Pengawalan Secara Geometri Lengkung Kubik Nisbah Alternatif
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Date
2002-09
Authors
Ahmad, Azhar
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Abstract
In this dissertation the discussion is centered with controling the shapes .of planar curves
geometrically. A representation of planar curve considered is rational Alternative cubic
curves. The method used \Yas .introduced by Jamaludin (1994a). With this method we are
able to preserve convexity of curves and inflecting curves, by detem1ining the constraints
of corresponding scalar weights with respect to the control points. The rational cubic curve
is characterised by two end points, two end slopes and an intermediate point. This study
show that only the end \Veights play the important role in construction and controlling the
shape of cunĀ·e segment when it inter-poled the shoulder point. This study also discusses the
generalisation to conic segments. Other possible shapes can occur when shoulder point is
located outside the control polygon, we will obtain double inflection, loop and cusp. By
using the barycentric coordinate, it will make related equations and inequations easier to
understand and to be manipulated. Lastly, we are going to present the method of controling
the inflection cun'e which interpolated a shoulder point and touching a shoulder line. The
result shows that the main factor for constructing and controling this cunre segment is the
location of the shoulder point and the value of end weights.
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Keywords
Geometri Lengkung