Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
The design and analysis of spatial data structures
The design and analysis of spatial data structures
K-d trees for semidynamic point sets
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Stalk: An Interactive System for Virtual Molecular Docking
IEEE Computational Science & Engineering
Geometric Manipulation of Flexible Ligands
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Defining, Computing, and Visualizing Molecular Interfaces
VIS '95 Proceedings of the 6th conference on Visualization '95
Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space
Computer Aided Geometric Design
Interface surfaces for protein-protein complexes
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
HAPTICS '06 Proceedings of the Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems
Presence: Teleoperators and Virtual Environments
Real-time KD-tree construction on graphics hardware
ACM SIGGRAPH Asia 2008 papers
Interaction interfaces in proteins via the Voronoi diagram of atoms
Computer-Aided Design
Euclidean Voronoi diagram of 3D balls and its computation via tracing edges
Computer-Aided Design
Euclidean voronoi diagrams of 3d spheres: their construction and related problems from biochemistry
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
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The interaction interface between two molecules can be represented as a bisector surface equidistant from the two sets of spheres of varying radii representing atoms. We recursively divide a box containing both sphere-sets into uniform pairs of sub-boxes. The distance from each new box to each sphere-set is conservatively approximated by an interval, and the number of sphere-box computations is greatly reduced by pre-partitioning each sphere-set using a kd-tree. The subdivision terminates at a specified resolution, creating a box partition (BP) tree. A piecewise linear approximation of the bisector surface is then obtained by traversing the leaves of the BP tree and connecting points equidistant from the sphere-sets. In 124 experiments with up to 16,728 spheres, a bisector surface with a resolution of 1/2^4 of the original bounding box was obtained in 28.8 ms on average.