# Properties of Conflict Sets in the Plane

Banach Center Publications (1999)

- Volume: 50, Issue: 1, page 267-276
- ISSN: 0137-6934

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topSiersma, Dirk. "Properties of Conflict Sets in the Plane." Banach Center Publications 50.1 (1999): 267-276. <http://eudml.org/doc/209013>.

@article{Siersma1999,

abstract = {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.},

author = {Siersma, Dirk},

journal = {Banach Center Publications},

keywords = {conflict set; bisector; Johnson-Mehl model},

language = {eng},

number = {1},

pages = {267-276},

title = {Properties of Conflict Sets in the Plane},

url = {http://eudml.org/doc/209013},

volume = {50},

year = {1999},

}

TY - JOUR

AU - Siersma, Dirk

TI - Properties of Conflict Sets in the Plane

JO - Banach Center Publications

PY - 1999

VL - 50

IS - 1

SP - 267

EP - 276

AB - 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.

LA - eng

KW - conflict set; bisector; Johnson-Mehl model

UR - http://eudml.org/doc/209013

ER -

## References

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- [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. Zbl0877.52010
- [Po] I. R. Porteous, Geometric Differentiation for the Intelligence of Curves and Surfaces, Cambridge Univ. Press, Cambridge, 1994. Zbl0806.53001
- [SSG] J. Sotomayor, D. Siersma, R. Garcia, Curvatures of conflict surfaces in Euclidean 3-space, this volume. Zbl0983.53003

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