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3D geometric designing using linear algebra.
(UMT Lahore, 2022-07-22) Roshi Anwar; Hafiza Arooj Azeem; Syeda Tayyiba Zamir; Rimsha Shahid
Interest in systems with a free license has grown over the past several years. The Blender is a robust system for 3D design that comes with a free license. A growing number of people are becoming interested in the Blender 3D graphic system because of its compact volume, lack of significant high hardware system needs, numerous benefits, and advancements. The adoption of the open-source Blender system in design practice is justified as being reasonable and correct given this trend's quick, nonlinear positive evolution. It is well known that a large range of software programs are available in the field of 3D graphic design. The makers of 3D software always work to add new features and improve the packages they provide. In actuality, some users may not be able to afford the costs of some of the premium 3D graphics tools. The right 3D system must also take into account its large data capacity and demanding hardware requirements. In recent years, the standards for the quality of the finished result have increased in relation to the computing power of software packages, the design methodologies used during computer design, and particularly the finished visualizations of static and animated models. Given these elements, selecting the best 3D graphics system is a crucial requirement for the design process. This supports the incorporation of a Blender into suggested design practice. Blender is a current technology program that many users like because of its free licensing, open source, easy interface, multilateral design characteristics, and light hardware needs.
An analysis of curvature types and their real world applications
(UMT Lahore, 2025) SABA AKRAM
Curvature plays a fundamental role in various scientific and engineering disciplines, influencing structural stability, motion dynamics, and spatial analysis. This study explores different types of curvature, including Gaussian, mean, and geodesic curvature, and their real-world applications across multiple fields. In engineering and architecture, curvature analysis ensures the optimal design of bridges, roads, and buildings, enhancing durability and safety. In aerospace and automotive industries, aerodynamic efficiency is achieved through curvature optimization in vehicle and aircraft design. Medical imaging and biomechanics utilize curvature principles for accurate diagnostics and treatment planning, particularly in orthopedics and radiology. Additionally, curvature analysis is integral to robotics, environmental modeling, and national security, aiding in precision manufacturing, terrain mapping, and biometric recognition. By understanding and applying curvature concepts, industries can develop more efficient, safe, and innovative solutions, demonstrating the significance of curvature analysis in modern technological advancements.
Analysis and applications of subdivision surfaces
(UMT Lahore, 2023-07) Samer Iqbal; Talha Naveed
The subdivision surface is a convenient way to model objects with arbitrary topologies. Using non-uniformly sampled data points, we reconstruct objects using a piecewise smooth subdivision scheme that we analyze in this dissertation. Subdivision surfaces are well-defined, smooth tangent plane surfaces (G1) that result from repeated refinement of a mesh of 3D control points. A great deal of attention has been paid to the analysis of smooth surface schemes with symmetrical rules around each vertex and edge in the scheme. Surfaces with sharp features, however, can be created in a scheme that does not exhibit this symmetry. By using eigen analysis and characteristic maps for quartic triangular B-spline surfaces, a piecewise smooth subdivision scheme is analyzed for such surfaces. Objects have been reconstructed from 3D data using subdivision surfaces as optimized surface fittings. Dense and uniform samples of data have been used to create accurate representations of objects in the past. As a practical low-cost alternative to the construction of subdivision surfaces by hand, we propose an algorithm that computes subdivision surfaces from data.
Application of regression and correlation in real life
(UMT Lahore, 2022) Majid Ali
The regression and the correlation is frequently used statistical methods to inspect the relationship between any two or more than two variables. In our life there are many problems in which the correlation and regression help us to solve the problem. Here in this project we have discussed some of the real-life problems and their solutions using correlation and regression. By using these methods, we can solve many different problems of different fields. It is also very helpful in finding the relationship between the stocks of the markets.
Application of topsis for real life mcdm problem of motor bike selection
(UMT Lahore, 2022) Hassan Naveed
In real life, multi criteria decision making is very important. Multi criteria decision making techniques are used for the best selection given the attributes. First of all, a universal set (∪), (𝐴) is the subset of 𝑈, (𝐴) is the set of bikes under consideration. ⊆𝑈 and (𝐸) is the set of attribute of (𝐴). The generalized results of TOPSIS on soft set from TOPSIS on fuzzy-soft-set. In this problem, we select a best bike for use in our daily life. Bike is a basic need of almost every person in Pakistan. Due to its increasing demand and the competition in the Pakistani market, all companies claim that their bike is the best. We use the fuzzy, soft set and fuzzy soft set on TOPSIS method for the selection of a bike by using data and scrutinize the relative ranking of the best motor bikes according to chosen parameters.
Applications of certain fuzzy clustering algorithms on cyclic networks
(UMT Lahore, 2022-08-23) Inayat Karim
The fuzzy c-medoids algorithm (FCMdd) and robust fuzzy c-medoid algorithm (RFCMdd) [16] are used in clustering relational data. In this paper, we have modified FCMdd (mFCMdd) and also modified RFCMdd (mRFCMdd) by introducing a similarity relation comparing with the Cn graph to make FCMdd and RFCMdd algorithms useful for cluster cyclic networks. These algorithms are based on the graph distance of object to object, where the number of edges in the shortest path between two objects is considered as a measure of dissimilarity. We have also added applications to mFCMdd and mRFCMdd.
Applications of RK method in physics and computer science.
(UMT Lahore, 2023-06-07) Qasim Raza
In unique research, the Runge-Kutta is the most popular technique with a large number of stages computed using the order method. The RK technique is the more generalized concept employed in the modified Euler approach. By using the RK approach to solve numerical solutions of ordinary equations like explicit, delay, and partial differential equations in modern concepts today. The current study indicates a review of modern computational approaches for more favorable solving large-scale differential equations employing the RK algorithm of many orders. We also used the RK method in C language with output. Additionally, running this process on Turbo C and available versions and other platforms must obtain a few modification steps to the modern code. Finally, comparisons of approaches with their precarious comments as remarks have been also included.
Applications of the Sumudu transform to fractional differential equations
(UMT Lahore, 2023-08) Maria Jabeen; Sadia Batool
The Sumudu transform's use with fractional differential equations is covered in this paper. A relatively advanced integral transform with a broad range of applications, the Sumudu transform has become more well-known in recent years. In this study, we embellish the efficiency of the Sumudu transform in solving differential equations with fractions by applying it to various kinds of problems. We provide various examples to demonstrate the use of the Sumudu transform and contrast its outcomes with those attained using alternative techniques. Our findings show that this Sumudu transform is capable of being used as an instrument for solving differential equations with fractions.
Bezier curve in 3D
(UMT Lahore, 2022) Zara Jamil; Khola Aftab
The objective of this undertaking was to make a 3D model of a certifiable model and prepare it into an import resource for be utilized for games and other displaying programming. Throughout recent years another industry has developed and created as the world's innovation turned out to be quicker, more remarkable and reasonable. This industry is 3D computer animation. Whether you watch motion pictures or TV, read magazines or papers, it is an interesting day when you don't see 3D PC pictures of some kind. 3D movement permitted the movies to look more reasonable and this innovation was embraced regardless of the way that making such a film is more enthusiastically. Character drawing is the initial step of 3D movement. To make a 3-deck model, the craftsman makes photos of characters according to however many viewpoints as could reasonably be expected. Almost similarly the person modeler involves earth or stone for making a genuine figure, he picks various strategies for cutting the cut model. The primary distinction is that on a virtual organization this is accomplished. The made undertaking for additional improvement of the model and study how this present reality can be moved to a game climate. Toward the end there ought to be a functioning 3D model resource for be utilized in ongoing tasks for game turn of events or further clean the model in a 3D displaying program. Animations is significant on the grounds that it empowers us to recount stories and express feelings and thoughts in a manner that is extraordinary to youngsters and grown-ups. It has basically been a method for making a wet, insightful story. Surprisingly realistic movies urge individuals to make biased focuses in light of a person entertainer's appearance and genuine character. Be that as it may, the person seems to be its own being as an enlivened person. The apparatuses utilized in this venture is Blender 3D displaying programming. The scene is created and the characters are moved by the illustrator who utilizes Blender to deliver the development deception by giving the underlying and the last places of the ideal moves. Along these lines, individuals need to see a daily existence like film. Obviously, it's one of the most widely recognized filmmaking modes.
Cluster Project
(UMT Lahore, 2022-07) Mahnoor
Comprehensive study of tangent plane and its applications
(UMT Lahore, 2024-09-02) ABDULLAH HASSAN
The comprehensive study of tangent planes holds significant national importance in that it advances engineering, technology, and industry processes as the means to economic growth and innovation. The role of the tangent plane in making accurate mathematical models used in the design and optimization of infrastructure like bridges, highways, and buildings for their safety and efficiency is very crucial. This contributes to the development of dependable and sustainable structures necessary for any national infrastructure. In technology and manufacturing, having some level of understanding about tangent planes can help in the designing of better systems and processes to bring about cost reduction with enhanced product quality. With such advancement, the competitive edge of any nation can be bolstered in global markets, helping along industrial innovation. These mathematical concepts also become very important for educational and research institutions that enable the availability of an able workforce which will help drive further technological innovations in the time to come. Moreover, from the point of view of sustainable development, with the application of mathematical modeling by using tangent planes, a number of more eco-friendly solutions can be devised, like optimized consumption of energy in buildings and transport. It is through the use of these modern mathematical methods that the nations will be able to gain sustainable growth, reduce environmental impacts, and enhance the quality of life for the citizens in order to become leaders both in technological and environmental respect.
Computation of reverse and hyper-reverse topological indices and polynomials of subdivision graphs of Sierpinski networks
(UMT Lahore, 2022-07-14) Muhammad Nouman
Computation of SEIR model of outbreak virus using RK4 method
(UMT Lahore, 2023-08) Zahrah Fatima; Kinza Shahzadi
In this study, we formulate the mathematical model of COVID-19 with the effects of partially and fully vaccinated individuals. Here, the purpose of formulating the model is to study these models numerically. It is very complex to solve the four equations of the SEIR model, so we use the fourth-order Runge-Kutta method to solve those equations. This method is very efficient and practically suited for solving initial value problems. That’s why we formulated the SEIR model with the incorporation of fully and partially vaccinated parameters. Then we try to solve our equations by converting them into the fourth-order Runge-Kutta method. Moreover, to make the model more realistic, we assume the outbreak of COVID-19 in Bangladesh. We used Python for simulation purposes.
Computer aided geometric design in animation using 3D graphic software
(UMT Lahore, 2023-06) Irfan Sharif; Ali Haider
Computer aided geometric design plays a crucial role in the field of animation, enabling the creation of realistic and visually captivating 3D graphics. This paper explores the application of computer aided geometric design techniques in animation using 3D graphic software. An overview of computer aided geometric design and its significance in the animation industry is presented. It highlights the fundamental principles and mathematical concepts that form the basis of computer aided geometric design, including spline curves and surfaces. It also explores the benefits of using computer aided geometric design in animation, highlighting how computer aided geometric design techniques facilitate efficient and precise control over geometric shapes, allowing animators to manipulate objects with greater flexibility and accuracy. The use of computer aided geometric design also enhances the realism of animations, as it enables the creation of smooth and organic motion, realistic deformations, and lifelike character models.
Curvature, torsion and its application
(UMT Lahore, 2023-06) Rao Muhammad Ibrar; Hafiz Shahzaib; Muhmmad Shoaib Akhtar; Kashif Ali
The twin paradox is a thought experiment in special relativity that explores the difference in aging between two twins, one of whom goes on a round-trip journey into space in a high-speed spacecraft, while the other remains on Earth. According to special relativity, time passes more slowly in a reference frame that is moving relative to an observer. In the context of the twin paradox, this means that the twin who travels into space will experience time dilation, or a slower passage of time, compared to the twin who remains on Earth. When the traveling twin returns to Earth, both twins will have aged differently, with the twin who traveled into space appearing younger. This paradoxical result arises because the traveling twin experiences time dilation only during the portion of the trip where he is moving away from Earth and toward the destination and back. During the portions of the trip where he is accelerating and returning to Earth, he experiences a different type of time dilation due to gravity. The twin paradox is a key example of how special relativity can lead to seemingly paradoxical results, and it has been the subject of much debate and discussion among physicists and philosophers. However, it is important to note that the paradox is only apparent and can be resolved by taking into account the differences in reference frames experienced by the two twins during the journey. The twin paradox highlights the fundamental nature of time and the importance of considering the relative motion of different observers in special relativity.
Early detection of potato leaf disease using convolutional neural network.
(UMT Lahore, 2024-07-31) Taha Shabbir; Amna Ilyas; Afifa Islam; Zainab Irshad.
Agriculture often is the only source of income in several countries with the losses of crops due to diseases. These ailments make the whole yield be obliterated by going after the harvests at various stages. It, therefore, dictates that farmers should be in a position to identify the particular disease that has attacked their crops to "save the crops" and thus increase their production. In any case, since there are so many sorts of ailments, it may be very provoking for ranchers to distinguish which kind has contaminated their yield. Here, in the project, we can study about the diseases that are going to affect the leaf. Potato development encounters serious obstructions with leaf diseases, influencing result and quality. Traditional detection methods are often imprecise and require a lot of human effort. The following research thus proposes an exciting approach for the early identification of potato leaf diseases that makes use of convolutional neural networks. The main objective is to create a reliable cnn model in order to classify diseases using images of potato-leaf diseases, which are trained by a dataset. The main goal is to create a reliable cnn model that can accurately classify diseases using image of potato leaf diseases that have been trained on a dataset. Further, this involves a user-friendly web application providing an easy interface for farmers and agricultural experts to submit photos of leaves in exchange for fast diagnosis results. The cnn architecture consists of convolutional layers for feature extraction and dense layers for classification. All of these layers are finely tuned through a rigorous training process. Model evaluation results manifest how well this model recognizes the different diseases potatoes have on leaves.
Einstein field equations
(UMT Lahore, 2022-07-06) Saba Yousaf
We examine the kinematical structure of the common theory of relativity and the result of gravitational fields on bodily systems. The solid center of the theory, however, consists of Einstein’s field equations, which relate the metric field to matter. After a discussion of the objective sense of the curve tensor, we shall first give a simple physical inspiration for the field equations and will then show that they are strong-minded by only a few natural requirements.
Exploring the Einstein field equations in different space-time structures
(UMT Lahore, 2025) Jawahir Waqqas; Tooba Tariq
This thesis explores the behavior of Einstein’s field equations in different space-time structures, with a particular focus on the stability of the Einstein static universe in modified theories of gravity. Einstein’s field equations form the core of general relativity by describing how matter and energy determine the curvature of space-time, essentially linking the distribution of mass-energy to the geometry of the universe. In this work, the equations are extended through modifications involving curvature and matter couplings, and then applied within anisotropic cosmological models, specifically the Bianchi type IX framework. Small homogeneous and anisotropic perturbations are introduced in the scale factor and matter fields to examine how the universe reacts to deviations from a static state. Static and perturbed versions of the field equations are derived and analyzed using a fluid equation of state, which simplifies the relation between pressure and energy density. The study evaluates specific functional forms of the modified gravity models and investigates whether stable static solutions exist under these perturbations. Through analytical and graphical methods, it is shown that unlike in standard general relativity, stable Einstein static universes can emerge in both curvature-based and matter-coupled theories. This highlights the deeper flexibility of extended gravity models and shows how the structure of space-time, governed by the field equations, can support a wider range of cosmological behavior than previously thought.
Exploring the impact of concentration
(UMT Lahore, 2023-08) Muhammad Tayyab Ilyas; Syeda Zafeera
This communication presents a theoretical framework for studying the behaviour of a tangent hyperbolic fluid with nano-biofilm. The fluid is subjected to an extending or shrinking sheet, resulting in a stagnation point flow. The framework also takes into account bioconvection induced by gyrotactic bacteria and chemical processes with activation energy. The research is made more novel by the fact that the study considers energetic thickness, thermal conductivity, nanoparticle mass permeability, and various transport properties of microbial organisms. Enhancing heat transport is the main objective of this effort. This is accomplished by formulating a system of partial differential equations with appropriate boundary conditions. The basic formulation is changed into a nonlinear differential equation by researchers using parallel transformation. Shooting method and R-K fourth categorize approach are used to collect observational data, and MATLAB script is used to generate numerical scheme. Through visual symbol, the property of various fluid move properties and various parameters on velocity, temperature, concentration, and dynamic density are assessed.
Fixed points, completeness, and quasi-metric spaces
(UMT Lahore, 2023) Hammad Ali
In order to generalize classical Banach contraction principle in the setup of quasi metric spaces, we introduce Suzuki-type f (f 1)-contractions of quasi metric spaces and prove some fixed point results. Examples have been furnished to make sure that generalizations we obtain are the proper ones. Moreover, we consider the existence of fixed points of generalized Suzuki type contractions of (so-called)-symmetric quasi-metric spaces.

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