Intersection Algorithms and CAGD

1. S. L. Abrams, W. Cho, C. Y. Hu, T. Maekawa, N. M. Patrikalakis, E. C. Sherbrooke, and Ye X. Methods for rounded interval arithmetic. Computer Aided Design, 30(8):657–666, 1998.

   Article  MATH  Google Scholar 

2. C. Bajaj. The emergence of algebraic curves and surfaces in geometric design. In Directions in Geometric Computing, pages 1–28. Information Geometers, 1993.

   Google Scholar 

3. S. Briseid, T. Dokken, T. R. Hagen, and J. O. Nygaard. Spline surface intersections optimized for GPUs. In V. N. Alexandrov, G. D. van Albada, P. M. A. Sloot, and J. Dongarra, editors, Computational Science-ICCS 2006: 6th International Conference, Reading, UK, May 28–31, 2006, Proceedings, Part IV, volume 3994 of Lecture Notes in Computer Science, pages 204–211, Berlin/Heidelberg, 2006. Springer.

   Google Scholar 

4. E. Cohen, R. F. Riesenfeld, and G. Elber. Geometric modeling with splines. A K Peters Ltd., Natick, MA, 2001. An introduction, With a foreword by Tom Lyche.

   MATH  Google Scholar 

5. O.J Dahl and D. Belsnes. Algorithms and Data Structures. Studentlitteratur, Lund, Sweden, 1973.

   MATH  Google Scholar 

6. C. de Boor, K. Höllig, and M. Sabin. High accuracy geometric Hermite interpolation. Comput. Aided Geom. Design, 4(4):269–278, 1987.

   Article  MATH  MathSciNet  Google Scholar 

7. T. Dokken. Reference Manual, B-spline Library. SINTEF (Senter for Industriforskning), Oslo, Norway, 1983.

   Google Scholar 

8. T. Dokken. Finding intersections of b-spline represented geometries using recursive subdivision techniques. Comput. Aided Geom. Design, 2:189–195, 1985.

   Article  MATH  Google Scholar 

9. T. Dokken. APS-SS: A subrouting package for modelling of sculptured surfaces. SINTEF (Senter for Industriforskning), Oslo, Norway, 1987.

   Google Scholar 

10. T. Dokken. The SINTEF Spline Library, version 4.0. SINTEF, Oslo, Norway, 1994.

    Google Scholar 

11. T. Dokken. Aspect of Intersection algorithms and Approximation, Thesis for the doctor philosophias degree. PhD thesis, University of Oslo, 1997.

    Google Scholar 

12. T. Dokken. Aspects of algorithms for manifold intersection. In Numerical methods and software tools in industrial mathematics, pages 365–380. Birkhauser, Boston, MA, 1997.

    Google Scholar 

13. T. Dokken. Approximate implicitization. In Mathematical methods for curves and surfaces (Oslo, 2000), Innov. Appl. Math., pages 81–102. Vanderbilt Univ. Press, Nashville, TN, 2001.

    Google Scholar 

14. T. Dokken, H. K. Kellermann, and C. Tegnander. An approach to weak approximate implicitization. In Mathematical methods for curves and surfaces (Oslo, 2000), Innov. Appl. Math., pages 103–112. Vanderbilt Univ. Press, Nashville, TN, 2001.

    Google Scholar 

15. T. Dokken, V. Skytt, and A.-M. Ytrehus. Recursive subdivision and iteration in intersections and related problems. In Mathematical methods in computer aided geometric design (Oslo, 1988), pages 207–214. Academic Press, Boston, MA, 1989.

    Google Scholar 

16. T. Dokken and J. B. Thomassen. Overview of approximate implicitization. In Topics in algebraic geometry and geometric modeling, volume 334 of Contemp. Math., pages 169–184. Amer. Math. Soc., Providence, RI, 2003.

    Google Scholar 

17. G. Farin, J. Hoschek, and M.-S. Kim, editors. Handbook of computer aided geometric design. North-Holland, Amsterdam, 2002.

    MATH  Google Scholar 

18. R. T. Farouki. Pythagorean-hodograph curves. In Handbook of computer aided geometric design, pages 405–427. North-Holland, Amsterdam, 2002.

    Google Scholar 

19. R. T. Farouki, C. Y. Han, J. Hass, and T.W. Sederberg. Topologically consistent trimmed surface approximations based on triangular patches. Comput. Aided Geom. Design, 21(5):459–478, 2004.

    MATH  MathSciNet  Google Scholar 

20. R. T. Farouki and V. T. Rajan. On the numerical condition of polynomials in Bernstein form. Comput. Aided Geom. Design, 4(3):191–216, 1987.

    Article  MATH  MathSciNet  Google Scholar 

21. R. T. Farouki and V. T. Rajan. Algorithms for polynomials in Bernstein form. Comput. Aided Geom. Design, 5(1):1–26, 1988.

    Article  MATH  MathSciNet  Google Scholar 

22. A. Gálvez, J. Puig-Pey, and A. Iglesias. Differential method for parametric surface intersection. In Computational Science and Its Applications — ICCSA 2004: International Conference, Assisi, Italy, May 14–17, 2004, volume 3044 of Lecture Notes in Comput. Sci., pages 651–660. Springer, Berlin, 2004.

    Google Scholar 

23. K. Hasund, T. Dokken, and S. Ulfsby. System specifications, sculptured surfaces. Technical Report 16, SINTEF (Sentralinstitutt for industriell forskning), Oslo, Norway, 1980.

    Google Scholar 

24. M. E. Hohmeyer. Robust and Efficient Surface Intersection for Solid Modelling. PhD thesis, Computer Science Division, University of California, 1992.

    Google Scholar 

25. K. Höllig and J. Koch. Geometric Hermite interpolation. Comput. Aided Geom. Design, 12(6):567–580, 1995.

    Article  MATH  MathSciNet  Google Scholar 

26. K. Höllig and J. Koch. Geometric Hermite interpolation with maximal order and smoothness. Comput. Aided Geom. Design, 13(8):681–695, 1996.

    Article  MATH  MathSciNet  Google Scholar 

27. C.-Y. Hu, T. Maekawa, N. M. Patrikalakis, and X. Ye. Robust interval algorithm for surface intersections. Computer-Aided Design, 29(9):617–627, 1997.

    Article  MATH  Google Scholar 

28. IEEE. Specification for binary floating point arithmetic for microprocessor systems, international standard, 1989.

    Google Scholar 

29. ISO. Industrial automation systems and integration-product data representation and exchange — part 42: Integrated generic resources: Geometric and topological representation, 1994.

    Google Scholar 

30. S. Krishnan and D. Manocha. An efficient surface intersection algorithm based on lower-dimensional formulation. ACM Trans. Graph., 16(1):74–106, 1997.

    Article  Google Scholar 

31. J. M. Lane and R. F. Riesenfeld. Bounds on a polynomial. BIT, 21(1):112–117, 1981.

    Article  MATH  MathSciNet  Google Scholar 

32. T. Maekawa, W. Cho, and N. M. Patrikalakis. Computation of self-intersections of offsets of bézier surface patches. Journal of Mechanical Design, ASME Transactions, 119:275–283, 1997.

    Article  Google Scholar 

33. H. Mukundan, K. H. Ko, T. Maekawa, T. Sakkalis, and N. M. Patrikalakis. Tracing surface intersections with a validated ode system solver. In G. Elber, N. Patrikalakis, and P. Brunet, editors, Proceedings of the Ninth EG/ACM Symposium on Solid Modeling and Applications, Genoa, Italy, June 2004, pages 249–254. Eurographics Press, 2004.

    Google Scholar 

34. N. M. Patrikalakis and T. Maekawa. Intersection problems. In Handbook of computer aided geometric design, pages 623–649. North-Holland, Amsterdam, 2002.

    Google Scholar 

35. N. M. Patrikalakis and T. Maekawa. Shape interrogation for computer aided design and manufacturing. Springer-Verlag, Berlin, 2002.

    MATH  Google Scholar 

36. N. M. Patrikalakis, T. Maekawa, K. H. Ko, and H. Mukundan. Surface to surface intersections. Computer-Aided Design & Applications, 1:449–458, 2004.

    Google Scholar 

37. J. Peters and X. Wu. Sleves for planar spline curves. In Computer Aided Geometric Design, pages 615–635, 2004.

    Google Scholar 

38. J. Puig-Pey, A. Gálvez, and A. Iglesias. A new differential approach for parametric-implicit surface intersection. In Computational science-ICCS 2003. Part I, volume 2657 of Lecture Notes in Comput. Sci., pages 897–906. Springer, Berlin, 2003.

    Google Scholar 

39. T. Sederberg, R. Goldman, and H. Du. Implicitizing rational curves by the method of moving algebraic curves. J. Symbolic Comput., 23(2–3):153–175, 1997. Parametric algebraic curves and applications (Albuquerque, NM, 1995).

    Article  MATH  MathSciNet  Google Scholar 

40. T. W. Sederberg. Implicit and parametric curves and surfaces for computer aided geometric design. PhD thesis, Purdue University, 1983.

    Google Scholar 

41. T. W. Sederberg. Planar piecewise algebraic curves. Computer Aided Geometric Design, 1(3):241–255, 1984.

    Article  MATH  Google Scholar 

42. T. W. Sederberg and R. J. Meyers. Loop detection in surface patch intersections. Comput. Aided Geom. Design, 5:161–171, 1988.

    Article  MATH  MathSciNet  Google Scholar 

43. T. W. Sederberg and Anderson D. C. and Goldman R. N. Implicit representation of parametric curves and surfaces. Computer Vision, Graphics, and Image Processing, 28:72–84, 1984.

    Article  Google Scholar 

44. T. W. Sederberg, J. Zheng, K. Klimaszewski, and T. Dokken. Approximate implicitization using monoid curves and surfaces. Graphical Models and Image Processing, 61(4):177–198, 1999.

    Article  Google Scholar 

45. T. W. Sederberg, J. Zheng, and Song X. A conjecture on tangent intersections of surface patches. Comput. Aided Geom. Design, 21(1):1–2, 2004.

    Article  MATH  MathSciNet  Google Scholar 

46. T. W. Sederberg and A. K. Zundel. Pyramids that bound surface patches. CVGIP: Graphical Model and Image Processing, 58(1):75–81, 1996.

    Article  Google Scholar 

47. P. Sinha, E. Klassen, and K.K. Wang. Exploiting topological and geometric properties for selective subdivision. In Symposium on Computational Geometry, pages 39–45. ACM Press, 1985.

    Google Scholar 

48. V. Skytt. Challenges in surface-surface intersections. In Computational methods for algebraic spline surfaces, pages 11–26. Springer, Berlin, 2005.

    Chapter  Google Scholar 

49. V. Skytt. A recursive approach to surface-surface intersections. In Mathematical methods for curves and surfaces: Troms, Mod. Methods Math., pages 327–338. Nashboro Press, Brentwood, TN, 2005.

    Google Scholar 

50. A. K. Zundel and T. W. Sederberg. Surface intersection loop destruction. In The mathematics of surfaces, VII (Dundee, 1996), pages 463–478. Info. Geom., Winchester, 1997.

    Google Scholar 

51. A.K. Zundel. Surface-Surface Intersection: Loop Destruction Using Bézier Clipping and Pyramidal Bounds. Thesis for Doctor of Philosophy. PhD thesis, Brigham Young University, 1994.

    Google Scholar 

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