منابع مشابه
Flipping Edges on Triangulations
In this paper we study the problem of flipping edges in triangulations of polygons and point sets. We prove that if a polygon Qn has k reflex vertices, then any triangulation of Qn can be transformed to another triangulation of Qn with at most O(n + k 2 ) flips. We produce examples of polygons with two triangulations T and T such that to transform T to T requires O(n ) flips. These results are ...
متن کاملFlipping edge-labelled triangulations
Flips in triangulations have received a lot of attention over the past decades. However, the problem of tracking where particular edges go during the flipping process has not been addressed. We examine this question by attaching unique labels to the triangulation edges. We introduce the concept of the orbit of an edge e, which is the set of all edges reachable from e via flips. We establish the...
متن کاملSimultaneous Edge Flipping in Triangulations
We generalize the operation of flipping an edge in a triangulation to that of flipping several edges simultaneously. Our main result is an optimal upper bound on the number of simultaneous flips that are needed to transform a triangulation into another. Our results hold for triangulations of point sets and for polygons.
متن کاملFlipping Edges in Triangulations of Point Sets, Polygons and Maximal Planar Graphs
A triangulation of a point set Pn is a partitioning of the convex hull Conv (Pn) into a set of triangles with disjoint interiors such that the vertices of these triangles are in Pn, and no element of Pn lies in the interior of any of these triangles. An edge e of a triangulation T is called flippable if it is contained in the boundary of two triangles of T , and the union of these triangles for...
متن کاملBraced edges in plane triangulations
A plane triangulation is an embedding of a maximal planar graph in the Euclidean plane. Foulds and Robinson (1979) first studied the problem of transforming one triangulation to another by a sequence of diagonal operations. where a diagonal operation deletes one edge and inserts the other diagonal of the resulting quadrilateral face. An edge which cannot be removed by a single diagonal operatio...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1999
ISSN: 0179-5376
DOI: 10.1007/pl00009464