Equivalence Classes for 3D Model Geometric Relationship Discovery
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Solution Overview
Problem
Existing PDM systems face challenges in efficiently representing and discovering geometric relationships in 3D models, particularly as models grow in size, leading to increased complexity and memory costs due to the need for n-squared binary relationships.
Innovation Solution
The use of Equivalence Classes (ECs) to compress and optimize the representation of geometric relationships, allowing for efficient discovery and maintenance of relationships like symmetry, parallelism, and mirroring, through the creation of an equivalence relationship graph and cache-based systems that only check relevant geometries during edits.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional binary relationship representation is used in PDM systems, then all geometric relationships can be captured, but memory costs and system complexity increase quadratically with model size
Solution Approach 1:
The patent segments the monolithic binary relationship matrix into multiple sparse relationship matrices, each representing a specific type of geometric relationship (e.g., parallelism, perpendicularity, coincidence). By dividing the relationship representation into modular segments, the system reduces memory requirements from O(n²) to O(k·m) where k is the average number of relationships per geometry and m is the number of geometry pairs, while maintaining complete geometric relationship tracking
Solution Approach 2:
The patent applies local quality by creating specialized relationship matrices for different geometric relationship types rather than using a uniform binary representation. Each matrix is optimized for its specific relationship type, storing only relevant geometric pairs. This allows the system to allocate memory efficiently based on the actual distribution and importance of different relationship types in the 3D model
2Reliability
If all geometric relationships are tracked in large 3D models, then design feature retention is improved, but processing time and computational resources increase
Solution Approach 1:
The patent performs preliminary action by pre-computing and storing geometric relationships in sparse matrix structures before design edits occur. The system establishes the initial relationship state and caches it, allowing rapid detection of relationship changes during subsequent edits without recalculating all relationships from scratch. This preliminary preparation enables efficient real-time relationship maintenance during model editing
Solution Approach 2:
The patent implements feedback mechanisms that monitor changes in the 3D model and automatically update the sparse relationship matrices. When geometries are modified, the system detects changes and propagates updates only to affected relationship matrices, maintaining accurate geometric relationship information without requiring full recalculation. This feedback loop ensures design feature retention while minimizing computational overhead
Data Source
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Figure 3A~3B
AI summary
Systems and methods for maintaining equivalence relations in product data management (PDM) systems. A method includes receiving a 3D model including a plurality of components, and receiving a selection of one of the plurality of components of the model. The method includes receiving a selection of at least one equivalence relation to be discovered in the 3D model and identifying at least one target component of the plurality of components of the model. The method includes completing the selected component with respect to each target component according to each selected equivalence relation. The method includes building and storing an equivalence relationship graph according to the completed selected component.