Algebraic tools in Computational Geometry (I/III)

Bentley-Ottmann sweep-line algorithm for computing the arrangement
of lines or line segments to a sweep-line algorithm for arbitrary
algebraic curves. I will point out the difficulties and then, in order
to solve these difficulties, introduce resultants and subresultants of
polynomials in detail. Another main topic will be generalized Jacobi
curves. They are a tool for locating tangential intersection points of
two curves.