  Shape preservation behavior of a spline consists of criterial conditions for
preserving convexity, inflection, collinearity, torsion and coplanarity shapes
of data polgonal arc. We present our results which acts as an improvement in
the definitions of and provide geometrical insight into each of the above shape
preservation criteria. We also investigate the effect of various results from
the literature on various shape preservation criteria. These results have not
been earlier refered in the context of shape preservation behaviour of splines.
We point out that each curve segment need to satisfy more than one shape
preservation criteria. We investigate the conflict between different shape
preservation criteria 1)on each curve segment and 2)of adjacent curve segments.
We derive simplified formula for shape preservation criteria for cubic curve
segments. We study the shape preservation behavior of cubic Catmull-Rom splines
and see that, though being very simple spline curve, it indeed satisfy all the
shape preservation criteria.
