Some engineering applications of new trigonometric cubic Bézier-like curves to free-form complex curve modeling

摘要

The construction of free-form complex curves is very hot topic in engineering and computer aided design/computer aided manufacturing (CAD/CAM). The trigonometric Bézier-like curves got more attention in the fields of mathematics and engineering in recent years because of their useful geometric properties as compared to classical Bézier curves as well as ordinary Bernstein basis functions. The new trigonometric cubic Bézier-like (or TC Bézier-like, for short) curves along with new trigonometric cubic Bernstein-like (or TC Bernstein-like, for short) basis functions with single shape parameter with continuity conditions are presented in this paper. The necessary and sufficient constraints for C ~(2) and G ~(2) between two contiguous TC Bézier-like curves are constructed in order to remove the difficulty to composite curves which they cannot often be constructed by means of single curve. The role of shape parameter on connected curves with detailed smooth continuity steps is also part of this study. The ellipses and parabolas can also be represented exactly by using the TC Bézier-like curves. Some important applications of TC Bézier-like curves as: approximate some conic curves, font designing and free form complex curves are discussed. Some modelling examples show that the proposed TC Bézier-like curve technique is time saving, very effective and efficient which they can easily be modelled and give a powerful tool to design engineering complex curves.