Object representation by means of nonminimal division quadtrees and octrees
ACM Transactions on Graphics (TOG)
Boolean operations of 2-manifolds through vertex neighborhood classification
ACM Transactions on Graphics (TOG)
Space division for ray tracing in CSG
IEEE Computer Graphics and Applications
A geometric modeller based on the exact octtree representation of polyhedra
Computer Graphics Forum
An Algorithm for Geometric Set Operations Using Cellular Subdivision Techniques
IEEE Computer Graphics and Applications
Extended octtree representation of free form surfaces
Computer Aided Geometric Design - Special issue: Topics in CAGD
Hierarchical Data Structures and Algorithms for Computer Graphics. Part I.
IEEE Computer Graphics and Applications
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Region representation: quadtrees from boundary codes
Communications of the ACM
Robust Set Operations on Polyhedral Solids
Robust Set Operations on Polyhedral Solids
Spatial decomposition of a tumor into a minimum number of spherical components
SAC '92 Proceedings of the 1992 ACM/SIGAPP symposium on Applied computing: technological challenges of the 1990's
Boundary evaluation using adaptive polygonization
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
NC milling error assessment and tool path correction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Topology-reducing surface simplification using a discrete solid representation
ACM Transactions on Graphics (TOG)
Approximate envelope reconstruction for moving solids
Mathematical Methods for Curves and Surfaces
IEEE Transactions on Visualization and Computer Graphics
IEEE Computer Graphics and Applications
An interactive modification data structure for 3D surfaces
Machine Graphics & Vision International Journal
Robust repair of polygonal models
ACM SIGGRAPH 2004 Papers
Automatic restoration of polygon models
ACM Transactions on Graphics (TOG)
Layer-Based Representation of Polyhedrons for Point Containment Tests
IEEE Transactions on Visualization and Computer Graphics
Dual Marching Tetrahedra: Contouring in the Tetrahedronal Environment
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Some Applications of Interval Arithmetic in Hierarchical Solid Modeling
Numerical Validation in Current Hardware Architectures
Fixing geometric errors on polygonal models: a survey
Journal of Computer Science and Technology
Combining SP-Octrees and impostors for the visualisation of multiresolution models
Computers and Graphics
Technical section: Point in solid strategies
Computers and Graphics
A reliable extended octree representation of CSG objects with an adaptive subdivision depth
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
A virtual reality system for the determination of critical machining-process parameters
International Journal of Intelligent Engineering Informatics
STEP-NC based high-level machining simulations integrated with CAD/CAPP/CAM
International Journal of Automation and Computing
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Solid modelers must be based on reliable and fast algorithms for Boolean operations. The octree model, as well as several generalizations (polytrees, integrated polytrees, extended octrees), is specially well suited for these algorithms and can be used either as a primary or as a secondary model in solid modeling systems. This paper is concerned with a precise definition of the extended octree model that allows the representation of nonmanifold objects with planar faces and, consequently, is closed under Boolean operations on polyhedrons. Boolean nodes and nearly vertex nodes are introduced, and the model is discussed in comparison with related representations. A fast algorithm for the direct generation of the extended octree from the geometry of the base polygon in extrusion solids is presented, and its complexity is studied. Boolean operation algorithms are introduced.