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

Positive Data Visualization Using Trigonometric Function

A piecewise rational trigonometric cubic function with four shape parameters has been constructed to address the problem of visualizing positive data. Simple data-dependent constraints on shape parameters are derived to preserve positivity and assure smoothness. The method is then extended to positive surface data by rational trigonometric bicubic function. The order of approximation of developed interpolant is

Constrained Interpolation By Parametric Rational Cubic Splines

Interpolasi terkekang adalah berguna dalam masalah seperti mereka bentuk sebuah Iengkung yang perlu dihadkan dalam suatu kawasan tertentu. Dalam disertasi ini, kami membincangkan interpolasi terkekang dengan menggunakan splin kubik nisbah yang diperkenalkan dalam (Goodman et aI, 1991). Terdapat dua kaedah pengubahsuaian lengkung disarankan, kaedah yang melibatkan modifikasi pemberat a,p berkaitan dengan titik hujung segmen lengkung dibincangkan dalam disertasi ini. Skim ini memperoleh sebuah G2 lengkung interpolasi yang terletak di sebelah garis-garis yang diberikan seperti data yang diberikan. Sebagai perkembangan daripada kertas ini, kami akan memperoleh satu skim interpolasi terkekang altematif dengan menggunakan lengkung kubik nisbah. Pemberat n, e yang berkaitan dengan titik kawalan dalaman diubah suai untuk memperoleh sebuah G1 lengkung interpolasi yang terletak di sebelah garis-garis yang diberikan seperti data yang diberikan. Constrained interpolation could be useful in problem like designing a curve that must be restricted within a specified region. In this dissertation, we discuss constrained interpolation using rational cubic splines introduced in (Goodman et aI, 1991). There are two curve modification methods suggested and the one which involves modification of the weights a ,fJ associated with the end points of the curve segments is discussed in this dissertation. This scheme obtains a G2 interpolating curve which lies on one side of the given lines as the given data. Extension from this paper, we will derive an alternative constrained interpolation scheme using rational cubic curve. The weights Q , e associated with the inner control points are modified to obtain a G1 interpolating curve which lies on one side of the given lines as the given data

Fitting Constrained Continuous Spline Curves.

Fitting a curve through a set of planar data which represents a positive quantity requires that the curve stays above the horizontal axis, The more general problem of designing parametric and non-parametric curves which do not cross the given constraint boundaries is considered. Several methods will be presented

Tabulation of cubic function fields via polynomial binary cubic forms

We present a method for tabulating all cubic function fields over $\mathbb{F}_q(t)$ whose discriminant $D$ has either odd degree or even degree and the leading coefficient of $-3D$ is a non-square in $\mathbb{F}_{q}^*$, up to a given bound $B$ on the degree of $D$. Our method is based on a generalization of Belabas' method for tabulating cubic number fields. The main theoretical ingredient is a generalization of a theorem of Davenport and Heilbronn to cubic function fields, along with a reduction theory for binary cubic forms that provides an efficient way to compute equivalence classes of binary cubic forms. The algorithm requires $O(B^4 q^B)$ field operations as $B \rightarrow \infty$. The algorithm, examples and numerical data for $q=5,7,11,13$ are included.Comment: 30 pages, minor typos corrected, extra table entries added, revamped complexity analysis of the algorithm. To appear in Mathematics of Computatio

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