3D Objects Representation for Real-Time Boolean Operations

The paper presents a comparative analysis of methods for the representation of three-dimensional objects to perform real-time Boolean operations in the Unity game engine environment. Four main approaches are considered: polygonal representation based on constructive solid geometry (CSG), sign distan...

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Veröffentlicht in:Automatic documentation and mathematical linguistics Jg. 59; H. Suppl 3; S. S189 - S197
Hauptverfasser: Plotnikov, I. E., Kostyuk, D. I.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Moscow Pleiades Publishing 01.11.2025
Springer Nature B.V
Schlagworte:
Accuracy
Algorithms
Application
Boolean
Boundary representation
Comparative analysis
Computer Science
Construction costs
Constructive solid geometry
Engines
Games
Geometry
Information Storage and Retrieval
Mathematical models
Methods
Multilayers
Pipelines
Polygons
Preservation
Real time operation
Representation
Simulators
Transformation
Virtual reality
Visual effects
Visualization
Boolean operations
3D modeling
constructive solid geometry
SDF
Unity
real-time
ray marching
polygonal meshes
signed distance functions
ISSN:0005-1055, 1934-8371
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Abstract The paper presents a comparative analysis of methods for the representation of three-dimensional objects to perform real-time Boolean operations in the Unity game engine environment. Four main approaches are considered: polygonal representation based on constructive solid geometry (CSG), sign distance functions (SDF), voxel methods, and CAD-systems with boundary representation (B-Rep) and NURBS-surfaces. An experimental study of the performance of polygonal algorithms of Boolean operations and SDF functions based on ray-marching implementation is conducted. It is revealed that polygonal methods are characterized by high initial system construction costs, but they provide stable performance during long operations and preservation of transformation results. SDF functions demonstrate high-speed operations and flexibility in creating smooth transitions between objects but are limited in their application to long-term tasks due to the peculiarities of the computational model. The areas of effective application of each approach are identified: polygonal methods are recommended for tasks that require precise geometric control and integration with traditional graphics pipelines, while SDF functions are optimal for procedural generation, multilayer material rendering, and the creation of dynamic visual effects. The results of this study can be used in the development of interactive simulators, game applications and virtual reality systems.
AbstractList The paper presents a comparative analysis of methods for the representation of three-dimensional objects to perform real-time Boolean operations in the Unity game engine environment. Four main approaches are considered: polygonal representation based on constructive solid geometry (CSG), sign distance functions (SDF), voxel methods, and CAD-systems with boundary representation (B-Rep) and NURBS-surfaces. An experimental study of the performance of polygonal algorithms of Boolean operations and SDF functions based on ray-marching implementation is conducted. It is revealed that polygonal methods are characterized by high initial system construction costs, but they provide stable performance during long operations and preservation of transformation results. SDF functions demonstrate high-speed operations and flexibility in creating smooth transitions between objects but are limited in their application to long-term tasks due to the peculiarities of the computational model. The areas of effective application of each approach are identified: polygonal methods are recommended for tasks that require precise geometric control and integration with traditional graphics pipelines, while SDF functions are optimal for procedural generation, multilayer material rendering, and the creation of dynamic visual effects. The results of this study can be used in the development of interactive simulators, game applications and virtual reality systems.
Author Plotnikov, I. E.
Kostyuk, D. I.
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  organization: Kazan Federal University
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  givenname: D. I.
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  surname: Kostyuk
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  organization: Kazan Federal University
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Copyright Allerton Press, Inc. 2025 ISSN 0005-1055, Automatic Documentation and Mathematical Linguistics, 2025, Vol. 59, Suppl. 3, pp. S189–S197. © Allerton Press, Inc., 2025.Russian Text © The Author(s), 2025, published in Elektronnye Biblioteki, 2025, Vol. 28, No. 3, pp. 484–505.
Allerton Press, Inc. 2025.
Copyright_xml – notice: Allerton Press, Inc. 2025 ISSN 0005-1055, Automatic Documentation and Mathematical Linguistics, 2025, Vol. 59, Suppl. 3, pp. S189–S197. © Allerton Press, Inc., 2025.Russian Text © The Author(s), 2025, published in Elektronnye Biblioteki, 2025, Vol. 28, No. 3, pp. 484–505.
– notice: Allerton Press, Inc. 2025.
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Keywords Boolean operations
3D modeling
constructive solid geometry
SDF
Unity
real-time
ray marching
polygonal meshes
signed distance functions
Language English
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SubjectTerms Accuracy
Algorithms
Application
Boolean
Boundary representation
Comparative analysis
Computer Science
Construction costs
Constructive solid geometry
Engines
Games
Geometry
Information Storage and Retrieval
Mathematical models
Methods
Multilayers
Pipelines
Polygons
Preservation
Real time operation
Representation
Simulators
Transformation
Virtual reality
Visual effects
Visualization
Title 3D Objects Representation for Real-Time Boolean Operations
URI https://link.springer.com/article/10.3103/S000510552570092X
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