Make Science Visible through Numerical Methods in Computer Graphics. Water Wave Equation through Graphical Bezier Solution
Abstract views: 44
/ 
PDF downloads: 59
Keywords:
Concepts, numerical methods, Numerical Simulations, design tools, spline curves, VisualizationAbstract
This article shows how computer graphics can be used to visualize science concepts and
operationalize inquiry practices in engineering design to support integrated learning and teaching of science
and engineering. The main results of the study demonstrate the importance of numerical methods in
computer graphics, particularly in terms of their ability to generate smooth curves, detailed surfaces, and
realistic transformations. This article provides real-world examples in the field of sustainable energy
engineering based on open-source design and analysis Web app. Simulations were performed to showcase
the capabilities of numerical methods. The graphics results obtained highlighted the strengths and
limitations of each technique, providing valuable insights for practitioners and researchers. Additionally,
the article discusses code simulations for B-spline curves, surface subdivision, and interpolation, providing
practical examples for implementation.
The findings of this study can be useful for researchers, practitioners, and students seeking to develop their
understanding and implementation of numerical methods in computer graphics. Based on these graphical
capabilities, generative design driven by evolutionary computation can also be visually illustrated to give
students a glimpse into how artificial intelligence is transforming engineering design.
Downloads
References
D. Fortus, R. C. Dershimer, J. Krajcik, R. W. Marx, and R. Mamlok-Naaman, “Design-based science and student learning,” J. Res. Sci. Technol., vol. 41, no. 10, pp. 1081–1110, 2014, doi: 10.1002/tea.20040.
Foley, J., van Dam, A., Feiner, S., & Hughes, J. (1990). Computer Graphics: Principles and Practice. Addison-Wesley Professional., 72-94 AND 123-128.
Kravitz, D. A., & Klineberg, S. L. (2000). Reactions to two versions of affirmative action action among Whites, Blacks, and Hispanics. Journal of Applied Psychology, 85(4), 597–611. https://doi.org/10.1037/0021-9010.85.4.597
Kosova, R., Naço, A., Hajrulla, S., & Kosova, A. M. (2024). Addressing Missing Data in Surveys and Implementing Imputation Methods with SPSS. International Journal of Advanced Natural Sciences and Engineering Researches, 8(2), 40-50.
C. E. Wieman, W. K. Adams, and K. K. Perkins, “PhET: Simulations that enhance learning,” Science, vol. 322, no. 5902, pp. 682–683, 2008, doi: 10.1126/science.1161948.
Hajrulla, S., Abou Jaoudeh, G. M., Kosova, R., & Isufi, H. (2024). Optimization Problems through Numerical Methods and Simulations.
Demir, T., & Hajrulla, S. Numerical methods on fractional Fourier transformation on Signal Processing.
Jones, R., & Johnson, A. (2015). Advanced Techniques in Computer Graphics. IEEE Computer Graphics and Applications, 35(2), 56-68.
Ali, L., Hajrulla, S., & Souliman, E. N. Extending the Wireless Sensor Network’Life by Using Parallel Processing of the Classification Mechanism.
S Hajrulla, A Uka, T Demir, F Hoxha, D Hajrulla, L Bezati, “Unimodular matrix on shallow water wave theory. Unimodularity through matrix method”, New trends in Mathematical Sciences. 10 (1), 25-31 (2022).
Hajrulla, S., Uka, A., & Demir, T. (2023). Simulations and Results for the Heat Transfer Problem. European Journal of Engineering Science and Technology, 6(1), 1-9. A. T.
Hajrulla, S., Ali, L., & Souliman, N. (2023). NORMAL DISTRIBUTION ON ENERGY SAVING PROBLEMS FOR THE WIRELESS SENSOR NETWORK LIFE ON THE VACATION PERIOD. Journal of Natural Sciences & Mathematics (JNSM), 8.
Ali, L., Hajrulla, S., & Souliman, N. Reducing the Wireless Sensor Networks' delay by reducing program’s complexity and by using parallel processing mechanism. EMSJ journal.
Hajrulla, S., Demir, T., Bezati, L., Kosova, R., & Hajrulla, D. (2023). Unimodular Matrix On Compound Mathematical Structures Applications and Results.
Kosova, R., Kapçiu, R., Hajrulla, S., & Kosova, A. M. (2023). The Collatz Conjecture: Bridging Mathematics and Computational Exploration with Python.
S Hajrulla, D Osmani, V Lino, D Avdiu, D Hajrulla “A Statistical Method to Estimate An Unkonown Price in Financial Markets” - PROCEEDINGS BOOK, 2022
Demir, Taylan & Hajrulla, Shkelqim. (2023). Discrete Fractional Operators and their applications. International Journal of Advanced Natural Sciences and Engineering Researches. 7. 289-294. 10.59287/as-ijanser.631.
Hajrulla, S., Ali, L., Sari, B., & Kosova, R. (2024). Numerical Method Evaluation on Leveraging Machine-Learning Innovations for Improved Patient Care. Comparison of Numerical Results.
Demir, Taylan & Hajrulla, Shkelqim & Bezati, Leonard & Hajrulla, Desantila. (2023). Application of Numerical Methods in Design of Industrial Structures. International Journal of Advanced Natural Sciences and Engineering Researches. 7. 295-300. 10.59287/as-ijanser.632.
S Hajrulla, G Hajrulla. “Applying Math Economics Instructions on International Relations e”, Procceding book 345.
Ali, L., & Hajrulla, S. Improving Information Retrieval Systems' Efficiency.
Layton, M. van dePanne, A numerically efficient and stable algorithm for animating water waves, The visual Computer, 18, 41-53 (2002).
Hajrulla, S., Uka, A., Demir, T., Hoxha, F., Hajrulla, D., & Bezati, L. (2022). Unimodular matrix on shallow water wave theory. Unimodularity through matrix method.
Hajrulla, S., Uka, A., Ali, L., & Demir, T. (2022). Numerical Methods and Approximations for the Heat Transfer Problem. In Proceedings of The International Conference on Academic Research in Science, Technology and Engineering (Vol. 1, No. 1, pp. 21-31).
Pişkin, E., Uysal, T., & Hajrulla, S. (2018). Exponential Decay of Solutions for a Higher Order Wave Equation with Logarithmic Source Term.
Hajrulla, Shkelqim & Bezati, Leonard. (2024). Camassa-Holm equation on shallow water wave equation. International Journal of Scientific Research and Management (IJSRM). 5. 7758-7764.
R. Bonney , “Next steps for citizen science,” Science, vol. 343, no. 6178, pp. 1436–1437, 2014, doi: 10.1126/science.1251554.
Hajrulla, S., Bezati, L., & Hoxha, F. (2018). Application of Initial Boundary Value Problem on Logarithmic Wave Equation in Dynamics.
V. Singh and N. Gu, “Towards an integrated generative design framework,” Des. Stud., vol. 33, no. 2, pp. 185–207, 2012, doi: 10.1016/j.destud.2011.06.001.
Bezati, L., Hajrulla, S., & Hamzallari, B. Comparison of Numerical Methods for SWW Equations.
Sh, H., Bezati, L., & Hoxha, F. Water Wave Equation Arising On Logarithmic Quantum Mechanics.
Hajrulla, S., Demir, T., Bezati, L., & Kosova, R. (2023). The impact of constructive learning applied to the teaching of numerical methods. CONSTRUCTIVE MATHEMATICS: FOUNDATION AND PRACTICE, 39.
Jones, R., & Johnson, A. (2015). Advanced Techniques in Computer Graphics. IEEE Computer Graphics and Applications, 35(2), 56-68.
B. Lang, The synthesis of wave forms using B´ezier curves with control point modulation, The Second CEMS Research Student Conference.
