SMOOTH MONOTONE QUARTIC AND QUINTIC BEZIER-LIKE SPLINE INTERPOLATION

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dc.contributor.authorNG, SEOU LING
dc.date.accessioned2016-01-12T03:31:44Z
dc.date.available2016-01-12T03:31:44Z
dc.date.issued2007-05
dc.description.abstractCurves that are easy to control are very useful in design. In many problems from science and engineering, it is an important requirement that interpolation methods produce curves that are smooth and represent physical reality as closely as possible. In this dissertation, we investigate the use of quartic and quintic Bezier-like curves in monotonicity preserving interpolation. Besides the control points, these polynomial curves have additional parameters for shape control. These parameters are grouped as ratios to form two parameters. The effect of the latter two parameters on the curve is analysed. Conditions on these parameters for the quartic Bezier-like curve to be monotonic are derived. Based on these conditions, a C1 monotonicity preserving quartic Bezier-like spline interpolation scheme is presented. It is a local scheme where each curve segment can be generated independently from one another. L We also derive the conditions on the parameters for monotonicity preservation of a quintic Bezier-like curve. A monotonicity preserving interpolation scheme with C2 continuity is developed from these monotonicity conditions and the C2 condition using the quintic Bezier-like splines. The interpolant is obtained through a constrained optimization which minimizes the mean curvature. We illustrate these two schemes with graphical examples.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/1394
dc.subjectQUARTICen_US
dc.subjectQUINTICen_US
dc.titleSMOOTH MONOTONE QUARTIC AND QUINTIC BEZIER-LIKE SPLINE INTERPOLATIONen_US
dc.typeThesisen_US
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Pusat Pengajian Sains Matematik - Tesis