Flipping Edges on Triangulations
نویسندگان
چکیده
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 then extended to triangulations of point sets. We also show that any triangulation of an n point set always has n − 4 2 edges that can be flipped.
منابع مشابه
The Edge-flipping Distance of Triangulations
An edge-flipping operation in a triangulation T of a set of points in the plane is a local restructuring that changes T into a triangulation that differs from T in exactly one edge. The edgeflipping distance between two triangulations of the same set of points is the minimum number of edge-flipping operations needed to convert one into the other. In the context of computing the rotation distanc...
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 کاملA Lower Bound on the Diameter of the Flip Graph
The flip graph is the graph whose nodes correspond to non-isomorphic combinatorial triangulations and whose edges connect pairs of triangulations that can be obtained one from the other by flipping a single edge. In this note we show that the diameter of the flip graph is at least
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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996