RATIONAL-RULED SURFACES - IMPLICITIZATION AND SECTION CURVES

This paper shows how to express the implicit equation of a degree 1 x n tenser product rational surface as a determinant of dimension at most n x n. If the rational surface has base points whose multiplicities sum to rho, the implicit equation can still be expressed in a single determinant with no extraneous factors. As part of the derivation, it is shown that the given ruled surface can be expressed using two directrices whose degrees sum to 2n - rho. It is also noted that any plane section curve of such a surface patch is rational, and formulas for the control points of the rational Bezier representation of that curve are given. (C) 1995 Academic Press, Inc.