Details:
Title  Implicitization, parameterization and singularity computation of Steiner surfaces using moving surfaces  Author(s)  Falai Chen, Xuhui Wang  Type  Article in Journal  Abstract  A Steiner surface is a quadratically parameterizable surface without base points. To make Steiner surfaces more applicable in Computer Aided Geometric Design and Geometric Modeling, this paper discusses implicitization, parameterization and singularity computation of Steiner surfaces using the moving surface technique. For implicitization, we prove that there exist two linearly independent moving planes with total degree one in the parametric variables. From this fact, the implicit equation of a Steiner surface can be expressed as a 3×3 determinant. The inversion formula and singularities for the Steiner surface can also be easily computed from the moving planes. For parameterization, we first compute the singularities of a Steiner surface in implicit form. Based on the singularities, we can find some special moving planes, from which a quadratic parameterization of the Steiner surface can be retrieved.  Keywords  Implicitization, Parameterization, Singularity, Inversion formula, Moving surface, Steiner surface  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111002227 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  6  Pages  733  750  Year  2012  Note  Advances in Mathematics Mechanization Mathematics Mechanization  Edition  0  Translation 
No  Refereed 
No 
