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토폴로지와 수치적 정확도를 통합한 기하모델링에 관한 연구: 곡면간 교차선
A Study on Unifying Topology and Numerical Accuracy in Geometric Modeling: Surface to Surface Intersections

고광희   (광주과학기술원UU0000201  );
  • 초록

    In this paper, we address the problem of robust geometric modeling with emphasis on surface to surface intersections. We consider the topology and the numerical accuracy of an intersection curve to find the best approximation to the exact one. First, we perform the topological configuration of intersection curves, from which we determine the starting and ending points of each monotonic intersection curve segment along with its topological structure. Next, we trace each monotonic intersection curve segment using a validated ODE solver, which provides the error bounds containing the topological structure of the intersection curve and enclosing the exact root without a numerical instance. Then, we choose one approximation curve and adjust it within the bounds by minimizing an objective function measuring the errors from the exact one. Using this process, we can obtain an approximate intersection curve which considers the topology and the numerical accuracy for robust geometric modeling.


  • 주제어

    surface to surface intersection .   geometric modeling .   robustness .   validated ODE solver .   topology .   accuracy.  

  • 참고문헌 (18)

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    6. Mukundan, H., Ko, K. H., Maekawa, T., Sakkalis, and Patrikalakis, N. M., 'Tracing Surface Intersections with a Validated ODE System Solver', Proceedings of the 9th EG/ACM Symposium on Solid Modeling and Applications, G. Elber, N. Patrikalakis and P. Brunet, editors. pp. 249-254. Genoa, Italy, Eurographics Press, 2004 
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    9. Song, X., Sederberg, T. W., Zheng, J., Farouki, R. T. and Hass, J., 'Linear Perturbation Methods for Topologically Consistent Representations of Free-form Surface Intersections', Computer Aided Geometric Design, Vol. 21, No. 3, pp. 303-319, 2004 
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    15. Lohner, R. J., 'Computation of Guaranteed Enclosures for the Solutions of Ordinary Initial and Boundary Value Problem', In Computational Ordinary Differential Equations, Cash J., Gladwell I., (Eds.), Clarendon Press, Oxford, pp. 425-235, 1992 
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