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Boolean Operations for Polygonal Meshes
Čižmarik, Roman ; Matýšek, Michal (referee) ; Španěl, Michal (advisor)
The aim of this work is to create a library for Boolean operations on 3D polygonal meshes. Resulting library has to support open models, its memory requirements shouldn't exceed those of existing solutions and it should, ideally, support multiple models. Most of the existing solutions are vulnerable to arithmetic inaccuracies, or do not support open meshes. The solution is based on Adaptive Mesh Booleans method which treats input models as adaptive surfaces. This method assumes that input models can be arbitrarily refined and no individual polygon is particularly important. Instead of computing exact polygon intersections, the input meshes are refined in intersection regions, intersecting polygons are discarded and created holes are closed. Advantages of this approach are robustness against numerical errors, support for open meshes, possibility to trade accuracy for computation time and ability to solve cases like co-planar and near-coincident regions. The resulting library offers three Boolean operations: union, difference and intersection.
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Analysis of General Polygon Boolean Operation Algorithms
Daněk, Tomáš ; Zemčík, Pavel (referee) ; Beran, Vítězslav (advisor)
This thesis deals with general polygon boolean operation algorithms. Boolean operations are e.g. intersection, union or difference. A general polygon can be e.g. a selfinterecting polygon with inner hole. Clipping of polygons against a rectangular window is probably the most familiar boolean operation on polygons. At first, basic definitions are listed. Then the principles of a selected set of boolean operation algorithms are reviewed. Finally, a complex comparison of the algorithms is undertaken. Performance as well as the ability to handle degenerate cases are tested. The output of this thesis is an overall evaluation of algorithm properties and a dynamic library that contains the implementation of all of the tested algorithms.
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Boolean Operations for Polygonal Meshes
Čižmarik, Roman ; Matýšek, Michal (referee) ; Španěl, Michal (advisor)
The aim of this work is to create a library for Boolean operations on 3D polygonal meshes. Resulting library has to support open models, its memory requirements shouldn't exceed those of existing solutions and it should, ideally, support multiple models. Most of the existing solutions are vulnerable to arithmetic inaccuracies, or do not support open meshes. The solution is based on Adaptive Mesh Booleans method which treats input models as adaptive surfaces. This method assumes that input models can be arbitrarily refined and no individual polygon is particularly important. Instead of computing exact polygon intersections, the input meshes are refined in intersection regions, intersecting polygons are discarded and created holes are closed. Advantages of this approach are robustness against numerical errors, support for open meshes, possibility to trade accuracy for computation time and ability to solve cases like co-planar and near-coincident regions. The resulting library offers three Boolean operations: union, difference and intersection.
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Analysis of General Polygon Boolean Operation Algorithms
Daněk, Tomáš ; Zemčík, Pavel (referee) ; Beran, Vítězslav (advisor)
This thesis deals with general polygon boolean operation algorithms. Boolean operations are e.g. intersection, union or difference. A general polygon can be e.g. a selfinterecting polygon with inner hole. Clipping of polygons against a rectangular window is probably the most familiar boolean operation on polygons. At first, basic definitions are listed. Then the principles of a selected set of boolean operation algorithms are reviewed. Finally, a complex comparison of the algorithms is undertaken. Performance as well as the ability to handle degenerate cases are tested. The output of this thesis is an overall evaluation of algorithm properties and a dynamic library that contains the implementation of all of the tested algorithms.
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