A resultant approach to detect intersecting curves in $\PP^3$

Details A resultant approach to detect intersecting curves in $\PP^3$ A resultant approach to detect intersecting curves in $\PP^3$

2003-01-09

arxiv.org/abs/math/0301088v1

Mathematics

Algebraic Geometry

21 pages, 2 figures

Scientific paper

Given two curves in $\PP^3$, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the inputs which vanishes if and only if the two curves intersect. This could be useful in Computer Aided Design, for computing the intersection of algebraic surfaces.

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