Minkowski roots of complex sets

Proceedings - Geometric Modeling and Processing 2000: Theory and Applications

Volumn , Issue , 2000, Pages 287-300

  Farouki, R T ^a   Gu, Weiqung ^b   Moon, Hwan Pyo ^a  

^a University of California Davis   (United States)

^b HARVEY MUDD COLLEGE   (United States)

Author keywords

lemniscate of Bernoulli; logarithmic convexity; minimal and maximal roots; Minkowski geometric algebra; Minkowski roots; ordinary roots; ovals of Cassini

Indexed keywords

ALGEBRA;

CASSINI; GEOMETRIC ALGEBRA; LEMNISCATE OF BERNOULLI; LOGARITHMIC CONVEXITY; MINIMAL AND MAXIMAL ROOTS; MINKOWSKI; ORDINARY ROOTS;

GEOMETRY;

EID: 0005263798     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/GMAP.2000.838260     Document Type: Conference Paper

References (23)

1. V. G. Boltyanskii (1964),Envelopes, Macmillan, New York.
2. J. W. Bruce and P. J. Giblin (1981), What is an envelope?, Math. Gazette 65, 186-192.
3. J. W. Bruce and P. J. Giblin (1984), Curves and Singularities, Cambridge Univ. Press.
4. P. J. Davis (1963), Interpolation and Approximation, Blaisdell Publishing Co., New York.
5. R. Deaux (1956), Introduction to the Geometry of Complex Numbers (translated from the French by H. Eves), F. Ungar, New York.
6. R. T. Farouki and J-C. A. Chastang (1992), Curves and surfaces in geometrical optics, Mathematical Methods in Computer Aided Geometric Design II, (T. Lyche & L. L. Schumaker, eds.), Academic Press, pp. 239-260.
7. R. T. Farouki, H. P. Moon, and B. Ravani (2000), Minkowski geometric algebra of complex sets, Geometriae Dedicata, to appear.
8. R. T. Farouki, H. P. Moon, and B. Ravani (1999), Algorithms for Minkowski products and implicitly-defined complex sets, preprint.
9. P. K. Ghosh (1988), A mathematical model for shape description using Minkowski operators, Comput. Vision, Graphics, Image Process. 44, 239-269.
10. F. Gomes Teixeira (1971), Traité des Courbes Spéciales Remarquables Planes et Gauches, Tome I, Chelsea (reprint), New York.
11. H. Hadwiger (1957), Vorlesungen über Inhalt, Oberfläche, und Isoperimetrie, Springer, Berlin.
12. A. Kaul (1993), Computing Minkowski sums, PhD Thesis, Columbia University.
13. A. Kaul and R. T. Farouki (1995), Computing Minkowski sums of plane curves, Int. J. Comput. Geom. Applic. 5, 413-432.
14. J. D. Lawrence (1972), A Catalog of Special Plane Curves, Dover, New York.
15. E. H. Lockwood (1967), A Book of Curves, Cambridge Univ. Press.
16. H. Minkowski (1903), Volumen und Oberfläche, Math. Ann. 57, 447-495.
17. R. E. Moore (1966), Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ.
18. R. E. Moore (1979), Methods and Applications of Interval Analysis, SIAM, Philadelphia.
19. T. Needham (1997), Visual Complex Analysis, Oxford Univ. Press.
20. H. Schwerdtfeger (1979), Geometry of Complex Numbers, Dover, New York.
21. D. H. Von Seggern (1993), CRC Standard Curves and Surfaces, CRC Press, Boca Raton.
22. J. Serra (1982), Image Analysis and Mathematical Morphology, Academic Press, London.
23. C. Zwikker (1963), The Advanced Geometry of Plane Curves and Their Applications, Dover, New York.