Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Spheres, molecules, and hidden surface removal
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Voronoi diagram of a circle set from Voronoi diagram of a point set: topology
Computer Aided Geometric Design
Voronoi diagram of a circle set from Voronoi diagram of a point set: geometry
Computer Aided Geometric Design
Principles of CAD/CAM/CAE Systems
Principles of CAD/CAM/CAE Systems
On the combinatorial complexity of euclidean Voronoi cells and convex hulls of d-dimensional spheres
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space
Computer Aided Geometric Design
Vertex-based boundary representation of nonmanifold geometric models
Vertex-based boundary representation of nonmanifold geometric models
Proximity and applications in general metrics
Proximity and applications in general metrics
Data Structures and Algorithms in Java
Data Structures and Algorithms in Java
Region-expansion for the Voronoi diagram of 3D spheres
Computer-Aided Design
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Computer-Aided Design
An efficient algorithm for three-dimensional β-complex and β-shape via a quasi-triangulation
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Molecular surfaces on proteins via beta shapes
Computer-Aided Design
A new digital watermarking scheme for 3D triangular mesh models
Signal Processing
Region-expansion for the Voronoi diagram of 3D spheres
Computer-Aided Design
Computer-Aided Design
Interaction interfaces in proteins via the Voronoi diagram of atoms
Computer-Aided Design
A sweepline algorithm for Euclidean Voronoi diagram of circles
Computer-Aided Design
Manifoldization of β-shapes in O(n) time
Computer-Aided Design
Real-time triangulation of molecular surfaces
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Multi-resolution protein model
ICCSA'07 Proceedings of the 2007 international conference on Computational science and Its applications - Volume Part II
Topologies of surfaces on molecules and their computation in O(n) time
Computer-Aided Design
Quasi-worlds and quasi-operators on quasi-triangulations
Computer-Aided Design
Three-dimensional beta-shapes and beta-complexes via quasi-triangulation
Computer-Aided Design
QTF: Quasi-triangulation file format
Computer-Aided Design
Anomalies in quasi-triangulations and beta-complexes of spherical atoms in molecules
Computer-Aided Design
Pedestrian position and pathway in the design of 3D mobile interactive navigation aid
Proceedings of the 10th International Conference on Advances in Mobile Computing & Multimedia
3D Maps in Mobile Devices: Pathway Analysis for Interactive Navigation Aid
International Journal of Mobile Computing and Multimedia Communications
Protein structure optimization by side-chain positioning via beta-complex
Journal of Global Optimization
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Given a set of spheres in 3D, constructing its Voronoi diagram in Euclidean distance metric is not easy at all even though many mathematical properties of its structure are known. This Voronoi diagram has been known for many important applications from science and engineering. In this paper, we characterize the Voronoi diagram of spheres in three-dimensional Euclidean space, which is also known as an additively weighted Voronoi diagram, and propose an algorithm to construct the diagram. Starting with the ordinary Voronoi diagram of the centers of the spheres, the proposed region-expansion algorithm constructs the desired diagram by expanding the Voronoi region of each sphere, one after another. We also show that the whole Voronoi diagram of n spheres can be constructed in O(n^3) time in the worst case.