Computational geometry: an introduction
Computational geometry: an introduction
On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
Combinatorial complexity bounds for arrangements of curves and spheres
Discrete & Computational Geometry - Special issue on the complexity of arrangements
A singly exponential stratification scheme for real semi-algebraic varieties and its applications
Theoretical Computer Science
Fat triangles determine linearly many holes
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Point location in fat subdivisions
Information Processing Letters
Efficient hidden surface removal for objects with small union size
Computational Geometry: Theory and Applications
The complexity of the free space for a robot moving amidst fat obstacles
Computational Geometry: Theory and Applications
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Ray Shooting, Depth Orders and Hidden Surface Removal
Ray Shooting, Depth Orders and Hidden Surface Removal
Fast analytical computation of Richards's smooth molecular surface
VIS '93 Proceedings of the 4th conference on Visualization '93
Fast and robust computation of molecular surfaces
Proceedings of the eleventh annual symposium on Computational geometry
Simple and practical geometric algorithms
ACM Computing Surveys (CSUR) - Special issue: position statements on strategic directions in computing research
A perturbation scheme for spherical arrangements with application to molecular modeling
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Fast collision detection among multiple moving spheres
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Analysis of a bounding box heuristic for object intersection
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
PVGS '99 Proceedings of the 1999 IEEE symposium on Parallel visualization and graphics
Analysis of a bounding box heuristic for object intersection
Journal of the ACM (JACM)
Analyzing bounding boxes for object intersection
ACM Transactions on Graphics (TOG)
Finite-resolution hidden surface removal
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Fast Collision Detection Among Multiple Moving Spheres
IEEE Transactions on Visualization and Computer Graphics
Defining, Computing, and Visualizing Molecular Interfaces
VIS '95 Proceedings of the 6th conference on Visualization '95
Reasoning about Molecular Similarity and Properties
CSB '04 Proceedings of the 2004 IEEE Computational Systems Bioinformatics Conference
Molecular surfaces on proteins via beta shapes
Computer-Aided Design
Triangulation of molecular surfaces
Computer-Aided Design
A dynamic data structure for flexible molecular maintenance and informatics
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
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
Real-time triangulation of molecular surfaces
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Three-dimensional beta-shapes and beta-complexes via quasi-triangulation
Computer-Aided Design
Reduction of the search space in the edge-tracing algorithm for the voronoi diagram of 3d balls
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
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
QTF: Quasi-triangulation file format
Computer-Aided Design
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We devise techniques to manipulate a collection of loosely interpenetrating spheres in three-dimensional space. Our study is motivated by the representation and manipulation of molecular configurations, modeled by a collection of spheres. We analyze the sphere model and point to its favorable properties that make it more easy to manipulate than an arbitrary collection of spheres. For this special sphere model we present efficient algorithms for computing its union boundary and for hidden surface removal. The efficiency and practicality of our approach are demonstrated by experiments on actual protein data.