Splines e modelagem geométrica.

Abstract

Splines, which are mathematically describable, have very nice properties for modeling curve. A curve defined by a function / satisfying a few conditions can be approximated by splines. Also, given a curve whose defining function / is unknown, splines provide a good approximation to this function from a given number of points in the curve. Furthermore, approximations built using splines can preserve many mathematical and geometrical properties of the curves. In computer graphics, the combination of the above properties warrants the accuracy of the model with respect to the object modelled. In the quest for this accuracy, many splines have been proposed: B-splines, Bezier, (3-splines, u-splines, r-splines, WF-splines, 7-splines, etc. This thesis attempts to answer the question of whether or not i t is possible to study splines in an unified way, rather than studying each kind of spline separately.