Generating avian egg using rational btzier quadratic curves
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Date
2010
Authors
Ishak, Noor Aziah
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Abstract
The main purpose of this research is to design an avian egg geometrically and
to estimate the egg volume by using Computer Aided Geometric DeSign (CAGD)
approach. One of the mp.thods of Computer Aided Geometric Design is Rational
Bezier Quadratic Curves which will be used to model the egg curve and will be
discussed further in this study. Since the Rational Bezier is depending on their
weighting, thus the best values of weighting need to be studied and will be
discovered in this research. In this study, the shape of an egg was assumed to be a
combination of semicircle and half ellipse. From the result, the best weighting for
circle part were Wo ="'l =1 dan w2 = 2 while for ellipse Wo = w2 = 1 and"'l = 0.6
were chosen. This study has proven that the curves of an avian egg generated from
Rational Bezier Quadratics were C1 for all of their joining paths.
By using the weighting and the experimental data. the volumes of egg were
generated using integration method by revolving the curve 360' about its
longitudinal axis. For this method. the calculations errors for volume did not exceed
3% from the average of experimental volumes.
The experimental data that used to design a closest curve to an avian egg
curvature by using Rational Bezier Quadratic Curves were maximum length (L).
maximum breadth (.8) and length of longitudinal axis from sharp pole to a crossing
point of longitudinal axis with the axis corresponding to the maximum diameter (L}).