Geometrical Design: Bézier Curves and Surfaces

Abstract

Many fields in the computational science area need descriptions of complex objects: virtual reality, computational graphics, geometric modeling, and computer-aided geometric design (CAGD). These descriptions are commonly obtained using basic elements: points, curves, surfaces, and volumes. Elementary tools used to handle these elements are mathematical functions, such as polynomials and rational functions, which allow easy graphical representation in many situations: union of objects, intersection, and complement. This chapter gives an introduction to geometrical design by studying some properties of the so-called Bézier curves and surfaces.