The Bezout number for linear piecewise algebraic curves

Authors:
Renhong Wang;Shaofan Wang
Affiliations:
Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116085, China;Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116085, China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

A piecewise algebraic curve is a curve determined by the zero set of a bivariate spline function. This paper discusses the Bezout number, the maximum number of intersections between two linear piecewise algebraic curves whose intersections are finite, on regular triangulations. We give an upper bound of the Bezout number for linear piecewise algebraic curves (BN(1,0;1,0;@D)) on the triangulation with an odd interior vertex. For the triangulations which satisfy a vertex coloring condition, we compute the exact value of the Bezout number BN(1,0;1,0;@D).