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

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 C2C^2 interpolatory subdivision schemes

Stationary interpolatory subdivision schemes which preserve shape properties such as convexity or monotonicity are constructed. The schemes are rational in the data and generate limit functions that are at least $C^2$. The emphasis is on a class of six-point convexity preserving subdivision schemes that generate $C^2$ limit functions. In addition, a class of six-point monotonicity preserving schemes that also leads to $C^2$ limit functions is introduced. As the algebra is far too complicated for an analytical proof of smoothness, validation has been performed by a simple numerical methodology

Local Convexity-Preserving C

We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data using C2 rational cubic spline. It involves three families of shape parameters in its representation. Data dependent sufficient constraints are imposed on single shape parameter to conserve the inherited shape feature of data. Remaining two of these shape parameters are used for the modification of convex curve to get a visually pleasing curve according to industrial demand. The scheme is tested through several numerical examples, showing that the scheme is local, computationally economical, and visually pleasing

Polynomial cubic splines with tension properties

In this paper we present a new class of spline functions with tension properties. These splines are composed by polynomial cubic pieces and therefore are conformal to the standard, NURBS based CAD/CAM systems

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

A tension approach to controlling the shape of cubic spline surfaces on FVS triangulations

We propose a parametric tensioned version of the FVS macro-element to control the shape of the composite surface and remove artificial oscillations, bumps and other undesired behaviour. In particular, this approach is applied to C1 cubic spline surfaces over a four-directional mesh produced by two-stage scattered data fitting methods