Abstract
Curve framing has numerous applications in computer graphics modeling, e.g., in the construction of extruded surfaces. Commonly used curve framing techniques such as the Frenet frame, parallel transport frame and ‘up-vector’ frame cannot handle all types of curves. Mismatch between the technique used and the curve being modeled may result in the extruded surfaces being twisted. We propose a simple end-to-end vector-projection approach to curve framing. Our results show that the technique yields less twists compared to those based on the Frenet frame.
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References
Poston, T., Fang, S., Lawton, W.: Computing and approximating sweeping surfaces based on rotation minimizing frames. In: Proceedings of the 4th International Conference on CAD/CG, Wuhan, China (1995)
Cripps, R.J., Mullineux, G.: Constructing 3D motions from curvature and torsion profiles. Computer-Aided Design 44, 379–387 (2012)
Wang, W., Jüttler, B., Zheng, D., Liu, Y.: Computation of rotation minimizing frames. ACM Transactions on Graphics 27(1), 1–18 (2008)
Bishop, R.L.: There is more than one way to frame a curve. Amer. Math. Monthly 82(3), 246–251 (1975)
Hill, F.S.: Computer Graphics Using OpenGL. Prentice Hall, New Jersey (2001)
Hanson, A.J., Ma, H.: Parallel transport approach to curve framing. Technical Report 425, Indiana University Computer Science Department (1995)
Bergou, M., Wardetzky, M., Robinson, S., Audoly, S.B., Grinspun, E.: Discrete elastic rods. ACM Transactions on Graphics 27(3), Article 63 (2008)
Fujiki, J., Tomimatsu, K.: Design algorithm of the strings - string dance with sound. International Journal of Asia Digital Art and Design 2, 11–16 (2005)
Wu, J., Popovic, Z.: Realistic modeling of bird flight animations. In: International Conference on Computer Graphics and Interactive Techniques, ACM SIGGRAPH 2003 Papers, pp. 888–895 (2003)
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Md. Said, A. (2013). Vector-Projection Approach to Curve Framing for Extruded Surfaces. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2013. ICCSA 2013. Lecture Notes in Computer Science, vol 7971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39637-3_47
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DOI: https://doi.org/10.1007/978-3-642-39637-3_47
Publisher Name: Springer, Berlin, Heidelberg
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