3D Solid Region Detection for Accurate CSG Segmentation
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Solution Overview
Problem
Traditional techniques for performing constructive solid geometry (CSG) operations fail to accurately identify and segregate disconnected components of 3D objects, leading to inaccuracies in the simulation of virtual environments.
Innovation Solution
A system and method for identifying connected components in a 3D object mesh using breadth-first search or depth-first search, determining topologically interconnected sections, and utilizing a disjoint-set data structure to detect distinct solid regions, with enhancements for early termination and preservation of vertex properties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional CSG operations are used to combine or subtract solid objects, then basic geometric operations can be performed, but accurate identification and segregation of disconnected components fails
Solution Approach 1:
The patent applies segmentation by dividing the 3D mesh into connected components using graph traversal algorithms. Each vertex is treated as a node in a graph, and edges represent connectivity. The algorithm segments the mesh by traversing connected nodes and grouping them into distinct components, enabling accurate identification of disconnected regions in CSG operations.
Solution Approach 2:
The patent introduces an intermediary data structure (disjoint-set/union-find) to mediate between the mesh geometry and the connectivity analysis. This intermediary structure efficiently tracks which vertices belong to the same connected component through path compression and union operations, resolving the contradiction by providing a reliable intermediate representation for component identification.
2Difficulty of detecting and measuring
If mesh traversal algorithms are implemented to identify connected components, then component detection capability is improved, but computational complexity increases
Solution Approach 1:
The patent creates a simplified copy of the mesh connectivity structure as a graph representation, where vertices become nodes and edges represent connectivity. This copied structure can be traversed efficiently using standard graph algorithms without modifying the original mesh data, reducing computational complexity while maintaining detection capability.
Solution Approach 2:
The patent replaces complex geometric analysis with a simpler graph theory approach. Instead of performing complex 3D geometric computations to determine connectivity, the system substitutes this with efficient graph traversal and disjoint-set operations, significantly reducing computational complexity while improving component detection.
3Reliability
If disconnected components are accurately identified and segregated, then simulation realism is improved, but processing time increases
Solution Approach 1:
The patent performs connected component analysis as a preliminary step before executing CSG operations or simulations. By pre-identifying and segregating disconnected components into separate data structures, the system prepares the geometry in advance, allowing subsequent simulation operations to proceed efficiently without re-analysis, thus reducing overall processing time while maintaining realism.
Data Source
AI summary
Implementations relate to methods, systems, and computer-readable media to detect connected solid regions in solid geometry objects. In some implementations, the method may include obtaining a mesh for a three-dimensional (3D) object, wherein the mesh includes a plurality of polygons, identifying, based on the plurality of polygons, connected components of the 3D object, determining, based on the connected components, two or more topologically interconnected sections of the 3D object, identifying a containment relationship between the two or more topologically interconnected sections of the 3D object, determining, based on the containment relationship, one or more distinct solid regions of the 3D object, determining an updated state of a first distinct solid region of the 3D object, wherein the updated state includes an updated position or an updated orientation, and causing the first distinct solid region of the 3D object in the updated state to be displayed within a virtual environment.