# A deterministic pseudorandom perturbation scheme for arbitrary polynomial predicates

- Published: 08 Aug 2013

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[1] Amenta, N., Choi, S., and Rote, G. Incremental constructions con brio. In Proceedings of the nineteenth annual symposium on Computational geometry (2003), ACM, pp. 211-219.

[2] Brönnimann, H., Burnikel, C., and Pion, S. Interval arithmetic yields efficient dynamic filters for computational geometry. Discrete Applied Mathematics 109, 1 (2001), 25-47.

[3] Burnikel, C., Mehlhorn, K., and Schirra, S. On degeneracy in geometric computations. In Proceedings of the fifth annual ACM-SIAM Symposium on Discrete algorithms (1994), Society for Industrial and Applied Mathematics, pp. 16-23.

[4] Devillers, O., Fronville, A., Mourrain, B., and Teillaud, M. Algebraic methods and arithmetic filtering for exact predicates on circle arcs. In Proceedings of the sixteenth annual symposium on Computational geometry (2000), ACM, pp. 139-147.

[5] Devillers, O., Karavelas, M., and Teillaud, M. Qualitative Symbolic Perturbation: a new geometry-based perturbation framework. Rapport de recherche RR-8153, INRIA, 2012.

[6] Edelsbrunner, H., and Mücke, E. P. Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics (TOG) 9, 1 (1990), 66-104.

[7] Emiris, I., and Canny, J. An efficient approach to removing geometric degeneracies. In Proceedings of the eighth annual symposium on Computational geometry (1992), ACM, pp. 74-82.

[8] Emiris, I. Z., and Canny, J. F. A general approach to removing degeneracies. SIAM Journal on Computing 24, 3 (1995), 650-664.

[9] Granlund, T., and the GMP development team. GNU MP: The GNU Multiple Precision Arithmetic Library, 5.0.5 ed., 2012. http://gmplib.org.

[10] Halperin, D., and Leiserowitz, E. Controlled perturbation for arrangements of circles. International Journal of Computational Geometry & Applications 14, 04n05 (2004), 277-310.

[11] Halperin, D., and Shelton, C. R. A perturbation scheme for spherical arrangements with application to molecular modeling. Computational Geometry 10, 4 (1998), 273-287. [OpenAIRE]

[12] Neidinger, R. D. Multivariable interpolating polynomials in Newton forms. In Joint Mathematics Meetings 2009 (2009), pp. 5-8.

[13] Olver, P. J. On multivariate interpolation. Studies in Applied Mathematics 116, 2 (2006), 201-240.

[14] Oruç, H., and Phillips, G. M. Explicit factorization of the Vandermonde matrix. Linear Algebra and its Applications 315, 1 (2000), 113-123. [OpenAIRE]

[15] Salmon, J. K., Moraes, M. A., Dror, R. O., and Shaw, D. E. Parallel random numbers: as easy as 1, 2, 3. In Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (New York, NY, USA, 2011), SC '11, ACM, pp. 16:1-16:12.

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- 1
- 2

[1] Amenta, N., Choi, S., and Rote, G. Incremental constructions con brio. In Proceedings of the nineteenth annual symposium on Computational geometry (2003), ACM, pp. 211-219.

[2] Brönnimann, H., Burnikel, C., and Pion, S. Interval arithmetic yields efficient dynamic filters for computational geometry. Discrete Applied Mathematics 109, 1 (2001), 25-47.

[3] Burnikel, C., Mehlhorn, K., and Schirra, S. On degeneracy in geometric computations. In Proceedings of the fifth annual ACM-SIAM Symposium on Discrete algorithms (1994), Society for Industrial and Applied Mathematics, pp. 16-23.

[4] Devillers, O., Fronville, A., Mourrain, B., and Teillaud, M. Algebraic methods and arithmetic filtering for exact predicates on circle arcs. In Proceedings of the sixteenth annual symposium on Computational geometry (2000), ACM, pp. 139-147.

[5] Devillers, O., Karavelas, M., and Teillaud, M. Qualitative Symbolic Perturbation: a new geometry-based perturbation framework. Rapport de recherche RR-8153, INRIA, 2012.

[6] Edelsbrunner, H., and Mücke, E. P. Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. ACM Transactions on Graphics (TOG) 9, 1 (1990), 66-104.

[7] Emiris, I., and Canny, J. An efficient approach to removing geometric degeneracies. In Proceedings of the eighth annual symposium on Computational geometry (1992), ACM, pp. 74-82.

[8] Emiris, I. Z., and Canny, J. F. A general approach to removing degeneracies. SIAM Journal on Computing 24, 3 (1995), 650-664.

[9] Granlund, T., and the GMP development team. GNU MP: The GNU Multiple Precision Arithmetic Library, 5.0.5 ed., 2012. http://gmplib.org.

[10] Halperin, D., and Leiserowitz, E. Controlled perturbation for arrangements of circles. International Journal of Computational Geometry & Applications 14, 04n05 (2004), 277-310.

[11] Halperin, D., and Shelton, C. R. A perturbation scheme for spherical arrangements with application to molecular modeling. Computational Geometry 10, 4 (1998), 273-287. [OpenAIRE]

[12] Neidinger, R. D. Multivariable interpolating polynomials in Newton forms. In Joint Mathematics Meetings 2009 (2009), pp. 5-8.

[13] Olver, P. J. On multivariate interpolation. Studies in Applied Mathematics 116, 2 (2006), 201-240.

[14] Oruç, H., and Phillips, G. M. Explicit factorization of the Vandermonde matrix. Linear Algebra and its Applications 315, 1 (2000), 113-123. [OpenAIRE]

[15] Salmon, J. K., Moraes, M. A., Dror, R. O., and Shaw, D. E. Parallel random numbers: as easy as 1, 2, 3. In Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (New York, NY, USA, 2011), SC '11, ACM, pp. 16:1-16:12.

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