Edge—edge relationships in geometric modelling
Computer-Aided Design
Verifiable implementation of geometric algorithms using finite precision arithmetic
Artificial Intelligence - Special issue on geometric reasoning
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Essential ray tracing algorithms
An introduction to ray tracing
Efficient exact arithmetic for computational geometry
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Polyhedral modelling with exact arithmetic
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Interval arithmetic yields efficient dynamic filters for computational geometry
Proceedings of the fourteenth annual symposium on Computational geometry
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Robust Set Operations on Polyhedral Solids
IEEE Computer Graphics and Applications
Winged edge polyhedron representation.
Winged edge polyhedron representation.
Towards and open curved kernel
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Improved Binary Space Partition merging
Computer-Aided Design
Robustness of Boolean Operations on Subdivision-Surface Models
Numerical Validation in Current Hardware Architectures
Solid modeling of polyhedral objects by Layered Depth-Normal Images on the GPU
Computer-Aided Design
Technical note: Fast and robust Booleans on polyhedra
Computer-Aided Design
Fast and accurate evaluation of regularized Boolean operations on triangulated solids
Computer-Aided Design
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We present a topologically robust algorithm for Boolean operations on polyhedral boundary models. The algorithm can be proved always to generate a result with valid connectivity if the input shape representations have valid connectivity, irrespective of the type of arithmetic used or the extent of numerical errors in the computations or input data. The main part of the algorithm is based on a series of interdependent operations. The relationship between these operations ensures a consistency in the intermediate results that guarantees correct connectivity in the final result. Either a triangle mesh or polygon mesh can be used. Although the basic algorithm may generate geometric artifacts, principally gaps and slivers, a data smoothing post-process can be applied to the result to remove such artifacts, thereby making the combined process a practical and reliable way of performing Boolean operations.