Automated High Curvature Region Detection on Arc-Length Parameterized Curves
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Solution Overview
Problem
Existing methods for analyzing two-dimensional curves and three-dimensional models of object surfaces are computationally expensive and require human intervention, especially when dealing with multi-piece designs and detecting features like corners and high curvature regions.
Innovation Solution
A method that involves arc length parameterization of a curve function, computation of local average curvature, and indication of regions where the curvature turns a predetermined angle over a given interval, allowing for automated detection of high curvature regions and corners without human input.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a multi-piece CAD model is reconstructed into a single-cell surface representation, then curvature-based feature detection becomes feasible, but computational cost increases significantly
Solution Approach 1:
The patent divides the curve into multiple intervals and processes each interval separately to detect high curvature regions. This segmentation allows the algorithm to work with smaller, manageable portions of the curve rather than requiring complete single-cell surface reconstruction, thereby reducing computational overhead while maintaining detection accuracy.
Solution Approach 2:
The patent extracts and analyzes only the specific curvature information needed for feature detection from the curve data. By computing local average curvature and identifying regions where curvature turns by at least a predetermined angle, the method extracts only the essential geometric features without performing the computationally expensive operation of complete single-cell surface reconstruction.
2Extent of automation
If automated algorithms are used to detect curvature features, then human intervention is eliminated, but detection precision may be reduced
Solution Approach 1:
The patent implements an automated system that self-adjusts by computing local average curvature and automatically identifying high curvature regions based on predetermined angle thresholds. The algorithm processes the arc-length parameterized curve function autonomously, eliminating the need for human intervention while maintaining precision through mathematical rigor in curvature computation and region identification.
Solution Approach 2:
The patent replaces manual visual inspection and human judgment with an automated computational algorithm. The system uses mathematical computations of arc-length parameterization and local average curvature to objectively identify high curvature regions, substituting human mechanical analysis with automated computational geometry processing that maintains or improves detection precision.
3Difficulty of detecting and measuring
If single-cell surface representation is used for analysis, then curvature features can be detected, but the model reconstruction process becomes computationally expensive
Solution Approach 1:
The patent performs preliminary arc-length parameterization of the curve before curvature analysis. This preliminary action transforms the curve into a standardized form that simplifies subsequent curvature computation and high curvature region detection, avoiding the need for complex single-cell surface reconstruction while maintaining the ability to detect curvature features effectively.
Solution Approach 2:
The patent changes the parameterization of the curve from its original form to arc-length parameterization. This parameter transformation simplifies the mathematical expressions for curvature computation and enables efficient detection of high curvature regions without requiring the complex model reconstruction processes associated with single-cell surface representations.
Data Source
AI summary
A method is provided for detecting regions of high curvature on a curve. The method comprises receiving a curve function and automatically arc length parameterizing the curve function. The local average curvature over the arc length parameterized curve function is automatically computed. One or more regions where the local average curvature turns at least a predetermined angle over a given interval are automatically indicated. The indicated regions are then output.