Abstract
The modeling of Bezier curves and surfaces with their shape parameters is the most popular area of research in computer aided geometric design/computer aided manufacturing (CAGD/CAM) due to their geometric characteristics. In this paper, we propose an important idea to tackle the problem in construction of some engineering symmetric revolutionary curves and symmetric rotation surfaces by using the generalized hybrid trigonometric Bezier (or GHT-Bezier, for short) curve. The shape of the curves and surfaces can be modified by the alteration of shape parameters. The free-form complex curves using GHT-Bezier curves with constraints of parametric continuity are constructed. Finally, by using the GHT-Bezier curves with their continuity conditions and symmetric formulas, we construct different types of symmetric figures, symmetric revolutionary curves and symmetric rotation surfaces in $\mathbb {R}^{2}$ and $\mathbb {R}^{3}$ to show the efficiency of modeling. These symmetric examples show that the proposed method is time saving, effective and efficient in construction of complex engineering symmetric curves and surfaces.
Highlights
In mathematics, manufacturing and engineering field, a solid of revolution is a surface which is obtained by revolving a plane curve
Hu et al [11] presented a new method for the construction of shape adjustable generalized Bézier rotation surfaces with the multiple shape parameters
Hu et al [13] presented the modeling of free form complex curves by using parametric and geometric continuities. They used the multiple shape parameters to modify and beautify the complex curves according to requirement
Summary
In mathematics, manufacturing and engineering field, a solid of revolution is a surface (solid) which is obtained by revolving a plane curve (area). Hu et al [8] constructed a Developable Bézier-like surfaces with their properties and presented different type of complex surfaces modeling by using C2 and G2 continuity conditions. Hu et al [11] presented a new method for the construction of shape adjustable generalized Bézier rotation surfaces with the multiple shape parameters. Hu et al [13] presented the modeling of free form complex curves by using parametric and geometric continuities They used the multiple shape parameters to modify and beautify the complex curves according to requirement. Sharma [29] constructed quartic trigonometric Bézier (QTB) curve with two different shape parameters, the properties of QTB curve with various modeling and shape control of the curve is discussed. A FAMILY OF GHT-BÉZIER CURVES The definition and general properties of GHT-Bézier curve are defined as follows
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