A univariate rational quadratic trigonometric interpolating spline to visualize shaped data

This study was concerned with shape preserving interpolation of 2D data. A piecewise C1 univariate rational quadratic trigonometric spline including three positive parameters was devised to produce a shaped interpolant for given shaped data. Positive and monotone curve interpolation schemes were presented to sustain the respective shape features of data. Each scheme was tested for plentiful shaped data sets to substantiate the assertion made in their construction. Moreover, these schemes were compared with conventional shape preserving rational quadratic splines to demonstrate the usefulness of their construction

Rational Cubic Ball Interpolants For Shape Preserving Curves And Surfaces

Interpolan pengekalan bentuk adalah satu teknik rekabentuk lengkung/ permukaan yang sangat penting dalam CAD/-CAM dan rekabentuk geometric Shape preserving interpolation is an essential curve/surface design technique in CAD/CAM and geometric desig

Interpolating yield curve data in a manner that ensures positive and continuous forward curves

This paper presents a method for interpolating yield curve data in a manner that ensures positive and continuous forward curves. As shown by Hagan and West (2006), traditional interpolation methods suffer from problems: they posit unreasonable expectations, or are not necessarily arbitrage-free. The method presented in this paper, which we refer to as the "monotone preserving r(t)r method", stems from the work done in the field of shape preserving cubic Hermite interpolation, by authors such as Akima (1970), de Boor and Swartz (1977), and Fritsch and Carlson (1980). In particular, the monotone preserving r(t)r method applies shape preserving cubic Hermite interpolation to the log capitalisation function. We present some examples of South African swap and bond curves obtained under the monotone r(t)r preserving method.http://www.sajems.org/am201

Local convexity preserving rational cubic spline curves

A scheme for generating plane curves which interpolates given data is described. A curve is obtained by patching together rational cubics and straight-line segments which, in general, is C1 continuous. It is a local scheme which controls the shape of the curve and preserves the shape of the data by being local convexity-preserving. A particular scheme is suggested which selects the tangent vectors required at each interpolation point for generating a curve. An algorithm is presented which constructs a curve by interpolating the given data points. This scheme provides a visually pleasant display of the curve's presentation. An extra feature of this curve scheme is that it allows subsequent interactive alteration of the shape of the default curve by changing the shape control parameters and the shape-preserving parameters associated with each curve segment. Thus, this feature is useful for further enhancing the user satisfaction, if desire

Local convexity preserving rational cubic spline curves

A scheme for generating plane curves which interpolates given data is described. A curve is obtained by patching together rational cubics and straight-line segments which, in general, is C1 continuous. It is a local scheme which controls the shape of the curve and preserves the shape of the data by being local convexity-preserving. A particular scheme is suggested which selects the tangent vectors required at each interpolation point for generating a curve. An algorithm is presented which constructs a curve by interpolating the given data points. This scheme provides a visually pleasant display of the curve's presentation. An extra feature of this curve scheme is that it allows subsequent interactive alteration of the shape of the default curve by changing the shape control parameters and the shape-preserving parameters associated with each curve segment. Thus, this feature is useful for further enhancing the user satisfaction, if desire

Visualization Of Curve And Surface Data Using Rational Cubic Ball Functions

This study considered the problem of shape preserving interpolation through regular data using rational cubic Ball which is an alternative scheme for rational Bézier functions. A rational Ball function with shape parameters is easy to implement because of its less degree terms at the end polynomial compared to rational Bézier functions. In order to understand the behavior of shape parameters (weights), we need to discuss shape control analysis which can be used to modify the shape of a curve, locally and globally. This issue has been discovered and brought to the study of conversion between Ball and Bézier curve

Shape Preserving Spline Interpolation

A rational spline solution to the problem of shape preserving interpolation is discussed. The rational spline is represented in terms of first derivative values at the knots and provides an alternative to the spline-under-tension. The idea of making the shape control parameters dependent on the first derivative unknowns is then explored. The monotonic or convex shape of the interpolation data can then be preserved automatically through the solution of the resulting non-linear consistency equations of the spline

Shape-preserving algorithms for curve and surface design

PhD ThesisThis thesis investigates, develops and implements algorithms for shape- preserving curve and surface design that aim to reflect the shape characteristics of the underlying geometry by achieving a visually pleasing interpolant to a set of data points in one or two dimensions. All considered algorithms are local and useful in computer graphics applications. The thesis begins with an introduction to existing methods which attempt to solve the shape-preserving 1 curve interpolation problem using C cubic and quadratic splines. Next, a new generalized slope estimation method involving a parameter t, which is used to control the size of the estimated slope and, in turn, produces a more visually pleasing shape of the resulting curve, is proposed. Based on this slope generation formula, new automatic and interactive algorithms for constructing 1 shape-preserving curves from C quadratic and cubic splines are developed and demonstrated on a number of data sets. The results of these numerical experiments are also presented. Finally, a method suggested by Roulier which 1 generates C surfaces interpolating arbitrary sets of convex data on rectangular grids is considered in detail and modified to achieve more visually pleasing surfaces. Some numerical examples are given to demonstrate the performance of the method.Ministry of Education, Government of Pakista