This study presents a Python-based framework for the construction and visualization of NURBS surfaces of revolution, specifically spheres and tori, using entirely open-source technologies. The main contribution lies in providing a methodological approach that combines algorithmic transparency, modular design, and adaptability for educational contexts, offering an effective resource for teaching computational geometry. The proposed implementation employs an object-oriented structure to define control points, weights, and knot vectors, enabling the generation of curves and surfaces through tensor product operations. This design ensures simplicity in implementation while maintaining numerical stability and computational efficiency. The framework promotes reproducibility and cross-platform integration, facilitating its use in virtual learning environments. Beyond its computational robustness, the approach supports the development of algorithmic thinking and geometric intuition, reinforcing key concepts in geometry, computational algebra, and computer-aided design. By leveraging open technologies, this work contributes to reducing barriers in technical education and provides a practical tool for active learning, fostering a deeper understanding of geometric modeling through reproducible, extensible, and transparent resources.

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Modeling of Spheres and Tori of Revolution Using NURBS Surfaces in Python

  • Yheff Alexander Castillo-Maza,
  • Ruben Teodoro Urbina-Guzman,
  • Ronald Paul Santamaria-Silupu,
  • Manuel Hernan Garcia-Saba,
  • Vanessa H. Silupu-Ortega,
  • Oscar H. Del-Rosario-Castillo

摘要

This study presents a Python-based framework for the construction and visualization of NURBS surfaces of revolution, specifically spheres and tori, using entirely open-source technologies. The main contribution lies in providing a methodological approach that combines algorithmic transparency, modular design, and adaptability for educational contexts, offering an effective resource for teaching computational geometry. The proposed implementation employs an object-oriented structure to define control points, weights, and knot vectors, enabling the generation of curves and surfaces through tensor product operations. This design ensures simplicity in implementation while maintaining numerical stability and computational efficiency. The framework promotes reproducibility and cross-platform integration, facilitating its use in virtual learning environments. Beyond its computational robustness, the approach supports the development of algorithmic thinking and geometric intuition, reinforcing key concepts in geometry, computational algebra, and computer-aided design. By leveraging open technologies, this work contributes to reducing barriers in technical education and provides a practical tool for active learning, fostering a deeper understanding of geometric modeling through reproducible, extensible, and transparent resources.