An Improved C1 rational Bernstein–Bézier triangular patch for scattered data interpolation

IF 1.4 Q2 MATHEMATICS, APPLIED Results in Applied Mathematics Pub Date : 2024-10-01 DOI:10.1016/j.rinam.2024.100501

Owen Tamin , Samsul Ariffin Abdul Karim , Mohammad Khatim Hasan

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Abstract

Scattered data interpolation is important in sciences, engineering, and medical-based problems. The degree smoothness attained is either

C^{1}

C^{2}

. However, based on our simulations, we found that, Hussain and Hussain (2011) scheme is not producing

C^{1}

everywhere. Motivated by this, in this study we will propose an improve sufficient condition for the

C^{1}

on each adjacent triangle. Our scheme is guaranteed to produce

C^{1}

everywhere. To support our claim, we have implemented both schemes and perform some numerical comparison including error measurement. From the results, our proposed scheme is producing

C^{1}

interpolating surface while the interpolating surface produced by Hussain and Hussain (2011) is not

C^{1}

everywhere. Furthermore, our proposed scheme give smaller error compared with Hussain and Hussain (2011) scheme. All numerical and graphical results are presented by using MATLAB programming.

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用于零散数据插值的改进型 C1 有理伯恩斯坦-贝塞尔三角形补丁

散点数据插值在科学、工程和医学问题中非常重要。达到的平滑度为 C1 或 C2。然而，根据我们的模拟，我们发现 Hussain 和 Hussain（2011 年）的方案并不是在所有地方都能达到 C1。有鉴于此，在本研究中，我们将提出一个改进的充分条件，使每个相邻三角形都能达到 C1。我们的方案保证在所有地方都能生成 C1。为了支持我们的主张，我们实施了这两种方案，并进行了一些数值比较，包括误差测量。从结果来看，我们提出的方案产生了 C1 插值面，而 Hussain 和 Hussain（2011 年）提出的方案产生的插值面并非处处都是 C1。此外，与 Hussain 和 Hussain（2011 年）的方案相比，我们提出的方案产生的误差更小。所有数值和图形结果均通过 MATLAB 编程呈现。

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