3D Model Radial Function Descriptors for CAD Search
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Solution Overview
Problem
Current CAD systems face inefficiencies in representing 3D models as rotation-invariant descriptors, particularly when dealing with complex parts or large databases, as traditional methods require extensive computations to ensure scale, translation, and rotation invariance, leading to slow descriptor extraction and comparison processes.
Innovation Solution
The method involves sampling random points on the surface of a 3D object model, determining normal vectors, and calculating radial functions and distributions, which are then stored as descriptors, allowing for faster computation and rotation-invariant representation using a process that reduces operations from O(N×T) to O(N+T+K), where K is independent of N and T.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional methods are used to represent 3D models as rotation-invariant descriptors, then the descriptors maintain scale, translation, and rotation invariance, but the computation time and complexity increase significantly
Solution Approach 1:
The patent segments the 3D model surface into discrete triangular facets and samples points on these facets. By dividing the continuous surface into discrete elements, the system can efficiently compute radial functions for each facet normal direction, achieving rotation-invariance without requiring exhaustive computations across all possible rotations. The segmentation of the sphere into discrete bins for storing radial function values also reduces computational complexity.
Solution Approach 2:
The patent pre-computes and stores radial functions for all possible normal vector directions in a lookup table structure before actual model comparison is needed. This preliminary action involves sampling points on the model surface, computing normal vectors, and storing the radial function values indexed by normal vector directions. When comparing models, the system simply retrieves pre-computed values rather than computing them in real-time, dramatically reducing computation time while maintaining rotation-invariance.
2Reliability
If traditional methods are used to ensure scale, translation, and rotation invariance, then the descriptors are robust for database searching, but the processing speed decreases
Solution Approach 1:
The patent extracts only the essential geometric information needed for rotation-invariance by computing radial functions along normal vector directions and storing them indexed by direction. Instead of processing the entire 3D model data structure with all its transformation properties, the system extracts and stores only the radial function values organized by normal vector directions. This extraction of essential features maintains robustness for database searching while significantly reducing processing speed requirements.
Solution Approach 2:
The patent transforms the 3D model representation from a coordinate-based system sensitive to transformations into a parameter-based system using radial functions indexed by normal vector directions. By changing the representation parameters from (x, y, z) coordinates to (normal vector direction, radial distance) pairs, the system achieves invariance to scale, translation, and rotation without requiring complex transformation computations during model processing or comparison.
3Measurement precision
If comprehensive sampling of 3D model surfaces is performed to ensure accurate descriptors, then the descriptor accuracy improves, but the computational operations increase from O(N×T) to O(N+T+K)
Solution Approach 1:
The patent introduces a new dimensional organization by indexing radial function values according to normal vector directions (spherical coordinates) rather than storing them in a continuous function form. This dimensional reorganization allows the system to achieve comprehensive sampling accuracy by evaluating radial functions at discrete directional bins across the sphere, while reducing computational complexity from O(N×T) to O(N+T+K) where K is the number of directional bins. The dimensionality change from continuous space to discrete directional bins maintains accuracy while simplifying computation.
Data Source
AI summary
A system, method, and computer program product for determining a radial function and distribution of a three-dimensional object model. One method includes retrieving a three-dimensional object model in a CAD system and sampling random points on the surface of the object model. The method also includes determining a normal vector corresponding to each of the random points and determining a radial function corresponding to each normal vector and respective random point. The method also includes determining, by the CAD system, a radial distribution corresponding to at least two of the radial functions and storing the radial distribution and average values of the radial functions in the CAD system.