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

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.

[1]  G. Bracchi,et al.  Man-machine communication in computer-aided tolerance analysis of electronic circuits , 1987 .

[2]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[3]  A. L. Dixon.  On a Form of the Eliminant of Two Quantics , 1908 .

[4]  B. Chazelle.  Computational geometry and convexity , 1980 .

[5]  Chandrajit L. Bajaj,et al.  Generation of configuration space obstacles: the case of a moving sphere , 1988, IEEE J. Robotics Autom..

[6]  C. Bajaj,et al.  Automatic parametrization of rational curves and surfaces II: cubics and cubicoids , 1987 .

[7]  Antonio Albano,et al.  NESTING TWO-DIMENSIONAL SHAPES IN RECTANGULAR MODULES , 1976 .

[8]  Leonidas J. Guibas,et al.  A kinetic framework for computational geometry , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[9]  Wayne Tiller,et al.  Offsets of Two-Dimensional Profiles , 1984, IEEE Computer Graphics and Applications.

[10]  Leonidas J. Guibas,et al.  Computing convolutions by reciprocal search , 1986, SCG '86.

[11]  George E. Collins,et al.  The Calculation of Multivariate Polynomial Resultants , 1971, JACM.

[12]  Lee E. Heindel.  Computation of Powers of Multivariate Polynomials over the Integers , 1972, J. Comput. Syst. Sci..

[13]  S. Abhyankar,et al.  Automatic parameterization of rational curves and surfaces 1: conics and conicoids , 1987 .

[14]  R. J. Walker.  Algebraic curves , 1950 .

[15]  F. S. Macaulay.  Some Formulæ in Elimination , 1902 .

[16]  Chandrajit L. Bajaj,et al.  Compliant motion planning with geometric models , 1987, SCG '87.

[17]  Leonidas J. Guibas,et al.  Computing convolutions by reciprocal search , 1986, SCG '86.

[18]  S. Abhyankar,et al.  Automatic Rational Parameterization of Curves and Surfaces II: Cubics and Cubicoids , 1986 .

[19]  A. L. Dixon.  The Eliminant of Three Quantics in two Independent Variables , 1909 .

[20]  Chandrajit L. Bajaj,et al.  Tracing surface intersections , 1988, Comput. Aided Geom. Des..

[21]  Tomás Lozano-Pérez,et al.  Spatial Planning: A Configuration Space Approach , 1983, IEEE Transactions on Computers.