Alcazar, Juan Gerardo; Sendra, Juan Rafael Local shape of offsets to algebraic curves. (English) Zbl 1123.14031 J. Symb. Comput. 42, No. 3, 338-351 (2007). Summary: We introduce the notion of local shape to describe the behavior of a real place of an algebraic curve around its center. We analyze how the local shape is affected by the offsetting process, and we relate this phenomenon to the curvature of the curve. Furthermore, we characterize the situations when the offsetting process behaves locally well, so that the local shape is preserved. Cited in 3 ReviewsCited in 12 Documents MSC: 14Q05 Computational aspects of algebraic curves 68W30 Symbolic computation and algebraic computation 14H20 Singularities of curves, local rings 14H50 Plane and space curves Keywords:offset curve; offset shape; offset topology; curvature Software:CASA PDFBibTeX XMLCite \textit{J. G. Alcazar} and \textit{J. R. Sendra}, J. Symb. Comput. 42, No. 3, 338--351 (2007; Zbl 1123.14031) Full Text: DOI References: [1] Alcazar, J.G., Schicho, J., Sendra, R., 2005. Computation of the topology types of the level curves of real algebraic surfaces. Tech. Report SFB 2006-2. RICAM, Austria; Alcazar, J.G., Schicho, J., Sendra, R., 2005. Computation of the topology types of the level curves of real algebraic surfaces. Tech. Report SFB 2006-2. RICAM, Austria · Zbl 1120.14049 [2] Alcazar, J.G., Sendra, R., 2006. Local shape of offsets to rational algebraic curves. Tech. Report SFB 2006-22. RICAM, Austria; Alcazar, J.G., Sendra, R., 2006. Local shape of offsets to rational algebraic curves. Tech. Report SFB 2006-22. RICAM, Austria · Zbl 1123.14031 [3] Arrondo, E.; Sendra, J.; Sendra, J. R., Parametric generalized offsets to hypersurfaces, Journal of Symbolic Computation, 23, 267-285 (1997) · Zbl 0878.68134 [4] Arrondo, E.; Sendra, J.; Sendra, J. R., Genus formula for generalized offset curves, Journal of Pure and Applied Algebra, 136, 3, 199-209 (1999) · Zbl 0944.14014 [5] Do Carmo, M., Differential Geometry of Curves and Surfaces (1976), Prentice-Hall · Zbl 0326.53001 [6] Farouki, R. T.; Neff, C. A., Analytic properties of plane offset curves, Computer Aided Geometric Design, 7, 83-99 (1990) · Zbl 0718.53003 [7] Farouki, R. T.; Neff, C. A., Algebraic properties of plane offset curves, Computer Aided Geometric Design, 7, 101-127 (1990) · Zbl 0724.65008 [8] Hemmecke, R.; Hillgarter, E.; Winkler, F., The CASA system, (Grabmeier, J.; Kaltofen, E.; Weispfenning, V., Handbook of Computer Algebra: Foundations, Applications, Systems (2001), Springer-Verlag) [9] Hoschek, J.; Lasser, D., Fundamentals of Computer Aided Geometric Design (1993), A.K. Peters Wellesley MA., Ltd · Zbl 0788.68002 [10] Leibnitz, G. W., Generalia de Natura Linearum, Anguloque Contactus et Osculi Provocationibis Aliisque Cognatis et Eorum Usibus Nonnullis, Acta Eruditorum (1692) [11] Lü, W., Offset-rational parametric plane curves, Computer Aided Geometric Design, 12, 601-617 (1995) · Zbl 0875.68853 [12] Pottmann, H., Rational curves and surfaces with rational offsets, Computer Aided Geometric Design, 12, 175-192 (1995) · Zbl 0872.65011 [13] Pottmann, H.; Peternell, M., A Laguerre geometric approach to rational offsets, Computer Aided Geometric Design, 15, 3, 223-249 (1998) · Zbl 0903.68190 [14] San Segundo, F.; Sendra, J. R., Degree formulae of offsets curves, Journal of Pure and Applied Algebra, 195, 3, 301-335 (2005) · Zbl 1093.14082 [15] Sendra, J. R., Normal parametrizations of algebraic plane curves, Journal of Symbolic Computation, 33, 863-885 (2002) · Zbl 1013.14009 [16] Sendra, J.; Sendra, J. R., Algebraic analysis of offsets to hypersurfaces, Mathematische Zeitschrift, 234, 697-719 (2000) · Zbl 0996.14027 [17] Sendra, J.; Sendra, J. R., Rationality analysis and direct parametrization of generalized offsets to quadrics, Applicable Algebra in Engineering, Communication and Computing, 11, 2, 111-139 (2000) · Zbl 1053.14068 [18] Sendra, J. R.; Winkler, F., Algorithms for rational real algebraic curves, Fundamenta Informaticae, 39, 1-2, 211-228 (1999) · Zbl 0951.68166 [19] Walker, R. J., Algebraic Curves (1950), Princeton University Press: Princeton University Press Princeton · Zbl 0039.37701 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.