Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Algorithms for packing squares: a probabilistic analysis
SIAM Journal on Computing
Penny-packing and two-dimensional codes
Discrete & Computational Geometry
Double-lattice packings of convex bodies in the plane
Discrete & Computational Geometry
Packing and covering the plane with translates of a convex polygon
Journal of Algorithms
SIAM Journal on Computing
The densest packing of equal circles into a parallel strip
Discrete & Computational Geometry
A packing problem with applications to lettering of maps
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Arrangements of curves in the plane—topology, combinatorics, and algorithms
Theoretical Computer Science
Linear-size nonobtuse triangulation of polygons
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
New results in the packing of equal circles in a square
Discrete Mathematics
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
A Delaunay based numerical method for three dimensions: generation, formulation, and partition
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Translational polygon containment and minimal enclosure using linear programming based restriction
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on Computing
Finding the largest area axis-parallel rectangle in a polygon
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Guaranteed-quality Delaunay meshing in 3D (short version)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Pipes, cigars, and kreplach: the union of Minkowski sums in three dimensions
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A new and simple algorithm for quality 2-dimensional mesh generation
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Efficient automatic part nesting on irregular and inhomogeneous surfaces
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Finding minimal convex nested polygons
SCG '85 Proceedings of the first annual symposium on Computational geometry
Densest translational lattice packing of non-convex polygons (extended abstract)
Proceedings of the sixteenth annual symposium on Computational geometry
Computing the arrangement of curve segments: divide-and-conquer algorithms via sampling
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Column-Based Strip Packing Using Ordered and Compliant Containment
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Approximation of Geometric Dispersion Problems
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Use of Shape for Automated, Optimized 3D Radiosurgical Treatment Planning
VBC '96 Proceedings of the 4th International Conference on Visualization in Biomedical Computing
A probabilistic analysis of multidimensional bin packing problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
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The problem of packing congruent spheres (i.e., copies of the same sph ere) in a bounded domain arises in many applications. In this paper, we present a new pack-and-shake scheme for packing congruent spheres in various bounded 2-D domains. Our packing scheme is based on a number of interesting ideas, such as a trimming and packing approach, optimal lattice packing under translation and/or rotation, shaking procedures, etc. Our packing algorithms have fairly low time complexities. In certain cases, they even run in nearly linear time. Our techniques can be easily generalized to congruent packing of other shapes of objects, and are readily extended to higher dimensional spaces. Applications of our packing algorithms to treatment planning of radiosurgery are discussed. Experimental results suggest that our algorithms produce reasonably dense packings.