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Generation of configuration space obstacles: The case of moving algebraic curves

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Abstract

We present algebraic algorithms to generate the boundary of planar configuration space obstacles arising from the translatory motion of objects among obstacles. Both the boundaries of the objects and obstacles are given by segments of algebraic plane curves.

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References

  • Abhyankar, S. (1983), Desingularization of Plane Curves,Proceedings of Symposia in Pure Mathematics,40, 1, 1–45.

    Google Scholar 

  • Abhyankar, S., and Bajaj, C. (1987a), Automatic Parametrization of Rational Curves and Surfaces I: Conics and Conicoids,Computer-Aided Design,19, 1, 11–14.

    Article  MATH  Google Scholar 

  • Abhyankar, S., and Bajaj, C. (1987b), Automatic Parametrization of Rational Curves and Surfaces II: Cubics and Cubicoids,Computer-Aided Design,19, 9, 499–502.

    Article  MATH  Google Scholar 

  • Abhyankar, S., and Bajaj, C. (1987c), Automatic Parametrization of Rational Curves and Surfaces III: Algebraic Plane Curves, Computer Science Technical Report CSD-TR-619, Purdue University.

  • Adamowicz, M., and Albano, A. (1976), Nesting Two-Dimensional Shapes in Rectangular Modules,Computer-Aided Design,2, 1, 27–33.

    Article  Google Scholar 

  • Bajaj, C., and Kim, M.-S. (1987a), Compliant Motion Planning with Geometric Models,Proceedings of the 3rd ACM Symposium on Computational Geometry, 171–180.

  • Bajaj, C., and Kim, M.-S. (1987b), Generation of Configuration Space Obstacles: The Case of a Moving Sphere,IEEE Journal on Robotics and Automation,4, 1, in press.

    Google Scholar 

  • Bajaj, C., Hoffmann, C., Hopcroft, J., and Lynch, R. (1987), Tracing Surface Intersections, Computer Science Technical Report CSD-TR-728, Purdue University.

  • Chazelle, B. (1980), Computational Geometry and Convexity, Carnegie-Mellon Technical Report CMU-CS-80-150, Carnegie-Mellon University.

  • Collins, G. (1971), The calculation of Multivariate Polynomial Resultants,Journal of the Association for Computing Machinery,18, 4, 515–532.

    MATH  MathSciNet  Google Scholar 

  • Freeman, H. (1975), On the Packing of Arbitrary Shaped Templates,Proceedings of the 2nd USA-Japan Computer Conference, 102–107.

  • Guibas, L., Ramshaw, L., and Stolfi, J. (1983), A Kinetic Framework for Computational Geometry,Proceedings of the 24th Annual Symposium on Foundations of Computer Science, 100–111.

  • Guibas, L., and Seidel, R. (1986), Computing Convolutions by Reciprocal Search,Proceedings of the 2nd ACM Symposium on Computational Geometry, 90–99.

  • Heindel, L. (1972), Computation of Powers of Multivariate Polynomials Over the Integers,Journal of Computer and System Sciences,6, 1–8.

    Article  MATH  MathSciNet  Google Scholar 

  • Kelley, P., and Weiss, M. (1979),Geometry and Convexity, Wiley, New York.

    Google Scholar 

  • Lozano-P'erez, T. (1983), Spatial Planning: A Configuration Space Approach,IEEE Transactions on Computers,32, 108–120.

    Article  MathSciNet  Google Scholar 

  • Lozano-P'erez, T., and Wesley, M. A. (1979), An Algorithm for Planning Collision-Free Paths Among Polyhedral Obstacles,Communications of the Association for Computing Machinery,22, 560–570.

    Google Scholar 

  • Macaulay, F. (1903), Some Formulae in Elimination,Proceedings of the London Mathematical Society,35, 1, 3–27.

    Article  Google Scholar 

  • Salmon, G. (1866),Modern Higher Algebra, second edition, Hodges, Smith, Dublin.

  • Tiller, W., and Hanson, E. (1984), Offsets of Two-Dimensional Profiles,IEEE Computer Graphics & Applications,4, 9, 36–46.

    Article  Google Scholar 

  • van der Waerden, B. (1950),Modern Algebra, vol. II, Ungar, New York.

    Google Scholar 

  • Walker, R. (1978),Algebraic Curves, Springer-Verlag, New York.

    MATH  Google Scholar 

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Communicated by John E. Hopcroft.

Research supported in part by NSF Grant MIP-85-21356 and a David Ross Fellowship. An earlier version of this paper appeared in theProceedings of the 1987 IEEE International Conference on Robotics and Automation, pp. 979–984.

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Bajaj, C.L., Kim, M.S. Generation of configuration space obstacles: The case of moving algebraic curves. Algorithmica 4, 157–172 (1989). https://doi.org/10.1007/BF01553884

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  • DOI: https://doi.org/10.1007/BF01553884

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