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) |
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