RECONSTRUCTION OF CONIC SECTIONS USING RATIONAL SPLINE

Qaisra, Fazal (2003) RECONSTRUCTION OF CONIC SECTIONS USING RATIONAL SPLINE. Doctoral thesis, University of the Punjab.

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Abstract

Designing of curves has been the main problem in computer graphics. In this regard, a number of schemes have been developed that posses C1 as well as C2 continuity in order to get smooth and peasant curves. Mohammad Sarfraz and Zyulifqar Habib [14] developed a C2 rational cubic spline with a family of shape parameters that are used to produce straight line segments and conics. For the smoothness of the curve two tangent schemes namely distance based derivative and second derivative continuity were discussed. Using interpolant introduced by Mohammad Sarfraz and Zulifqar Habib [14], a method has been developed to reconstruct the conic sections instead of a part of conic imposing distance based derivative continuity in different ways respectively. To implement the method, different examples of reconstruction of ellipses, hyperbolas and parabolas from the given data are also considered and compared with the original ellipses, parabolas and hyperbolas.

Item Type: Thesis (Doctoral)
Uncontrolled Keywords: rational spline, conic sections, ellipses, hyperbolas, spline functions, parabolas, cubic hermite spline, curve designing, rational cubic spline, curve, polynomials
Subjects: Q Science > QA Mathematics
Depositing User: Muhammad Khan Khan
Date Deposited: 10 Nov 2016 07:39
Last Modified: 10 Nov 2016 07:39
URI: http://eprints.hec.gov.pk/id/eprint/3285

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