A Novel Approach of Hybrid Trigonometric Bézier Curve to the Modeling of Symmetric Revolutionary Curves and Symmetric Rotation Surfaces

The modeling of Bézier 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 Bézier (or GHT-Bézier, 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-Bézier curves with constraints of parametric continuity are constructed. Finally, by using the GHT-Bézier curves with their continuity conditions and symmetric formulas, we construct different types of symmetric figures, symmetric revolutionary curves and symmetric rotation surfaces in R
²
and 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.