Boundary evaluation for interval Bézier curve

The objective of this paper is to provide an efficient and reliable algorithm for representing and evaluating the boundary of the interval Bézier curve in 2- and 3-D. The boundary of the planar Bézier curve is represented by a sequence of Bézier curve segments with same degree and line segments in the order they are encountered when marching counter-clockwise along its boundary. The boundary can also be represented as a single B-spline curve having the same degree with the interval Bézier curve. The boundary of the 3-D interval Bézier curve is made up of trimmed Bézier surface patches and rectangular patches. Some examples illustrate our algorithms.