akhlaq ahmad name

The difference between scattered data interpolation and scattered data fitting was also demonstrated in the survey. For example, meteorological measurements at different weather stations [ 1 ], density measurements on different positions within the human body, heart potential measurements at random points in the diagnosis of various ailments of heart [ 2 ], 3D photography, aeronautical engineering and industrial design, structural graph networks [ 3 ], graph entropy [ 4 ], [ 5 ], [ 6 ]. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited. Author information Article notes Copyright and License information Disclaimer. Positivity is attained by deriving data dependent condition on half of the parameters in the description of C 1 rational trigonometric cubic function [ 13 ].

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Orthogonality of trigonometric function assures much smoother surface as compared to polynomial functions. Table 2 A Positive scattered data set II. Section 5 demonstrates the developed algorithm and presents graphical results. Positive Scatter Data Interpolation This section ahamd the derivation of sufficient conditions for C 1 triangular patches to be positive.


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Applied Mathematics and Computation. Special Awards from Nigar Xkhlaq. The C 1 rational trigonometric cubic function [ 13 ] with four parameter has been used for the interpolation along boundary and radial curve of the triangle. The resulting surface S xy described as.

Muhammad Akhlaq Ahmed – Wikipedia

The side-vertex method for interpolation in triangles. Numerical Examples This section illustrates the positivity preserving scheme for scattered data devised in Section 4. Akhlaq debuted as a singer in the film, Pazaib with music by Lal Mohammad Iqbal.

R 3 and R 4 are the directional derivatives at Mame 2 and S 2. Positivity of data was achieved by imposing sufficient conditions on Bezier ordinates in each namd patch.

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The scheme suggested in this paper does ah,ad suffer this detriment. The rational trigonometric cubic function Eq 1 satisfy the following properties:. Hussain MZ, Hussain M. Cubic and quintic Hermite interpolants were used for preserving monotonicity, positivity and convexity of discrete data by [ 8 ]. Introduction Data measured or amassed from many engineering and scientific fields, is often positioned at sparse points.

Likewise, radial curve Q 2 connecting vertex V 2 to the points S 2 on the opposite edges e 2 is nme as. International Journal of Numerical Methods in Engineering.

Muhammad Akhlaq Ahmed

He was a member of shmad famous singing group from Karachi with two other artists,film playback singer Masood Rana and film actor Nadeem. His song tally is under hundred songs.


His wife, an employee at PIA admitted him at a hospital in London. The author mainly examined radial basis function method, tetrahedral interpolation, cubic akhpaq interpolation, triangle based blending interpolation, inverse distance method and neutral neighbourhood. Section 2 reviews the ratonal trigonometric cubic function [ 13 ]. GhazalPlayback singing. Articles with hCards Articles containing Urdu-language text All stub articles.

Constraints on half of the parameters are obtained to guarantee the positive shape of data while half are set free for users modification. Probabilistic inequalities for evaluating structural network measures. Since the barycentric coordinates at the vertices of triangle is simultaneously zero, the interpolant Eq 4 takes the following values:.

Final surface patch was obtained by convex combination of interpolants. He died on August 4,at London.

Akhlaq Ahmed – Wikipedia

A C 1 local rational cubic Bernstein Bezier interpolatory scheme was proposed by Hussain and Hussain [ 12 ] to retain positivity of scattered data. Section 5 summarizes this research and draws conclusion. Support Center Support Center. C 1 Quadratic splines and Powell-Sabin splines were used as interpolating function to tackle the problem of range restricted univariate and bivariate scattered data by Aohlaq et.