منابع مشابه
Polygons Cuttable by a Circular Saw
We introduce and characterize a new class of polygons that models wood, stone, glass, and ceramic shapes that can be cut with a table saw, lapidary trim saw, or other circular saw. In this model, a circular saw is a line segment (in projection) that can move freely in empty space, but can only cut straight into a portion of material. Once a region of material is separated from the rest, it can ...
متن کاملCutting Out Polygons with a Circular Saw
Given a simple (cuttable) polygon Q drawn on a piece of planar material R, we cut Q out of R by a (small) circular saw with a total number of cuts no more than twice the optimal. This improves the previous approximation ratio of 2.5 obtained by Demaine et al. in 2001.
متن کاملCutting out polygon collections with a saw
I) Given a segment-cuttable polygon P drawn on a planar piece of material Q, we show how to cut P out of Q by a (short) segment saw with a total length of the cuts no more than 2.5 times the optimal. We revise the algorithm of Demaine et al. (2001) so as to achieve this ratio. (II) We prove that any collection R of n disjoint1 axis-parallel rectangles drawn on a planar piece of material Q is cu...
متن کاملHierarchical Decompositions and Circular Ray Shooting in Simple Polygons
A hierarchical decomposition of a simple polygon is introduced. The hierarchy has depth O(log n), linear size, and its regions have at most three neighbors. Using this hierarchy, circular ray shooting queries in a simple polygon can be answered in O(log n) query time and O(n log n) space. If the radius of the circle is xed, the query time can be improved to O(log n) and the space to O(n).
متن کاملPartitioning Regular Polygons into Circular Pieces II:Nonconvex Partitions
In [DO03] we explored partitioning regular k-gons into “circular” convex pieces. Circularity of a polygon is measured by the aspect ratio: the ratio of the diameters of the smallest circumscribing circle to the largest inscribed disk. We seek partitions with aspect ratio close to 1, ideally the optimal ratio. Although we start with regular polygons, most of the machinery developed extends to ar...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computational Geometry
سال: 2001
ISSN: 0925-7721
DOI: 10.1016/s0925-7721(01)00036-0