Abstract
Two conditions on the signs of the coefficients of a bivariate polynomial which ensure that the zero set is a single curve are derived. The first condition demands that all but one of the coefficients has the same sign. The second requires that the signs are ‘split’ by any straight line. Both properties are demonstrated by generalizing the set of isoparametric lines to a certain two-parameter family of curves. Equivalent curves are found for power, tensor-product Bernstein, exponential and triangular Bernstein polynomials. The second property will allow greater freedom when using algebraic curves for geometric modelling.
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Communicated by T.N.T. Goodman
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Floater, M.S. On zero curves of bivariate polynomials. Adv Comput Math 5, 399–415 (1996). https://doi.org/10.1007/BF02124753
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DOI: https://doi.org/10.1007/BF02124753