Algorithms for Minkowski products and implicitly-defined complex sets

Advances in Computational Mathematics

Volumn 13, Issue 3, 2000, Pages 199-229

  Farouki, Rida T ^a   Moon, Hwan Pyo ^a   Ravani, Bahram ^a  

^a University of California Davis   (United States)

Author keywords

Boundary evaluation algorithms; Envelopes; Families of curves; Implicitly defined complex sets; Logarithmic curvature; Logarithmic Gauss map; Minkowski geometric algebra; Minkowski sums and products; Set inclusion

Indexed keywords

EID: 23044517624     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. J.W. Bruce and P.J. Giblin, Curves and Singularities, 2nd ed. (Cambridge Univ. Press, Cambridge, 1992).
2. R. Deaux, Introduction to the Geometry of Complex Numbers (translated from the French by H. Eves) (F. Ungar, New York, 1956).
3. M.P. do Carmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, Englewood Cliffs, NJ, 1976).
4. G. Farin, Curves and Surfaces for CAGD, 3rd ed. (Academic Press, Boston, 1993).
5. R.T. Farouki and T.N.T. Goodman, On the optimal stability of the Bernstein basis, Math. Comp. 65 (1996) 1553-1566.
6. R.T. Farouki, H.P. Moon and B. Ravani, Minkowski geometric algebra of complex sets, Geom. Dedicata (2000) to appear.
7. R.T. Farouki and C.A. Neff, Analytic properties of plane offset curves & Algebraic properties of plane offset curves, Comput. Aided Geom. Design 7 (1990) 83-99 & 101-127.
8. R.T. Farouki and C.A. Neff, Hermite interpolation by Pythagorean-hodograph quintics, Math. Comp. 64 (1995) 1589-1609.
9. R.T. Farouki and V.T. Rajan, On the numerical condition of polynomials in Bernstein form, Comput. Aided Geom. Design 4 (1987) 191-216.
10. P.K. Ghosh, A mathematical model for shape description using Minkowski operators, Comput. Vision Graphics Image Process. 44 (1988) 239-269.
11. H. Hadwiger, Vorlesungen über Inhalt, Oberfläche, und Isoperimetrie (Springer, Berlin, 1957).
12. A. Kaul, Computing Minkowski sums, Ph.D. thesis, Columbia University (1993).
13. A. Kaul and R.T. Farouki, Computing Minkowski sums of plane curves, Internat. J. Comput. Geom. Appl. 5 (1995) 413-432.