Properties of Conflict Sets in the Plane

• Autorzy: Dirk Siersma
• Języki publikacji: EN

Abstrakty

EN

This paper studies the smoothness and the curvature of conflict sets of the distance function in the plane. Conflict sets are also well known as 'bisectors'. We prove smoothness in the case of two convex sets and give a formula for the curvature. We generalize moreover to weighted distance functions, the so-called Johnson-Mehl model.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1999
• Tom: 50
• Numer: 1
• Strony: 267-276

Daty

wydano

1999

Twórcy

autor

Dirk Siersma

• Mathematisch Instituut, Universiteit Utrecht, Postbus 80.010, 3508 TA Utrecht, The Netherlands

Bibliografia

• [Be] M. Berger, Geometry I and II, Universitext, Springer, Berlin, 1987.
• [BG] J. W. Bruce, P. J. Giblin, Curves and Singularities, Cambridge Univ. Press, Cambridge, 1984.
• [Cox] H. S. M. Coxeter, Introduction to Geometry, Wiley, New York, 1961.
• [Go] A. Goddijn, Smoothness Properties of Conflict Sets (in Dutch), Nascholingscursus Achtergronden van de Meetkunde, Utrecht, 1997 (translation in preparation).
• [Ma] M. van Manen, Thesis Project on Conflict Sets (in progress), Utrecht University.
• [Mi] J. Milnor, Morse Theory, Ann. of Math. Stud. 51, Princeton Univ. Press, Princeton, 1963.
• [Ok] A. Okabe, B. Boots, K. Sugihara, Spatial Tesselations: Concepts and Applications of Voronoi Diagrams, Wiley Ser. Probab. Math. Statist. Appl. Probab. Statist., Wiley, Chichester, 1992.
• [Po] I. R. Porteous, Geometric Differentiation for the Intelligence of Curves and Surfaces, Cambridge Univ. Press, Cambridge, 1994.
• [SSG] J. Sotomayor, D. Siersma, R. Garcia, Curvatures of conflict surfaces in Euclidean 3-space, this volume.