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A new type of cubic trigonometric Bézier curve has been introduced in
[1]. This trigonometric curve has two global shape parameters λ and µ. We
give a lower boundary to the shape parameters where the curve has lost the
variation diminishing property. In this paper the relationship of the two shape
parameters and their geometric effect on the curve is discussed. These shape
parameters are independent and we prove that their geometric effect on the
curve is linear. Because of the independence constrained modification is not
unequivocal and it raises a number of problems which are also studied. These
issues are generalized for surfaces with four shape parameters. We show that
the geometric effect of the shape parameters on the surface is parabolic.
Keywords: trigonometric curve, spline curve, constrained modificatio
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