{"title":"Circular Approximation by Trigonometric B\u00e9zier Curves","authors":"Maria Hussin, Malik Zawwar Hussain, Mubashrah Saddiqa","volume":97,"journal":"International Journal of Computer and Information Engineering","pagesStart":30,"pagesEnd":34,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10000225","abstract":"We present a trigonometric scheme to approximate a \r\ncircular arc with its two end points and two end tangents\/unit \r\ntangents. A rational cubic trigonometric Bézier curve is constructed \r\nwhose end control points are defined by the end points of the circular \r\narc. Weight functions and the remaining control points of the cubic \r\ntrigonometric Bézier curve are estimated by variational approach to \r\nreproduce a circular arc. The radius error is calculated and found less \r\nthan the existing techniques.<\/p>\r\n","references":"[1]\tL. Fang, \u201cCircular arc approximation by quintic polynomial curves,\u201dComputer Aided Geometric Design, vol. 15, 1998, pp. 843-861.\r\n[2]\tM. Goldapp, \u201cApproximation of circular arcs by cubic polynomials,\u201dComputer Aided Geometric Design,vol. 8, 1991, pp. 227-238.\r\n[3]\tX. Han, \u201cQuadratic trigonometric polynomial curves with a shape parameter,\u201dComputer Aided Geometric Design, vol. 19, 2002, pp. 503-512.\r\n[4]\tX. Han, \u201cCubic trigonometric polynomial curves with a shape parameter,\u201dComputer Aided Geometric Design, vol. 21, 2004, pp. 535-548.\r\n[5]\tI. K. Lee, M. S. Kim and G. Elber, \u201cPlaner curve offset based on circular approximation,\u201dComputer Aided Design,vol.28, no. 8, 1996, pp. 617-630.\r\n[6]\tI. J. Schoenberg, \u201cOn trigonometric spline interpolation,\u201dJournalof Mathematics and Mechanics,vol. 13, no. 5, 1964, pp. 795-825.\r\n[7]\tG. Wang, Q. ChenandM. Zhou, \u201cNUAT B-spline curves,\u201dComputer Aided Geometric Design,vol. 21, 2004, pp. 193-205.\r\n","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 97, 2015"}

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