02/01/1995 09:00 AM
Computer Science
L-bases and B-bases are two important classes of polynomial bases used for representing surfaces in CAGD. The Bezier and multinomial bases are special cases of both L-bases and B- bases. We establish that certain proper subclasses of bivariate Lagrange and Newton bases are L-bases and certain proper subclasses of power and Newton dual bases are B-bases. A geometric point-line duality between B-bases and L-bases is described and used to investigate the duality between geometric representations for bivariate Bezier and multinomial bases, Lagrange and power bases, and Newton and Newton dual bases for surfaces. Under this geometric duality, lines in L-bases correspond to points or vectors in B-bases and concurrent lines map to collinear points and vice-versa. The generalized de Boor-Fix formula for surfaces also provides an algebraic duality between L-bases and B-bases. This algebraic duality between B-bases and L-bases can be used to develop change of basis algorithms between any two of these bases. We describe, in particular, a change of basis algorithm from a bivariate Lagrange L-basis to a bivariate Bezier basis.