Parametric Model for Kitchen Product Based on Cubic T-Bézier Curves with Symmetry

Abstract

The parametric method of product design is a pivotal and practical technique in computer-aided design and manufacturing (CAD/CAM) and used in many manufacturing sectors. In this paper, we presented a novel parametric method to design a kitchen product in the residential environment, a kitchen cabinet, by using cubic T-Bézier curves with constraints of geometric continuities. First, we introduced a class of cubic T-Bézier curves with two shape parameters and derived the G1 and G2 continuity conditions of the cubic T-Bézier curves. Then, we constructed shape-controlled complex contour curves of the kitchen cabinet by using closed composite cubic T-Bézier curves. The shapes of the contour curves can be adjusted intuitively and predictably by altering the values of the shape parameters. Finally, we studied shape optimization and representation of ellipses for the contour curves of the kitchen cabinet by finding optimal shape parameters and applicable control points respectively. The provided modeling examples showed that our method in this paper can improve the design and scheme adjustment effectively in the conceptual design stage of kitchen products.

A quartic trigonometric interpolatory spline with local free parameters

“…Such as the trigonometric Be´zier curves, [1][2][3][4] the trigonometric B-spline curves, [5][6][7] the trigonometric Hermite curves, 8,9 the trigonometric rational curves, 10,11 etc. The curves constructed in trigonometric function space have been applied in signal analysis, 12 kitchen product design, 13 robot path planning, 14 and other engineering problems.…”

Frenet Frames of Trigonometric B'ezier Curves

“…Misro et al examined the quintic trigonometric Bézier curve with two shape parameters [7]. Also, Sun and Ji gave a novel parametric method to design a kitchen product in the residential environment, a kitchen cabinet, by using cubic T-Bézier curves with constraints of geometric continuities [10]. Then, Ammad and Misro get a class of quintic trigonometric Bézier like basis functions, which is an extension of a traditional Bernstein basis and constructed three different types of shape adjustable surfaces such as general surface, swept surface and swung surface according to these basis functions [1].…”