Uzma Bashir

Data Visualization Using Rational Trigonometric Spline

This paper describes the use of trigonometric spline to visualize the given planar data. The goal of this work is to determine the smoothest possible curve that passes through its data points while simultaneously satisfying the shape preserving features of the data. Positive, monotone, and constrained curve interpolating schemes, by using a piecewise rational cubic trigonometric spline with four shape parameters, are developed. Two of these shape parameters are constrained and the other two are set free to preserve the inherited shape features of the data as well as to control the shape of the curve. Numerical examples are given to illustrate the worth of the work.

The G2 and C2 rational quadratic trigonometric Bézier curve with two shape parameters with applications

The rational quadratic trigonometric Bezier curve with two shape parameters is presented in this paper, which is new in literature. The purposed curve inherits all the geometric properties of the traditional rational quadratic Bezier curve. The presence of shape parameters provides a control on the shape of the curve more than that of traditional Bezier curve. Moreover the weight offers an additional control on the curve. Simple constraints for shape parameters are derived using the end points curvature so that their values always fall within the defined range. The composition of two segments of curve using G^2 and C^2 continuity is given. The new curves can accurately represent some conics and best approximates the traditional rational quadratic Bezier curve.

The Rational Quadratic Trigonometric Bézier Curve with Two Shape Parameters

In this paper, a newly constructed rational quadratic trigonometric Bézier curve with two shape parameters is presented. The purposed curve enjoys all the geometric properties of the traditional rational quadratic Bézier curve. The local control on the shape of the curve can be attained by altering the values of the shape parameters as well as the weight. The curve exactly represents some quadratic trigonometric curves such as the arc of an ellipse and the arc of a circle and best approximates the ordinary rational quadratic Bézier curve.

A rational trigonometric spline to visualize positive data

In this paper, we construct a cubic trigonometric Bezier curve with two shape parameters on the basis of cubic trigonometric Bernstein-like blending functions. The proposed curve has all geometric properties of the ordinary cubic Bezier curve. Later, based on these trigonometric blending functions a C1 rational trigonometric spline with four shape parameters to preserve positivity of positive data is generated. Simple data dependent constraints are developed for these shape parameters to get a graphically smooth and visually pleasant curve.

The Quartic Trigonometric Bézier Curve with Two Shape Parameters

A quartic trigonometric Bézier curve with two shape parameters based on newly constructed trigonometric basis functions is presented in this paper. The curve is drawn by using end point curvature conditions and carries all the geometric features of the ordinary quartic Bézier curve. The presence of shape parameters provides an opportunity to adjust the shape of the curve by simply altering their values. The G2 and C2 continuity under appropriate conditions is achieved by joining two pieces of trigonometric curve.