| Bezier curves and surfaces are commonly seen in CAGD. They are the most basic type of curves and surfaces with many powerful properties. Much research has been done on these curves and surfaces but little attention has been given to their integral properties. In this thesis, we discuss how to obtain upper and lower bounds for their arclength and surface area.; Bezier curves and surfaces can be subdivided to smaller segments using the de Casteljau Algorithm, (Farin89). We investigate the convergence of the bounds for the arclength and surface area under recursive subdivision. Then using subdivision procedures together with the bounds, we construct adaptive algorithms to approximate the arclength and surface area of Bezier curves and surfaces. We investigate both integral and rational Bezier curves, as well as Bezier triangles. |
