Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
Boolean set operations on non-manifold boundary representation objects
Computer-Aided Design - Beyond solid modelling
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Algorithmic geometry
On the definition and the construction of pockets in macromolecules
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
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
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
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
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Computer-Aided Design
Convex hull and voronoi diagram of additively weighted points
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Topologies of surfaces on molecules and their computation in O(n) time
Computer-Aided Design
Three-dimensional beta-shapes and beta-complexes via quasi-triangulation
Computer-Aided Design
Querying simplexes in quasi-triangulation
Computer-Aided Design
QTF: Quasi-triangulation file format
Computer-Aided Design
Technical Section: Efficient construction of the Čech complex
Computers and Graphics
Anomalies in quasi-triangulations and beta-complexes of spherical atoms in molecules
Computer-Aided Design
Protein structure optimization by side-chain positioning via beta-complex
Journal of Global Optimization
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Quasi-triangulation is the dual structure of the Voronoi diagram of spheres, and it has been used as a convenient and powerful geometric construct for representing the proximity among spherical particles with different radii. In this paper, we present the formalism of the quasi-triangulation based on a quasi-world model and define primitive query operators called quasi-operators for correct and efficient topology traversal on the quasi-triangulation. Algorithms for the quasi-operators are also presented based on the extended inter-world data structure. The proposed quasi-operators have the potential to be a fundamental platform on which efficient algorithms for application problems on quasi-triangulation can be correctly and easily developed. The recently announced powerful constructs of the @b-complex and the @b-shape are such examples.