Abstract
Let P and Q be polyhedra one of which is convex. Let n and m be the number of edges of P and Q respectively and let s be the number of edges of the intersection P ∩ Q. We show how to compute P ∩ Q in time O((n + m + s) log(n + m + s)). Previously only algorithms with running time O(nm) were known.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
5. References
H. Edelsbrunner, H.A. Maurer: “Finding Extreme Points in Three Dimensions and Solving the Post-Office Problem in the Plane”, Information Processing Letters, to appear.
St. Hertel, M. Mäntylä, K. Mehlhorn, J. Nievergelt: “Space Sweep Solves Intersection of Two Convex Polyhedra Elegantly”, Acta Informatica, 21, 501–519, 1984.
St. Hertel, K. Mehlhorn: “Fast Triangulation of Simple Polygons”, FCT 83, LNCS Vol 158, 207–218.
D.P. Dobkin, D.G. Kirkpatrick: “Fast Detection of Polyhedral Intersections”, 9th ICALP, LNCS 140, 154–165, 1982.
D. Kirkpatrick: “Optimal Search in Planar Subdivisions”, SICOMP 12, 28–35, 1983.
K. Mehlhorn: “Data Structures and Efficient Algorithms”, Vol 3: “Multi-dimensional Data Structures and Computational Geometry”, Springer Verlag, EATCS Monographs in Computer Science, 1984.
D.E. Muller, F.P. Preparata: “Finding the Intersection of Two Convex Polyhedra”, TCS 7, 217–236, 1978.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mehlhorn, K., Simon, K. (1985). Intersecting two polyhedra one of which is convex. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1985. Lecture Notes in Computer Science, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028837
Download citation
DOI: https://doi.org/10.1007/BFb0028837
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15689-5
Online ISBN: 978-3-540-39636-9
eBook Packages: Springer Book Archive