Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Closing the gap: A workstation-mainframe connection
Computers in Mechanical Engineering
Fast constructive-solid geometry display in the pixel-powers graphics system
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Boundary to constructive solid geometry mappings: a focus on 2D issues
Computer-Aided Design
Offsetting operations in solid modelling
Computer Aided Geometric Design
Solid modeling for production design
IBM Journal of Research and Development
Eliminating Redundant Primitives from Set-Theoretic Solid Models by a Consideration of Constituents
IEEE Computer Graphics and Applications
Efficient intersection tests for objects defined constructively
International Journal of Robotics Research
Constraints in constructive solid geometry
I3D '86 Proceedings of the 1986 workshop on Interactive 3D graphics
AML/X: a programming language for design and manufacturing
ACM '86 Proceedings of 1986 ACM Fall joint computer conference
A null-object detection algorithm for constructive solid geometry
Communications of the ACM
Introduction to Switching Theory and Logical Design
Introduction to Switching Theory and Logical Design
Blending and offsetting solid models (cad/cam, computational geometry, representations, curves, surfaces, approximation)
IBM Journal of Research and Development - Mathematics and computing
Rendering CSG models with a ZZ-buffer
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
The WINSOM solid modeller and its application to data visualization
IBM Systems Journal
Depth-order point classification techniques for CSG display algorithms
ACM Transactions on Graphics (TOG)
An efficient algorithm for CSG to b-rep conversion
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
An efficient intersection algorithm for polyhedral cellular decompositions
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Approximation hierarchies and S-bounds
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
The n-dimensional extended convex differences tree (ECDT) for representing polyhedra
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
The Ray casting engine and Ray representatives
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Determination of mass properties of polygonal CSG objects in parallel
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Refinement methods for geometric bounds in constructive solid geometry
ACM Transactions on Graphics (TOG)
Interactive inspection of solids: cross-sections and interferences
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Efficient parallel evaluation of CSG tree using fixed number of processors
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Obtaining robust Boolean set operations for manifold solids by avoiding and eliminating redundancy.
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Computing CSG tree boundaries as algebraic expressions
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Face-based data structure and its application to robust geometric modeling
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Orthogonal polyhedra as geometric bounds in constructive solid geometry
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Consistent updates in dual representation systems
Proceedings of the fifth ACM symposium on Solid modeling and applications
Applying parallel processing techniques to classification problems in constructive solid geometry
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
IEEE Computer Graphics and Applications
Geometric Reasoning for Extraction of Manufacturing Features in Iso-Oriented Polyhedrons
IEEE Transactions on Pattern Analysis and Machine Intelligence
Blister: GPU-based rendering of Boolean combinations of free-form triangulated shapes
ACM SIGGRAPH 2005 Papers
Boolean Operations with Implicit and Parametric Representation of Primitives Using R-Functions
IEEE Transactions on Visualization and Computer Graphics
Improved Binary Space Partition merging
Computer-Aided Design
HelSweeper: Screw-sweeps of canal surfaces
Computer-Aided Design
Direct rendering of Boolean combinations of self-trimmed surfaces
Computer-Aided Design
Correct shading of regularized CSG solids using a depth-interval buffer
EGGH'90 Proceedings of the Fifth Eurographics conference on Advances in Computer Graphics Hardware: rendering, ray tracing and visualization systems
Accurate scanconversion of triangulated surfaces
EGGH'91 Proceedings of the Sixth Eurographics conference on Advances in Computer Graphics Hardware: rendering, visualization and rasterization hardware
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Solids defined by Boolean combinations of solid primitives may be represented in constructive solid geometry (CSG) as binary trees. Most CSG-based algorithms (e.g., for boundary evaluation, graphic shading, interference detection) do various forms of set-membership classification by traversing the tree associated with the solid. These algorithms usually generate intermediate results that do not contribute to the final result, and hence may be regarded as redundant and a source of inefficiency. To reduce such inefficiencies, we associate with each primitive A in a tree S an active zone Z that represents the region of space where changes to A affect the solid represented by S, and we use a representation of Z instead of S for set-membership classification. In the paper we develop a mathematical theory of active zones, prove that they correspond to the intersection of certain nodes of the original trees, and show how they lead to efficient new algorithms for boundary evaluation, for detecting and eliminating redundant nodes in CSG trees, for interference (null-set) detection, and for graphic shading.