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Abstract: The objective of this paper is to compute the singularities of a normal offset of a planar integral polynomial curve and the intersections of two specific normal offsets of two planar integral polynomial curves. Singularities includeirregular points (such asisolated points andcusps) andself-intersections. The key element in the above techniques is the computation ofall real roots within a finite @? of systems of nonlinear equations involving polynomials and square roots of polynomials. The curves that we are investigating are described by polynomial functions, but their offset curve representations involve polynomials and square roots of polynomials. A methodology based on adaptive subdivision techniques to solve the resulting systems of nonlinear equations is investigated. Key components of our methods are the reduction of the problems into solutions of systems of polynomial equations of higher dimensionality through the introduction ofauxiliary variables and the use ofrounded interval arithmetic in the context of Bernstein subdivision to enhance the robustness of floating point implementation. Examples illustrate our techniques.