Boundary Representation Intersection Precision via Uncertainty Aggregation
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Solution Overview
Problem
Conventional boundary representation modeling methods face inaccuracies due to floating-point precision issues, leading to truncation errors that violate topological consistency in computational models, particularly in geological formations and CAD applications.
Innovation Solution
The method involves computing intersections of boundary segments, determining uncertainties associated with these intersections, and aggregating or consolidating them based on topological consistency requirements and geometrical predicates to ensure precise and accurate representation, thereby maintaining the integrity of the boundary representation model.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If conventional floating-point arithmetic is used for boundary segment intersection computations, then computational speed is improved, but numerical precision deteriorates leading to topological inconsistencies
Solution Approach 1:
The computation process is segmented into distinct phases: first computing intersections using fast floating-point arithmetic, then separately evaluating uncertainty and aggregating results. This segmentation allows each phase to use appropriate precision methods without compromising overall speed.
Solution Approach 2:
An uncertainty evaluation mechanism acts as an intermediary between the fast floating-point computation and the final topological consistency requirement. This intermediary assesses whether computed intersections are reliable enough to be aggregated, bridging the gap between speed and precision.
2Productivity
If floating-point truncation is accepted for computational efficiency, then productivity is improved, but model reliability deteriorates due to topological inconsistencies
Solution Approach 1:
The system implements feedback by evaluating uncertainty for each computed intersection and using this information to decide whether to aggregate it. This feedback loop ensures that only reliable intersections contribute to the final model, maintaining topological consistency while preserving computational efficiency.
Solution Approach 2:
The methodology changes the parameter of precision by introducing uncertainty evaluation as an additional parameter. Instead of using fixed floating-point precision, the system dynamically adjusts the effective precision based on the uncertainty of each intersection computation.
3Measurement precision
If high-precision arithmetic is used to eliminate truncation errors, then measurement precision is improved, but computational complexity increases
Solution Approach 1:
The system applies partial precision enhancement by evaluating uncertainty for each intersection individually and only applying high-precision aggregation when necessary. This partial action approach avoids the excessive complexity of using high-precision arithmetic for all computations unconditionally.
Data Source
AI summary
Precise boundary segment intersection methods and systems for boundary representation are described. For example, in one embodiment, a method includes computing a plurality of intersections of a plurality of segments, computing an uncertainty associated with each intersection of the plurality of intersections, and determining whether to aggregate at least one of the plurality of intersections with another of the plurality of intersections based on one or more of the determined uncertainties. In another embodiment, the method may further include determining whether to consolidate at least one non-aggregated intersection with at least one other intersection based on a topological consistency requirement.