PENGGUNAAN PARAMETER BENTUK DALAM PENGAWALAN LENGKUNG

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Date
2004
Authors
ABDUL MAJID, NORADZIMAH
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Abstract
Efficient algorithms for shape preserving approximation to curves are very important in shape design and modelling in CAGD system. The design of curved shapes have always posed a problem. For example, cusps and excessive oscillation have caused the shape of a curve to vary from the one suggested data. These weaknesses have encouraged scientist to introduce ways that can control the shape of a curve. The main aim of this dissertation is to study how shape parameter can preserve the smoothness of a curve. Traditional method by using interpolation and control points are studied to form Bezier curve, Conic segment, Alternative curve and Beta-Splines curve. Conic segment which is rational Bezier curve is obtained from Bezier curve by using certain weights as tension parameter. It is characterised by two end points, Mo end slopes and an immediate point. From the study, it shows that only wei~~t plays an important role in constructing and controlling the shape of a curve segment to form elips, parabola and hyperbola. By using an alternative method, the shape of a curve can be controlled to preserve the convexity of the curve or to produce inflection curve through certain parameters and weight by determining the constraints of corresponding scalar weight with respect to the control points. This study also discusses about the generalization to conic segment by using the reduced rational cubic curve. The value of weight to construct elips, parabola and hyperbola is also analysed. For Beta-Splines curve, the use of bias parameter(Pl) and tension parameter( P2) to control the shape and the smoothness of a curve are also studied. To proof the result of the study, examples are presented graphically for discussion.
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PARAMETER , LENGKUNG
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