Degree Elevation of Interval Bezier Curves Using Legendre-Bernstein Basis Transformations

This paper presents a simple matrix form for degree elevation of interval Bezier curve using LegendreBernstein basis transformations. The four fixed Kharitonov's polynomials (four fixed Bezier curves) associated with the original interval Bezier curve are obtained. These four fixed Bezier curves are expressed in terms of the Legendre polynomials. The process of degree elevations r times are applied to the four fixed Bezier curves of degreen to obtain the four fixed Bezier curves of degreen + r. The four fixed Bezier curves are transformed to the Bernstein polynomials. Finally the new interval vertices {[qi , qi ]}i=0 n+r of the new interval polygon are obtained from vertices of the new fixed polygons of the four fixed Bezier curves. An illustrative example is included in order to demonstrate the effectiveness of the proposed method. Index Term— Computer graphics, image processing, CAGD, degree elevation, interval Beziercurves.