title: Finding the Axis of Revolution of an Algebraic Surface of Revolution.
abstract: We present an algorithm for extracting the axis of revolution from the implicit equation of an algebraic surface of revolution based on three distinct computational methods: factoring the highest order form into quadrics, contracting the tensor of the highest order form, and using univariate resultants and gcds. We compare and contrast the advantages and disadvantages of each of these three techniques and we derive conditions under which each technique is most appropriate. In addition, we provide several necessary conditions for an implicit algebraic equation to represent a surface of revolution.
authors.forename: Juan G
authors.initials: JG
authors.lastname: Alcazar
authors.forename: Ron
authors.initials: R
authors.lastname: Goldman