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.
Similar content being viewed by others
References
Abhyankar, S. (1983), Desingularization of Plane Curves,Proceedings of Symposia in Pure Mathematics,40, 1, 1–45.
Abhyankar, S., and Bajaj, C. (1987a), Automatic Parametrization of Rational Curves and Surfaces I: Conics and Conicoids,Computer-Aided Design,19, 1, 11–14.
Abhyankar, S., and Bajaj, C. (1987b), Automatic Parametrization of Rational Curves and Surfaces II: Cubics and Cubicoids,Computer-Aided Design,19, 9, 499–502.
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.
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.
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.
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.
Kelley, P., and Weiss, M. (1979),Geometry and Convexity, Wiley, New York.
Lozano-P'erez, T. (1983), Spatial Planning: A Configuration Space Approach,IEEE Transactions on Computers,32, 108–120.
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.
Macaulay, F. (1903), Some Formulae in Elimination,Proceedings of the London Mathematical Society,35, 1, 3–27.
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.
van der Waerden, B. (1950),Modern Algebra, vol. II, Ungar, New York.
Walker, R. (1978),Algebraic Curves, Springer-Verlag, New York.
Author information
Authors and Affiliations
Additional information
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.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01553884