properties of classical Bézier curve-like partition of unity, symmetric property, linear independent, geometric invariance, and convex hull property and have been proved. The C 3 and G 3 continuity conditions between two curve segments have also been achieved. To check the applicability of proposed functions, different types of open and closed curves have been constructed. The effect of shape parameter and control points has been observed. It is observed that, by decreasing the value of shape parameter, the curve moves toward the control polygon and vice versa. The CT-Bézier curve is closer to the cubic Bézier curve for a fixed value of shape parameter. The proposed CT-Bézier curve can be used to represent ellipse. Using proposed basis functions, we have constructed the spiral segment which is very useful to construct fair curves and desirable to design trajectories of mobile robots, highway, and railway routes’ designing.
Highlights
Spline curves have been considered a major tool for the geometric modelling in computer aided geometric design
Trigonometric Bezier-like functions and curves have attained the attention in computer aided geometric design, computer aided design, and bio-modelling [1, 2]. e concept of trigonometric B-spline (TBS) was introduced by [3], and the scheme of trigonometric B-spline with recurrence relation of the arbitrary order has been presented in [4]
A technique based on cubic Bezier curves (CBC) with the association of a shape parameter is proposed by [5]. is technique is useful for the construction of planer curves and the shape parameter is used to control the curve
Summary
Spline curves have been considered a major tool for the geometric modelling in computer aided geometric design. A technique, based on quadratic trigonometric Bezier (QTB) basis functions using one shape parameter, has been introduced in [10]. Chouby and Ojha [17] proposed the trigonometric spline curve In this scheme, the shape parameter is a variable which is helpful in adjusting and controlling the curve and surface locally. Trigonometric B-spline basis functions of degree 2 and the quadratic NUAT-B-spline curve of many shape parameters are proposed in [20, 21]. E generalized developable H-Bezier surfaces are designed by using control planes with generalized H-Bezier basis functions, and their shapes can be adjusted by altering the values of shape parameters. New trigonometric Bezier basis functions with a shape parameter are constructed. Cubic trigonometric Bezier curves, their properties, effect of shape parameter, and parametric and geometric continuity are part of Section 3.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
