Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Boolean operations of 2-manifolds through vertex neighborhood classification
ACM Transactions on Graphics (TOG)
Constructive solid geometry for polyhedral objects
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Primitives for the manipulation of three-dimensional subdivisions
SCG '87 Proceedings of the third annual symposium on Computational geometry
Towards implementing robust geometric computations
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
On the representation and manipulation of rigid solids
On the representation and manipulation of rigid solids
The synthesis of solids bounded by many faces
Communications of the ACM
Using tolerances to guarantee valid polyhedral modeling results
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Incremental Boundary Evaluation Using Inference of Edge Classifications
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Error-free boundary evaluation using lazy rational arithmetic: a detailed implementation
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
Computational geometry: a retrospective
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Polyhedral modelling with exact arithmetic
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Boundary representation modelling with local tolerances
SMA '95 Proceedings of the third 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
Accelerated occlusion culling using shadow frusta
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Computing exact geometric predicates using modular arithmetic with single precision
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
IEEE Transactions on Computers
Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Converting sets of polygons to manifold surfaces by cutting and stitching
Proceedings of the conference on Visualization '98
Use of topological constraints in construction and processing of robust solid models
Proceedings of the sixth ACM symposium on Solid modeling and applications
Cutting and Stitching: Converting Sets of Polygons to Manifold Surfaces
IEEE Transactions on Visualization and Computer Graphics
Removing Zero-Volume Parts from CAD Models for Layered Manufacturing
IEEE Computer Graphics and Applications
An optimal algorithm for the minimum edge cardinality cut surface problem
Proceedings of the nineteenth annual symposium on Computational geometry
Handling degeneracies in exact boundary evaluation
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Technical section: A new algorithm for Boolean operations on general polygons
Computers and Graphics
SGP '09 Proceedings of the Symposium on Geometry Processing
Practical boolean operations on point-sampled models
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Technical note: Fast and robust Booleans on polyhedra
Computer-Aided Design
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An algorithm for performing regularized Boolean operation on polyhedral solids is described. Robustness is achieved by adding symbolic reasoning as a supplemental step to resolve possible numerical uncertainty. Additionally, numerical redundancy and numerical computation based on derived quantities are reduced as much as possible. Experience with an implementation of the algorithm, using a unit-cube example as a simple test object for robustness, is discussed.