Introduction to Solid Modeling
Introduction to Solid Modeling
A solid modelling system free from topological inconsistency
Journal of Information Processing
Boolean set operations on non-manifold boundary representation objects
Computer-Aided Design - Beyond solid modelling
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
On the definition and the construction of pockets in macromolecules
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
Matchmaker: manifold BReps for non-manifold r-sets
Proceedings of the fifth ACM symposium on Solid modeling and applications
Principles of CAD/CAM/CAE Systems
Principles of CAD/CAM/CAE Systems
Cutting and Stitching: Converting Sets of Polygons to Manifold Surfaces
IEEE Transactions on Visualization and Computer Graphics
Nonmanifold Topology Based on Coupling Entities
IEEE Computer Graphics and Applications
Vertex-based boundary representation of nonmanifold geometric models
Vertex-based boundary representation of nonmanifold geometric models
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
A Combinatorial Analysis of Boundary Data Structure Schemata
IEEE Computer Graphics and Applications
Molecular surfaces on proteins via beta shapes
Computer-Aided Design
Triangulation of molecular surfaces
Computer-Aided Design
Region-expansion for the Voronoi diagram of 3D spheres
Computer-Aided Design
Computer-Aided Design
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Computer-Aided Design
Manifoldization of β-shapes by topology operators
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
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
Protein-ligand docking based on beta-shape
Transactions on computational science IX
Protein-ligand docking based on beta-shape
Transactions on computational science IX
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The @b-shape and the @b-complex are recently announced geometric constructs which facilitate efficient reasoning about the proximity among spherical particles in three-dimensional space. They have proven to be very useful for the structural analysis of bio-molecules such as proteins. Being non-manifold, however, the topology traversal on the boundary of the @b-shape is inconvenient for reasoning about the surface structure of a sphere set. In this paper, we present an algorithm to transform a @b-shape from being non-manifold to manifold without altering any of the geometric characteristics of the model. After locating the simplexes where the non-manifoldness is defined on the @b-shape, the algorithm augments the @b-complex which corresponds to the @b-shape so that all the non-manifoldness is resolved on such simplexes. The algorithm runs in O(n) time, without any floating-point operation, in the worst case for protein models where n is the number of spherical atoms. We also provide some experimental results obtained from real protein models available from the Protein Data Bank.