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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Keywords
PARAMETER , LENGKUNG