Details:
Title  On the parallel lines for nongenerate conics  Author(s)  Rafal Ablamowicz, Jane Liu  Type  Technical Report, Misc  Abstract  Computation of parallel lines (envelopes) to parabolas, ellipses, and hyperbolas is of importance in structure engineering and theory of mechanisms. Homogeneous polynomials that implicitly define parallel lines for the given offset to a conic are found by computing Groebner bases for an elimination ideal of a suitably defined affine variety. Singularity of the lines is discussed and their singular points are explicitly found as functions of the offset and the parameters of the conic. Critical values of the offset are linked to the maximum curvature of each conic. Application to a finite element analysis is shown.  Keywords  Affine variety, elimination ideal, \Grobner basis, homogeneous polynomial, singularity, family of curves, envelope, pitch curve, undercutting, cam surface  Length  40 
URL 
http://www.math.tntech.edu/techreports/techreports.html 
Language  English  Journal  Technical Report  Volume  2006  Number  1  Pages  40  Year  2006  Month  January  Edition  0  Translation 
No  Refereed 
No  Organization 
Tennessee Technological University  Institution 
Department of Mathematics (Tennessee Technological University) 
