8 research outputs found
Quintic trigonometric Bézier curve with two shape parameters
The fifth degree of trigonometric Bézier curve called quintic with two shapes parameter is presented in this paper. Shape parameters provide more control on the shape of the curve compared to the ordinary Bézier curve. This technique is one of the crucial parts in constructing curves and surfaces because the presence of shape parameters will allow the curve to be more flexible without changing its control points. Furthermore, by changing the value of shape parameters, the curve still preserves its geometrical features thus makes it more convenient rather than altering the control points. But, to interpolate curves from one point to another or surface patches, we need to satisfy certain continuity constraints to ensure the smoothness not just parametrically but also geometrically
Constrained modification of the cubic trigonometric Bézier curve with two shape parameters
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
Geometric properties and constrained modification of trigonometric spline curves of Han
New types of quadratic and cubic trigonometrial polynomial curves have
been introduced in [2] and [3]. These trigonometric curves have a global shape
parameter λ. In this paper the geometric effect of this shape parameter on the
curves is discussed. We prove that this effect is linear. Moreover we show that
the quadratic curve can interpolate the control points at λ = √2. Constrained
modification of these curves is also studied. A curve passing through a given
point is computed by an algorithm which includes numerical computations.
These issues are generalized for surfaces with two shape parameters. We show
that a point of the surface can move along a hyperbolic paraboloid
A new class of trigonometric B-Spline Curves
We construct one-frequency trigonometric spline curves with a de Boor-like algorithm for evaluation and analyze their shape-preserving properties. The convergence to quadratic B-spline curves is also analyzed. A fundamental tool is the concept of the normalized B-basis, which has optimal shape-preserving properties and good symmetric properties