Boundary evaluation for interval Bézier curve

The objective of this paper is to provide an ef®cient and reliable algorithm for representing and evaluating the boundary of the interval Be Âzier curve in 2-and 3-D. The boundary of the planar Be Âzier curve is represented by a sequence of Be Âzier curve segments with same degree and line segments in the order they are encountered when marching counterclockwise along its boundary. The boundary can also be represented as a single B-spline curve having the same degree with the interval Be Âzier curve. The boundary of the 3-D interval Be Âzier curve is made up of trimmed Be Âzier surface patches and rectangular patches. Some examples illustrate our algorithms. q 2002 Elsevier Science Ltd. All rights reserved.