Visualization of surface data to preserve positivity and other simple constraints

Brodlie, Ken; Mashwama, Petros; Butt, Sohail

doi:10.1016/0097-8493(95)00036-c

Cited by 51 publications

(42 citation statements)

References 4 publications

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“…Schmidt and Heβ [14] used cubic polynomial interpolant and constrained its derivative at knots to preserve the positive shape of curve data. Brodlie et al [1] constructed a piecewise bi-cubic function f (x, y) from data on a rectangular grid, such that f (x, y) is positive. Sufficient conditions for positivity were derived in terms of the first partial derivatives and mixed partial derivatives at the grid points.…”

Section: Introductionmentioning

confidence: 99%

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Positive interpolation by trigonometric functions

Hussain

Saddiqa

2015

Afr. Mat.

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A C 1 rational quadratic trigonometric interpolating function with three parameters is developed. The order of approximation of the developed C 1 trigonometric interpolant is O(h 2 i ). The C 1 rational quadratic trigonometric function is extended to a C 1 bivariate rational quadratic trigonometric function. The developed C 1 bivariate trigonometric interpolant has six parameters in each rectangular patch. Automatic selection schemes for parameters are developed to preserve the positive shape of curve and surface data using C 1 rational quadratic trigonometric function and C 1 bivariate rational quadratic trigonometric function respectively. Performing the result, it is noticed that developed positivity preserving interpolation schemes are fast, efficient and well suited for all data types. Several numerical examples are presented to ascertain the correctness and usability of developed schemes.

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Section: Introductionmentioning

confidence: 99%

“…The significant contributions towards the problem of positivity preserving interpolation are Brodlie et al [1], Butt and Brodlie [2], Lamberti and Manni [9], Schmidt and Heβ [14]. Butt and Brodlie [2] and Lamberti and Manni [9] used cubic Hermite interpolant for stitching of data.…”

Section: Introductionmentioning

confidence: 99%

Positive interpolation by trigonometric functions

Hussain

Saddiqa

2015

Afr. Mat.

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“…The algorithm of Butt and Brodlie [3] works by inserting one or two extra knots, wherever necessary, to preserve the shape of positive data. Brodlie, M ashwama and Butt [2] developed a scheme to preserve the shape of positive surface data by the rearrangement of data and inserted one or more knots, where ever required, to preserve the shape of the data. Piah, Goodman and Unsworth [10] discussed the problem of positivity preservation for scattered data.…”

Section: Introductionmentioning

confidence: 99%

“…The problem of shape preservation has been discussed by a number of authors. In recent years, a good amount of work has been published [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] that focuses on shape preserving curves and surfaces. The motivation of the work, in this paper, is due to the past work of many authors.…”

Section: Introductionmentioning

confidence: 99%

Shape Preserving Surfaces for the Visualization of Positive and Convex Data using Rational Biquadratic Splines

Hussain¹,

Sarfraz²,

Shakeel³

2011

IJCA

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A smooth surface interpolation scheme for positive and convex data has been developed. This scheme has been extended from the rational quadratic spline function of Sarfraz [11] to a rational bi-quadratic spline function. Simple data dependent constraints are derived on the free parameters in the description of rational bi-quadratic spline function to preserve the shape of 3D positive and convex data. The rational spline scheme has a unique representation.The developed scheme is computationally economical and visually pleasant.

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“…Besides, the data that lie on one side of a constraint surface need to have an interpolant on the same side of the constraint. In recent years, a decent number of preservation methods have been published, such as [1], [2], [3], [4] and [5].…”

Section: Introductionmentioning

confidence: 99%