Duality between L-bases and B-bases
نویسندگان
چکیده
abstract L-bases and B-bases are two important classes of polynomial bases used for representing surfaces in CAGD. The B ezier 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 B ezier 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 B ezier basis.
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