arXiv subjects

D. K. Lobiyal

Publications and source records attributed to D. K. Lobiyal.

6 recordsLinked to original sources

arXiv2020

Algorithms and Identities for B$\acute{e}$zier curves via Post Quantum Blossom

In this paper, a new analogue of blossom based on post quantum calculus is introduced. The post quantum blossom has been adapted for developing identities and algorithms for Bernstein bases and B$\acute{e}$zier curves. By applying the post quantum blossom, various new identities and formulae expressing the monomials in terms of the post quantun Bernstein basis functions and a post quantun variant of Marsden's identity are investigated. For each post quantum B$\acute{e}$zier curves of degree $m,$ a collection of $m!$ new, affine invariant, recursive evaluation algorithms are derived.

cs.GR↗

arXiv2016

B$\acute{e}$zier curves based on Lupaş $(p,q)$-analogue of Bernstein polynomials in CAGD

In this paper, we use the blending functions of Lupaş type (rational) $(p,q)$-Bernstein operators based on $(p,q)$-integers for construction of Lupaş $(p,q)$-B$\acute{e}$zier curves (rational curves) and surfaces (rational surfaces) with shape parameters. We study the nature of degree elevation and degree reduction for Lupaş $(p,q)$-B$\acute{e}$zier Bernstein functions. Parametric curves are represented using Lupaş $(p,q)$-Bernstein basis. We introduce affine de Casteljau algorithm for Lupaş type $(p,q)$-Bernstein B$\acute{e}$zier curves. The new curves have some properties similar to $q$-B$\acute{e}$zier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain $(u, v) \in [0, 1] \times [0, 1] $ depending on four parameters. We also study the de Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain. We get $q$-B$\acute{e}$zier surfaces for $(u, v) \in [0, 1] \times [0, 1] $ when we set the parameter $p_1=p_2=1.$ In comparison to $q$-B$\acute{e}$zier curves and surfaces based on Lupaş $q$-Bernstein polynomials, our generalization gives us more flexibility in controlling the shapes of curves and surfaces. We also show that the $(p,q)$-analogue of Lupaş Bernstein operator sequence $L^{n}_{p_n,q_n}(f,x)$ converges uniformly to $f(x)\in C[0,1]$ if and only if $0 0$ fixed and $p \neq 1,$ the sequence $L^{n}_{p,q}(f,x)$ converges uniformly to $f(x)~ \in C[0,1]$ if and only if $f(x)=ax+b$ for some $a, b \in \mathbb{R}.$

cs.GR↗

arXiv2015

A de Casteljau Algorithm for Bernstein type Polynomials based on (p,q)-integers

In this paper, a de Casteljau algorithm to compute (p,q)-Bernstein Bezier curves based on (p,q)-integers is introduced. We study the nature of degree elevation and degree reduction for (p,q)-Bezier Bernstein functions. The new curves have some properties similar to q-Bezier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain (u, v) \in [0, 1] \times [0, 1] depending on four parameters. We also study the de Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain. Furthermore, some fundamental properties for (p,q)-Bernstein Bezier curves are discussed. We get q-Bezier curves and surfaces for (u, v) \in [0, 1] \times [0, 1] when we set the parameter p1 = p2 = 1.

cs.GR↗

arXiv2015

Bezier curves and surfaces based on modified Bernstein polynomials

In this paper, we use the blending functions of Bernstein polynomials with shifted knots for construction of Bezier curves and surfaces. We study the nature of degree elevation and degree reduction for Bezier Bernstein functions with shifted knots. Parametric curves are represented using these modified Bernstein basis and the concept of total positivity is applied to investigate the shape properties of the curve. We get Bezier curve defined on [0, 1] when we set the parameter α=βto the value 0. We also present a de Casteljau algorithm to compute Bernstein Bezier curves and surfaces with shifted knots. The new curves have some properties similar to Bezier curves. Furthermore, some fundamental properties for Bernstein Bezier curves and surfaces are discussed.

cs.GR↗

arXiv2015

Performance evaluation of different optimization techniques for coverage and connectivity control in backbone based wireless networks

In this paper, performance evaluation of Newton-Raphson and Conjugate Gradient method has been studied in comparison to Steepest Decent method for coverage and connectivity control in backbone based wireless networks. In order to design such wireless networks, the main challenge is to ensure network requirements such as network coverage and connectivity. To optimize coverage and connectivity, backbone nodes will be repositioned by the use of mobility control based on above mentioned methods. Thus the network get self organized which autonomously achieve energy minimizing configuration. Furthermore by simulation using MATLAB R2010a, methods are compared on the basis of optimized cost, number of iterations and elapsed time i.e. total time taken to execute the algorithm.

cs.NI↗

arXiv2012

Performance Evaluation of Realistic Vanet Using Traffic Light Scenario

Vehicular Ad-hoc Networks (VANETs) is attracting considerable attention from the research community and the automotive industry to improve the services of Intelligent Transportation System (ITS). As today's transportation system faces serious challenges in terms of road safety, efficiency, and environmental friendliness, the idea of so called "ITS" has emerged. Due to the expensive cost of deployment and complexity of implementing such a system in real world, research in VANET relies on simulation. This paper attempts to evaluate the performance of VANET in a realistic environment. The paper contributes by generating a real world road Map of JNU using existing Google Earth and GIS tools. Traffic data from a limited region of road Map is collected to capture the realistic mobility. In this work, the entire region has been divided into various smaller routes. The realistic mobility model used here considers the driver's route choice at the run time. It also studies the clustering effect caused by traffic lights used at the intersection to regulate traffic movement at different directions. Finally, the performance of the VANET is evaluated in terms of average delivery ratio, packet loss, and router drop as statistical measures for driver route choice with traffic light scenario. This experiment has provided insight into the performance of vehicular traffic communication for a small realistic scenario.

cs.NI↗