koz"Вестник Северо-Казахстанского университета имени Манаша Козыбаева"Bulletin of Manash Kozybayev North Kazakhstan University2958-003X2958-0048М. Қозыбаев атындағы СҚУ10.54596/2958-0048-2025-3-181-192koz-2282Research ArticleИНФОРМАЦИОННО-КОММУНИКАЦИОННЫЕ ТЕХНОЛОГИИINFORMATION AND COMMUNICATION TECHNOLOGIESИнтеллектуальный алгоритм оценки почерка с использованием сплайна Кэтмулл-РомаIntelligent handwriting assessment algorithm using the Catmull-Rom splinehttps://orcid.org/0000-0002-6211-5634ШапореваА. В.ShaporevaA. V.

Анна Васильевна Шапорева - PhD, доцент кафедры «Строительство и дизайн»,

Петропавловск

Anna Vasilevna Shaporeva - PhD, Associate Professor of the Department of Construction and Design,

Petropavlovsk

annvolkova@mail.ruhttps://orcid.org/0000-0002-6299-3728КопноваО. Л.KopnovaO. L.

Оксана Леонидовна Копнова - PhD, старший преподаватель кафедры «Математика и физика»,

Петропавловск

Oxana Leonidovna Kopnova - PhD, Senior Lecturer of the Department of Mathematics and Physics,

Petropavlovsk

okopnova@ku.edu.kzhttps://orcid.org/0000-0003-1128-6924АйтымоваА. М.AitymovaA. M.

Алия Муратовна Айтымова - PhD, старший преподаватель кафедры «Начальное, дошкольное и специальное образование»,

Петропавловск

Aliya Muratovna Aitymova - PhD, Senior Lecturer of the Department of Primary, Preschool and Special Education,

Petropavlovsk

amakasheva@ku.edu.kzhttps://orcid.org/0000-0002-0451-0644АйтымовЖ. Г.AitymovZh. G.

магистр, старший преподаватель кафедры физического воспитания и спорта,

Петропавловск

Zhanat Gabbasovich Aitymov - master, Senior Lecturer of the Department of Physical education and sports,

Petropavlovsk

aitimov_z_1980@mail.ruНАО «Северо-Казахстанский университет имени Манаша Козыбаева»КазахстанManash Kozybayev North Kazakhstan University NPLCKazakhstan20252410202503 (67)181192Copyright © Шапорева А.В., Копнова О.Л., Айтымова А.М., Айтымов Ж.Г., 20252025Шапорева А.В., Копнова О.Л., Айтымова А.М., Айтымов Ж.Г.Shaporeva A.V., Kopnova O.L., Aitymova A.M., Aitymov Z.G.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.ku.edu.kz/jour/article/view/2282

Статья посвящена разработке и применению алгоритма анализа графомоторных траекторий письма в цифровых образовательных системах с использованием сплайна Кэтмулл-Рома. Рассматривается задача повышения точности и устойчивости обработки пользовательского ввода, полученного с сенсорных устройств (стилус или палец), в контексте цифрового обучения письму. Предложенный метод включает этапы сбора координатных данных, нормализации, фильтрации шумов и сглаживания траекторий. Сплайн Кэтмулл-Рома используется для обеспечения непрерывности кривых и сохранения ключевых особенностей движения, что повышает точность сравнения с эталонными шаблонами.

В работе представлен вычислительный алгоритм, реализующий автоматическую оценку качества начертания букв по ряду параметров: кривизна, угловые отклонения, стабильность скорости и количество штрихов. Алгоритм интегрирован в систему цифровой диагностики, способную формировать детализированные отчёты, выявлять типовые ошибки и предлагать персонализированные задания. Разработанное решение может применяться в интеллектуальных обучающих платформах, системах биометрической аутентификации, нейропсихологической диагностике и компьютерной криминалистике.

Предложенный подход демонстрирует высокую адаптивность к различным сценариям ввода и обеспечивает основу для построения более сложных систем машинного обучения, ориентированных на распознавание, анализ и генерацию рукописного текста.

The article is devoted to the development and application of an algorithm for analyzing graphomotor writing trajectories in digital educational systems using the Catmull-Rom spline. The problem of improving the accuracy and stability of processing user input received from touch devices (stylus or finger) in the context of digital writing learning is considered. The proposed method includes the stages of coordinate data collection, normalization, noise filtering, and trajectory smoothing. The Catmull-Roma spline is used to ensure the continuity of curves and preserve key motion features, which increases the accuracy of comparison with reference patterns.

The paper presents a computational algorithm that implements an automatic assessment of the quality of letter writing based on a number of parameters: curvature, angular deviations, speed stability and the number of strokes. The algorithm is integrated into a digital diagnostic system capable of generating detailed reports, identifying common errors, and offering personalized tasks. The developed solution can be used in intelligent learning platforms, biometric authentication systems, neuropsychological diagnostics and computer forensics.

The proposed approach demonstrates high adaptability to various input scenarios and provides the basis for building more complex machine learning systems focused on recognizing, analyzing, and generating handwritten text.

Catmull–Rom splineалгоритмический анализцифровая диагностикаобработка траекторий письмаинтеллектуальные системыматематическое моделированиеобразовательные технологииCatmull–Rom splinealgorithmic analysisdigital diagnosticsprocessing of writing trajectoriesintelligent systemsmathematical modelingeducational technologiesReferencesAl Kendi, W., Gechter, F., Heyberger, L., & Guyeux, C. (2024). Advancements and Challenges in Handwritten Text Recognition: A Comprehensive Survey. Journal of Imaging, 10(1), 18. https://doi.ore/10.3390/iimaging10010018Al Kendi, W., Gechter, F., Heyberger, L., & Guyeux, C. (2024). Advancements and Challenges in Handwritten Text Recognition: A Comprehensive Survey. Journal of Imaging, 10(1), 18. https://doi.ore/10.3390/iimaging10010018Amruth, A., Mohanty, M., Vimal, C., Ramanan, R., & Beena, B. (2024). Advanced Handwriting Recognition System for Handwritten Scripts With AutoCorrect Feature. 1-9. https://doi.org/10.1109/icccnt61001.2024.10724995Amruth, A., Mohanty, M., Vimal, C., Ramanan, R., & Beena, B. (2024). Advanced Handwriting Recognition System for Handwritten Scripts With AutoCorrect Feature. 1-9. https://doi.org/10.1109/icccnt61001.2024.10724995P.B., Likhitha, L.K., & Rajesh, D.S. (2021). Handwritten Digit Recognition Using Deep Learning. International Journal of Scientific Research in Science and Technology, 7(4), 153-158. https://doi.org/10.32628/CSEIT217439P.B., Likhitha, L.K., & Rajesh, D.S. (2021). Handwritten Digit Recognition Using Deep Learning. International Journal of Scientific Research in Science and Technology, 7(4), 153-158. https://doi.org/10.32628/CSEIT217439Wehbi, M., Hamann, T., Barth, J., & Eskofier, B. M. (2021). Digitizing Handwriting with a Sensor Pen: A Writer-Independent Recognizer. https://doi.org/10.1109/ICFHR2020.2020.00061Wehbi, M., Hamann, T., Barth, J., & Eskofier, B. M. (2021). Digitizing Handwriting with a Sensor Pen: A Writer-Independent Recognizer. https://doi.org/10.1109/ICFHR2020.2020.00061Rane, D., Verma, P., & Lahiri, U. (2022). How Good is your Drawing? Quantifying Graphomotor Skill Using a Portable Platform (pp. 409-422). https://doi.org/10.1007/978-3-031-22131-6_31Rane, D., Verma, P., & Lahiri, U. (2022). How Good is your Drawing? Quantifying Graphomotor Skill Using a Portable Platform (pp. 409-422). https://doi.org/10.1007/978-3-031-22131-6 31Dinehart, L.H. (2014). Handwriting in early childhood education: Current research and future implications. Journal of Early Childhood Literacy, 15(1), 97-118. https://doi.org/10.1177/1468798414522825Dinehart, L.H. (2014). Handwriting in early childhood education: Current research and future implications. Journal of Early Childhood Literacy, 15(1), 97-118. https://doi.org/10.1177/1468798414522825Barker, J. (2022). Characteristics and Graphomotor Skills of Young Children’s Writing and Drawing on a Tablet Screen. 23(3), 273-296. https://doi.org/10.22154/jcle.23.3.12Barker, J. (2022). Characteristics and Graphomotor Skills of Young Children’s Writing and Drawing on a Tablet Screen. 23(3), 273-296. https://doi.org/10.22154/jcle.23.3.12Ceccacci, S., Taddei, A., Del Bianco, N., Giaconi, C., Forteza Forteza, D., & Moreno-Tallon, F. (2024). Preventing Dysgraphia: Early Observation Protocols and a Technological Framework for Monitoring and Enhancing Graphomotor Skills. Information, 15(12), 781. https://doi.org/10.3390/info15120781Ceccacci, S., Taddei, A., Del Bianco, N., Giaconi, C., Forteza Forteza, D., & Moreno-Tallon, F. (2024). Preventing Dysgraphia: Early Observation Protocols and a Technological Framework for Monitoring and Enhancing Graphomotor Skills. Information, 15(12), 781. https://doi.org/10.3390/info15120781Safarova, K., Mekyska, J., Urbanek, T., Galaz, Z., Mucha, J., Zvoncak, V., & Bednarova, J. (2022). Grafomotoricke dovednosti. https://doi.org/10.5817/cz.muni.m280-0257-2022Safarova, K., Mekyska, J., Urbanek, T., Galaz, Z., Mucha, J., Zvoncak, V., & Bednarova, J. (2022). Grafomotoricke dovednosti. https://doi.org/10.5817/cz.muni.m280-0257-2022Kopnova, O.L., Aytymova, A.M., Abildinova, G., Safaraliev, B.S., Koleva, N.S., & Panova, M. (2024). Assessment of the level of formation of graphomotor skills of preschool and primary school students using graphic tablets. Sovremennye Naukoemkie Tehnologii, 1(5), 154-159. https://doi.org/10.17513/snt.40021Kopnova, O.L., Aytymova, A.M., Abildinova, G., Safaraliev, B.S., Koleva, N.S., & Panova, M. (2024). Assessment of the level of formation of graphomotor skills of preschool and primary school students using graphic tablets. Sovremennye Naukoemkie Tehnologii, 1(5), 154-159. https://doi.org/10.17513/snt.40021Devillaine, L., Lambert, R., Boutet, J., Aloui, S., Brault, V., Jolly, C., & Labyt, E. (2021). Analysis of Graphomotor Tests with Machine Learning Algorithms for an Early and Universal Pre-Diagnosis of Dysgraphia. Sensors, 21(21), 7026. https://doi.org/10.3390/S21217026Devillaine, L., Lambert, R., Boutet, J., Aloui, S., Brault, V., Jolly, C., & Labyt, E. (2021). Analysis of Graphomotor Tests with Machine Learning Algorithms for an Early and Universal Pre-Diagnosis of Dysgraphia. Sensors, 21(21), 7026. https://doi.org/10.3390/S21217026Tayebi Arasteh, S., Kalisz, A. Conversion Between Cubic Bezier Curves and Catmull-Rom Splines. SN COMPUT. SCI. 2, 398 (2021). https://doi.org/10.1007/s42979-021-00770-xTayebi Arasteh, S., Kalisz, A. Conversion Between Cubic Bezier Curves and Catmull-Rom Splines. SN COMPUT. SCI. 2, 398 (2021). https://doi.org/10.1007/s42979-021-00770-xLi, J., & Chen, S. (2016). The Cubica-Catmull-Rom Spline. Mathematical and Computational Applications, 21(3), 33. https://doi.org/10.3390/mca21030033Li, J., & Chen, S. (2016). The Cubica-Catmull-Rom Spline. Mathematical and Computational Applications, 21(3), 33. https://doi.org/10.3390/mca21030033Wu, T., Bai, B., & Wang, P. (2013). Parallel Catmull-Rom Spline Interpolation Algorithm for Image Zooming Based on CUDA. Applied Mathematics & Information Sciences, 7, 533-537. https://www.naturalspublishing.com/Article.asp?ArtcID=1048Wu, T., Bai, B., & Wang, P. (2013). Parallel Catmull-Rom Spline Interpolation Algorithm for Image Zooming Based on CUDA. Applied Mathematics & Information Sciences, 7, 533-537. https://www.naturalspublishing.com/Article.asp?ArtcID=1048Tony D. DeRose and Brian A. Barsky. 1988. Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines. ACM Trans. Graph. 7, 1 (Jan. 1988), 1-41. https://doi.org/10.1145/42188.42265Tony D. DeRose and Brian A. Barsky. 1988. Geometric continuity, shape parameters, and geometric constructions for Catmull-Rom splines. ACM Trans. Graph. 7, 1 (Jan. 1988), 1-41. https://doi.org/10.1145/42188.42265C. Kong, A. Luo, S. Wang, H. Li, A. Rocha, and A. Kot, “Pixel -inconsistency modeling for image manipulation localization,” IEEE Trans. Pattern Anal. and Mach. Intell., vol. 47, no. 6, pp. 4455-4472, 2025. https://arxiv.org/abs/2310.00234C. Kong, A. Luo, S. Wang, H. Li, A. Rocha, and A. Kot, “Pixel -inconsistency modeling for image manipulation localization,” IEEE Trans. Pattern Anal. and Mach. Intell., vol. 47, no. 6, pp. 4455-4472, 2025. https://arxiv.org/abs/2310.00234C. Yu, X. Zhang, Y. Duan, S. Yan, Z. Wang, Y. Xiang, S. Ji, and W. Chen, “Diff-id: An explainable identity difference quantification framework for deepfake detection,” IEEE Trans. Dependable Secure Comput., pp. 1-18, 2024. https://arxiv.org/abs/2303.18174C. Yu, X. Zhang, Y. Duan, S. Yan, Z. Wang, Y. Xiang, S. Ji, and W. Chen, “Diff-id: An explainable identity difference quantification framework for deepfake detection,” IEEE Trans. Dependable Secure Comput., pp. 1-18, 2024. https://arxiv.org/abs/2303.18174Lyu, S., Pan, X. & Zhang, X. Exposing Region Splicing Forgeries with Blind Local Noise Estimation. Int J Comput Vis 110, 202-221 (2014). https://doi.org/10.1007/s11263-013-0688-yLyu, S., Pan, X. & Zhang, X. Exposing Region Splicing Forgeries with Blind Local Noise Estimation. Int J Comput Vis 110, 202-221 (2014). https://doi.org/10.1007/s11263-013-0688-ySteve Marschner. Cornell CS4620 Fall 2020. CS 4620 Lecture 14. https://www.cs.cornell.edu/courses/cs4620/2020fa/slides/14splines.pdfSteve Marschner. Cornell CS4620 Fall 2020. CS 4620 Lecture 14. https://www.cs.cornell.edu/courses/cs4620/2020fa/slides/14splines.pdfLi, Q., Gong, R., & Hase, K. (2024). A Comprehensive Objective Evaluation Method for Handwriting Assistive Devices Using a Tablet and Digital Pen for Individuals with Upper Limb Dysfunction. A p p lie d Sciences, 14(23), 11190. https://doi.org/10.3390/app142311190Li, Q., Gong, R., & Hase, K. (2024). A Comprehensive Objective Evaluation Method for Handwriting Assistive Devices Using a Tablet and Digital Pen for Individuals with Upper Limb Dysfunction. A p p lie d Sciences, 14(23), 11190. https://doi.org/10.3390/app142311190Begum, N., Akash, M.A.H., Rahman, S., Shin, J., Islam, M.R., & Islam, M.E. (2021). User Authentication Based on Handwriting Analysis of Pen-Tablet Sensor Data Using Optimal Feature Selection Model. F u tu re In tern et, 13(9), 231. https://doi.org/10.3390/fi13090231Begum, N., Akash, M.A.H., Rahman, S., Shin, J., Islam, M.R., & Islam, M.E. (2021). User Authentication Based on Handwriting Analysis of Pen-Tablet Sensor Data Using Optimal Feature Selection Model. F u tu re In tern et, 13(9), 231. https://doi.org/10.3390/fi13090231Rahim, M.A., Farid, F.A., Miah, A.S.M., Puza, A.K., Alam, M.N. et al. (2024). An Enhanced Hybrid Model Based on CNN and BiLSTM for Identifying Individuals via Handwriting Analysis. Computer Modeling in Engineering & Sciences, 140(2), 1689-1710. https://doi.org/10.32604/cmes.2024.048714Rahim, M.A., Farid, F.A., Miah, A.S.M., Puza, A.K., Alam, M.N. et al. (2024). An Enhanced Hybrid Model Based on CNN and BiLSTM for Identifying Individuals via Handwriting Analysis. Computer Modeling in Engineering & Sciences, 140(2), 1689-1710. https://doi.org/10.32604/cmes.2024.048714Mekyska, J. et al. (2023). Assessment of Developmental Dysgraphia Utilising a Display Tablet. In: Parziale, A., Diaz, M., Melo, F. (eds) Graphonomics in Human Body Movement. Bridging Research and Practice from Motor Control to Handwriting Analysis and Recognition. IGS 2023. Lecture Notes in Computer Science, vol 14285. Springer, Cham. https://doi.org/10.1007/978-3-031-45461-5_2Mekyska, J. et al. (2023). Assessment of Developmental Dysgraphia Utilising a Display Tablet. In: Parziale, A., Diaz, M., Melo, F. (eds) Graphonomics in Human Body Movement. Bridging Research and Practice from Motor Control to Handwriting Analysis and Recognition. IGS 2023. Lecture Notes in Computer Science, vol 14285. Springer, Cham. https://doi.org/10.1007/978-3-031-45461-5 2

The authors declare that there are no conflicts of interest present.