ABSTRACT
The representation of three-dimensional (3D) surfaces that we have considered so far is limited to the polygon mesh. However, it is not an accurate representation but an approximation of a smooth surface. In general, a smooth surface is defined as a continuous function of parameters. Such parametric surfaces were developed in areas of computer-aided design and manufacturing but are increasingly garnering attention in the interactive graphics field especially because the Graphics Processing Unit (GPU) began to accept them. This chapter presents the simplest among them, the Beier surface, which was named after Pierre Bezier, a French engineer at Renault. The Bezier curve has many interesting properties, and one of them is its affine invariance. The chapter presents Bezier patches. Bezier curves form the foundations of Bezier patches. To present Bezier curves, it is preceded from the line segment to the quadratic Bezier curve, and then to the cubic Bezier curve.
