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Monotone cubic interpolation

About: Monotone cubic interpolation is a research topic. Over the lifetime, 1740 publications have been published within this topic receiving 38111 citations.


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TL;DR: In this paper, the problem of monotonicity preservation of surfaces through 3D monotone data is discussed using a rational bi-cubic blended function that is an extension of a rational cubic function in the form of a cubic numerator and quadratic denominator.
Abstract: We discuss the problem of monotonicity preservation of surfaces through 3D monotone data. This can be done using a rational bi-cubic blended function that is an extension of a rational cubic function in the form of a cubic numerator and quadratic denominator. The function involves twelve shape parameters in each rectangular patch. Data- dependent constraints are derived on four of these shape parameters to conserve the shape of the data while the other eight are left free to modify the monotone surface as desired. Several numerical examples are presented to show the effectiveness and capability of the scheme. The present scheme isC 1 , flexible, simple, local, and economical.

5 citations

Journal ArticleDOI
TL;DR: These methods are based on discrete weighted cubic splines and results in two algorithms with automatic selection of the shape control parameters: one to preserve the data monotonicity and other to retain the data convexity.
Abstract: This paper presents methods for shape preserving spline interpolation. These methods are based on discrete weighted cubic splines. The analysis results in two algorithms with automatic selection of the shape control parameters: one to preserve the data monotonicity and other to retain the data convexity. Discrete weighted cubic B-splines and control point approximation are also considered.

5 citations

Journal ArticleDOI
TL;DR: An efficient interpolating method based on the tension trigonometric splines with various properties, such as partition of unity, geometric invariance and convex hull property, etc is applied to construct curves and surfaces.
Abstract: In this work a family of tension trigonometric curves analogous to those of cubic Bézier curves is presented. Some properties of the proposed curves are discussed. We propose an efficient interpolating method based on the tension trigonometric splines with various properties, such as partition of unity, geometric invariance and convex hull property, etc. This new interpolating method is applied to construct curves and surfaces. Moreover, one can adjust the shape of the constructed curves and surfaces locally by changing the tension parameter, the latter is included mainly because of its importance for object visualization. To illustrate the performance and the practical value of this model as well as its accuracy and efficiency, we present some modeling examples. Mathematics Subject Classification: 65T40, 65D05, 65D17, 76B45.

5 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202316
202227
20191
201812
201740
201652