Algorithmic Analysis and Comparative Evaluation of Conical Curve Construction Methods
DOI:
https://doi.org/10.29304/jqcsm.2023.15.41367Keywords:
Automated analysis,, Comparative Evaluation, Conical CurvesAbstract
This article analyzes and compares conical curve creation methods using algorithms. The four methods investigated were linear interpolation, Bézier curve, geometric form approximation, and numerical differential equation solutions. Using mathematics, this research dissects these strategies to understand their underpinnings. Comparisons of accuracy, computing efficiency, and adaptability reveal each method's strengths and drawbacks. This article hopes to help practitioners and academics choose conical curve building techniques based on their construction applications.
Downloads
References
V. Pratt, “Techniques for conic splines,” ACM SIGGRAPH Computer Graphics, vol. 19, no. 3, pp. 151–160, 1985.
T. Igarashi, T. Moscovich, and J. F. Hughes, “Spatial keyframing for performance-driven animation,” in ACM SIGGRAPH 2006 Courses, 2006, pp. 17-es.
D. Kirikkaleli, F. F. Adedoyin, and F. V. Bekun, “Nuclear energy consumption and economic growth in the UK: evidence from wavelet coherence approach,” Journal of Public Affairs, vol. 21, no. 1, p. e2130, 2021.
S.-X. Liu, S.-M. Hu, Y.-J. Chen, and J.-G. Sun, “Reconstruction of curved solids from engineering drawings,” Computer-Aided Design, vol. 33, no. 14, pp. 1059–1072, 2001.
Y. Liu, H. Pottmann, J. Wallner, Y.-L. Yang, and W. Wang, “Geometric modeling with conical meshes and developable surfaces,” in ACM SIGGRAPH 2006 Papers, 2006, pp. 681–689.
T. Lu and F. Chen, “Quantitative analysis of molecular surface based on improved Marching Tetrahedra algorithm,” Journal of Molecular Graphics and Modelling, vol. 38, pp. 314–323, 2012.
P. Thévenaz, T. Blu, and M. Unser, “Interpolation revisited [medical images application],” IEEE Transactions on medical imaging, vol. 19, no. 7, pp. 739–758, 2000.
P. Desmet, “Effects of interpolation errors on the analysis of DEMs,” Earth surface processes and landforms: The Journal of the British Geomorphological Group, vol. 22, no. 6, pp. 563–580, 1997.
G. T. Herman, J. Zheng, and C. A. Bucholtz, “Shape-based interpolation,” IEEE Computer Graphics and Applications, vol. 12, no. 03, pp. 69–79, 1992.
H. N. Fitter, A. B. Pandey, D. D. Patel, and J. M. Mistry, “A review on approaches for handling Bezier curves in CAD for manufacturing,” Procedia Engineering, vol. 97, pp. 1155–1166, 2014.
L. H. Pérez, M. C. M. Aguilar, N. M. Sánchez, and A. F. Montesinos, “Path planning based on parametric curves,” Advanced Path Planning for Mobile Entities, pp. 125–143, 2018.
O. Coskun and H. S. Turkmen, “Multi-objective optimization of variable stiffness laminated plates modeled using Bézier curves,” Composite Structures, vol. 279, p. 114814, 2022.
S. David Müzel, E. P. Bonhin, N. M. Guimarães, and E. S. Guidi, “Application of the finite element method in the analysis of composite materials: A review,” Polymers, vol. 12, no. 4, p. 818, 2020.
W. L. Oberkampf, S. M. DeLand, B. M. Rutherford, K. V. Diegert, and K. F. Alvin, “Error and uncertainty in modeling and simulation,” Reliability Engineering & System Safety, vol. 75, no. 3, pp. 333–357, 2002.
F. Li, G. Hu, M. Abbas, and K. T. Miura, “The generalized H-Bézier model: geometric continuity conditions and applications to curve and surface modeling,” Mathematics, vol. 8, no. 6, p. 924, 2020.
Y. Chen, Y. Cai, J. Zheng, and D. Thalmann, “Accurate and efficient approximation of clothoids using Bézier curves for path planning,” IEEE Transactions on Robotics, vol. 33, no. 5, pp. 1242–1247, 2017.
J.-D. Durou, M. Falcone, and M. Sagona, “Numerical methods for shape-from-shading: A new survey with benchmarks,” Computer Vision and Image Understanding, vol. 109, no. 1, pp. 22–43, 2008.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Ahmed M. Mahdi
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.