• Corpus ID: 81326

Partitioning Regular Polygons into Circular Pieces I: Convex Partitions

@inproceedings{Damian2003PartitioningRP,
  title={Partitioning Regular Polygons into Circular Pieces I: Convex Partitions},
  author={Mirela Damian and Joseph O'Rourke},
  booktitle={CCCG},
  year={2003}
}
We explore an instance of the question of partitioning a polygon into pieces, each of which is as “circular” as possible, in the sense of having an aspect ratio close to 1. The aspect ratio of a polygon is the ratio of the diameters of the smallest circumscribing circle to the largest inscribed disk. The problem is rich even for partitioning regular polygons into convex pieces, the focus of this paper. We show that the optimal (most circular) partition for an equilateral triangle has an… 
3 Citations

Figures and Tables from this paper

Towards an evolved lower bound for the most circular partition of a square
TLDR
The problem of partitioning a square into convex polygons which are as circular as possible is examined and a solution which is “good enough” with the help of evolutionary algorithms is planned.
30 POLYGONS
TLDR
This chapter describes a collection of results on polygons with both combinatorial and algorithmic flavors.

References

SHOWING 1-10 OF 30 REFERENCES
Decomposing a Polygon into Simpler Components
  • J. Keil
  • Computer Science
    SIAM J. Comput.
  • 1985
TLDR
This paper considers decompositions which do not introduce Steiner points, and applies a technique for improving the efficiency of dynamic programming algorithms to achieve polynomial time algorithms for the problems of decomposing a simple polygon into the minimum number of each of the component types.
Optimal Convex Decompositions
Range Searching and Point Location among Fat Objects
We present a data structure that can store a set of disjoint fat objects in 2- and 3-space such that point location and bounded-size range searching with arbitrarily shaped regions can be performed
Mathematics: From the Birth of Numbers
This extraordinary work takes the reader on a long and fascinating journey--from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry,
Motion planning amidst fat obstacles
TLDR
It is shown that, under some realistic assumptions, the complexity of the free space of a robot moving amidst fat obstacles is linear in the number of obstacles.
Computer graphics—principles and practice
TLDR
These are the short notes for a two hour tutorial on principles and practice of computer graphics and scientific visualization and they cannot completely replace the contents of the tutorial transparencies and slides since restrictions in space and print quality do not permit the inclusion of figures and example images.
Open problems from cccg 2001
TLDR
A list of the problems presented at the open-problem session of the 14th Canadian Conference on Computational Geometry held in Lethbridge, Alberta, Canada on August 12, 2002.
Norton
Analogamente a quanto accade con i generatori di tensione, anche per i generatori di corrente esiste la possibilità di costruire idealmente un generatore di corrente equivalente in grado di
...
...