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Design and implementation of maple packages for processing offsets and conchoids. (English) Zbl 1371.65018
Summary: In this paper we present two packages, implemented in the computer algebra system Maple, for dealing with offsets and conchoids to algebraic curves, respectively. Help pages and procedures are described. Also in an annex, we provide a brief atlas, created with these packages, and where the offset and the conchoid of several algebraic plane curves are obtained, their rationality is analyzed, and parametrizations are computed. Practical performance of the implemented algorithms shows that the packages execute in reasonable time; we include time cost tables of the computation of the offset and conchoid curves of two rational families of curves using the implemented packages.
65D17 Computer-aided design (modeling of curves and surfaces)
65Y15 Packaged methods for numerical algorithms
68W30 Symbolic computation and algebraic computation
14Q05 Computational aspects of algebraic curves
Conchoid; Maple; Offset
Full Text: DOI
[1] Arrondo, E; Sendra, J; Sendra, JR, Parametric generalized offsets to hypersurfaces, J. Symb. Comput., 23, 267-285, (1997) · Zbl 0878.68134
[2] Arrondo, E; Sendra, J; Sendra, JR, Genus formula for generalized offset curves, J. Pure Appl. Algebra, 136, 199-209, (1999) · Zbl 0944.14014
[3] Farouki, RT; Ne, CA, Analytic properties of plane offset curves, Comput. Aided Geom. Des., 7, 83-99, (1990) · Zbl 0718.53003
[4] Farouki, RT; Ne, CA, Algebraic properties of plane offset curves, Comput. Aided Geom. Des., 7, 100-127, (1990) · Zbl 0724.65008
[5] Hoffmann, C.M.: Geometric and Solid Modeling. Morgan Kaufmann Publisher (1993)
[6] Kerrick, AH, The limaçon of Pascal as a basis for computed and graphic methods of determining astronomic positions, J. Instit. Navig., 6, 5, (1959)
[7] Menschik, F, The hip joint as a conchoid shape, J. Biomech., 30, 971-3 9302622, (1997)
[8] Peternell, M., Gruber, D.: Conchoid surfaces of quadrics. J. Symb. Comput. (2013). doi:http://dx.doi.org/10.1016/j.jsc.2013.07.003 · Zbl 1291.14078
[9] Peternell, M; Gruber, D; Sendra, J, Conchoid surfaces of rational ruled surfaces, Comp. Aided Geom. Des., 28, 427-435, (2011) · Zbl 1232.65031
[10] Peternell, M; Gruber, D; Sendra, J, Conchoid surfaces of spheres, Comp. Aided Geom. Des., 30, 35-44, (2013) · Zbl 1255.65055
[11] Peternell, M; Gotthart, L; Sendra, J; Sendra, JR, Offsets, conchoids and pedal surfaces, J. Geom., 106, 321-339, (2015) · Zbl 1319.51016
[12] Peternell, M; Pottmann, H, A Laguerre geometric approach to rational offsets, Comput. Aided Geom. Des., 15, 223-249, (1998) · Zbl 0903.68190
[13] Sendra, J; Sendra, JR, Algebraic analysis of offsets to hypersurfaces, Math. Z., 234, 697-719, (2000) · Zbl 0996.14027
[14] Sendra, J; Sendra, JR, Rationality analysis and direct parametrization of generalized offsets to quadrics, AAECC, 11, 111-139, (2000) · Zbl 1053.14068
[15] Sendra, J; Sendra, JR, An algebraic analysis of conchoids to algebraic curves, AAECC, 19, 413-428, (2008) · Zbl 1192.14027
[16] Sendra, J; Sendra, JR, Rational parametrization of conchoids to algebraic curves, AAECC, 21, 413-428, (2010) · Zbl 1195.14077
[17] Sendra, JR; Sevilla, D, Radical parametrizations of algebraic curves by adjoint curves, J. Symb. Comput., 46, 1030-1038, (2011) · Zbl 1218.14053
[18] Sendra, JR; Sevilla, D, First steps towards radical parametrization of algebraic surfaces, Comput. Aided Geom. Des., 30, 374-388, (2013) · Zbl 1266.65032
[19] Sultan, A, The limaçon of Pascal: mechanical generating fluid processing, J. Mech. Eng. Sci., 219, 813-822, (2005)
[20] Weigan, L., Yuang, E., Luk, K.M.: Conchoid of Nicomedes and Limaçon of Pascal as electrode of static field and a wavwguide of high frecuency wave. In: Progress in Electromagnetics Research Symposium, PIER, vol. 30, pp 273-284 (2001)
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