The Generalized H-Bézier Model: Geometric Continuity Conditions and Applications to Curve and Surface Modeling

The local controlled generalized H-Bézier model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is owed to its good geometric properties, e.g., symmetry and shape adjustable property. In this paper, some geometric continuity conditions for the generalized cubic H-Bézier model are studied for the purpose of constructing shape-controlled complex curves and surfaces in engineering. Firstly, based on the linear independence of generalized H-Bézier basis functions (GHBF), the conditions of first-order and second-order geometric continuity (namely, G1 and G2 continuity) between two adjacent generalized cubic H-Bézier curves are proposed. Furthermore, following analysis of the terminal properties of GHBF, the conditions of G1 geometric continuity between two adjacent generalized H-Bézier surfaces are derived and then simplified by choosing appropriate shape parameters. Finally, two operable procedures of smooth continuity for the generalized H-Bézier model are devised. Modeling examples show that the smooth continuity technology of the generalized H-Bézier model can improve the efficiency of computer design for complex curve and surface models.

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

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.

Optimizing the Shape Parameters of Beta-Spline Using Particle Swarm Optimization

Beta-spline is an alternative curve for 2D font representation. It is preferred since it has G2 continuity and two shape parameters, that can be used to control the curve shape. These shape parameters can also be used to optimize the error between fitted curve and original data points. Commonly, most of the researcher use value of shape parameters of beta-spline as and or some of the researcher choose any random value of these two shape parameters that suitable to be used in beta-spline curve fitting. The values of shape parameters are very important since the values affect the total error of the fitted curves. Thus, in this paper, Particle Swarm Optimization (PSO) is employed to determine the optimum value of the two shape parameters that will optimize the approximation error of the fitted curve. The technique is applied on two fonts: ى and δ, and tested using various number of iterations and populations.

Optimization of Tooth Root Profile Using Bezier Curve with G2 Continuity to Reduce Bending Stress of Asymmetric Spur Gear Tooth

This research describes simple and innovative approach to reduce bending stress at tooth root of asymmetric spur gear tooth which is desire for improve high load carrying capacity. In gear design at root of tooth circular-filleted is widely used. Blending of the involute profile of tooth and circular fillet creates discontinuity at root of tooth causes stress concentration occurs. In order to minimize stress concentration, geometric continuity of order 2 at the blending of gear tooth plays very important role. Bezier curve is used with geometric continuity of order 2 at tooth root of asymmetric spur gear to reduce bending stress.