This article primarily focuses on the utilization and importance of parametric curves in surface design. It delves into the construction and applications of parametric curves, exploring the implementation of trigonometric polynomial basis functions that possess two shape parameters. Initially, these basis functions are employed in constructing both rational and non-rational curves. Later, they are employed to define the surfaces generated by these curves. The discussion includes rational surfaces, tensor product surfaces, and various specialized surfaces. The aim is to provide a comprehensive understanding of the role and potential of parametric curves in surface design.

This paper proposes an optical sensor based on nanoscale metamaterial structures. The design of the sensor has been explored with respect to biosensing applications through numerical modeling and analysis. The sensor comprises silica substrate and diamond nanostructures, both of which represent dielectrics. The sensing principle is based on the detection of ambient refractive index change. As the analyte properties change, the refractive index changes, as well. The refractive index change has been detected by striking electromagnetic waves onto the structure and noting the spectral response. Ultraviolet waves have been utilized for recording spectral responses and evaluating sensor performance. The sensor displays multiple sharp resonance peaks in the reflected beam. By altering the refractive index of the analyte present around the sensor, the peaks can be seen choosing different wavelengths. The resonance peaks have been investigated to observe electric and magnetic field dipoles in the sensor structure. The spectrum peaks have also been studied to understand fabrication tolerances. The sensor displays a linear response, along with a large Quality (Q) factor. The maximum value of the achieved Quality (Q) factor for the proposed sensor is 1229 while operating across the refractive index range of 1.4–1.45. The claim has been supported by comparison with contemporary works on similar platforms. A range of other sensing parameters have also been calculated and benchmarked. Metamaterial-based optical sensors can provide smaller device sizes, faster response times and label-free detection.

Geometric modelling of several intricate and complex structures such as trees, mountains, clouds, ferns, geographic topography, and coastlines is challenging in computer graphics. Traditional splines such as trigonometric, polynomial, exponential, and rational fail to simulate this significant class of complex structures, which are highly irregular in nature. For this purpose, this research develops a novel cutting-edge method for synthesizing and modelling structures. The proposed technique; C 1 fractal interpolation function (FIF) builds an iterated function system (IFS) by integrating fractal calculus and rational cubic polynomial functions. Appropriate conditions on scaling and shape parameters are derived to help maintain the inherited shape qualities of the data. Experiments in numerous scientific domains, such as the pharmaceutical and chemical industries have been presented as an example, to confirm the usefulness of the suggested model. Moreover, the graphic results demonstrated that the developed monotone hybrid model (MHM) offers a heterogeneous method for gathering data with a monotone structure.

In this study, shape preserving data driven rational cubic schemes are developed. A rational cubic piecewise function (quadratic denominator and cubic numerator) with two parameters was transformed to C¹ rational cubic piecewise function. Constraints were derived on free parameters by means of some mathematical derivations to train and demonstrate convex curve. The scheme, then, was advanced to partially blended rational bi-cubic function with eight free parameters which were controlled to ascertain convex surface. A numerical comparison with certain existing schemes manifested that the proposed method was economical. The proposed scheme was put into visualization of convex 2D and 3D data using MATLAB software packet. Additionally, the suggested approach produced a more visually appealing interpolating curve for scientific visualization for specific data sets.