SMOOTH MONOTONE QUARTIC AND QUINTIC BEZIER-LIKE SPLINE INTERPOLATION
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Date
2007-05
Authors
NG, SEOU LING
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Abstract
Curves 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.
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Keywords
QUARTIC , QUINTIC