Polygon Correction for Simple Boundaries and Valid Holes
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Solution Overview
Problem
Existing methods for generating polygons with holes often result in non-simple polygons, leading to robustness issues in computational geometry programs and increased debugging burdens, as they fail to ensure that the outer boundary and internal holes meet the necessary conditions for correct algorithm execution.
Innovation Solution
A method to correct non-simple polygons by generating at least two simple polygons based on the original polygon, determining their inclusion relationships, and using one as the new outer boundary while identifying internal holes, thereby ensuring the corrected polygons meet the simple polygon criteria without altering the geometric shape.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a preset geometric algorithm is used to generate a polygon with holes, then the effective area can be represented, but the outer boundary cannot be ensured to be a simple polygon
Solution Approach 1:
The algorithm segments the polygon boundary into multiple chains and processes each chain separately to identify and correct non-simple polygon conditions. By dividing the boundary representation into manageable segments, the algorithm can systematically ensure simplicity while maintaining the effective area representation.
2Reliability
If an arrangement is constructed by base primitives to generate a polygon with holes, then the effective area can be represented, but the outer boundary cannot be ensured to be a simple polygon
Solution Approach 1:
The algorithm implements feedback mechanisms by continuously checking the simplicity condition of the outer boundary during the polygon generation process. When non-simple conditions are detected, the algorithm adjusts the boundary construction accordingly, ensuring that the final polygon meets the simplicity requirement while preserving the effective area.
3Area of stationary object
If a non-simple polygon is used to represent an effective area, then the area representation is achieved, but the robustness of computational geometry programs decreases and debugging burden increases
Solution Approach 1:
The algorithm performs preliminary actions by validating and correcting the polygon boundary simplicity before the polygon is used in subsequent computational geometry operations. This preliminary correction ensures that all polygons entering the computational geometry program meet the simple polygon criterion, thereby enhancing program robustness and reducing debugging requirements.
Data Source
AI summary
This application provides a polygon correction method and apparatus, a polygon generation method and apparatus, a device, and a computer-readable storage medium. The polygon correction method includes: obtaining a to-be-corrected polygon, and generating at least two simple polygons based on an original outer boundary of the to-be-corrected polygon; determining an inclusion relationship between the at least two simple polygons; determining at least one first simple polygon as a new outer boundary of the corrected polygon from the at least two simple polygons based on the inclusion relationship between the at least two simple polygons; determining an internal hole corresponding to each first simple polygon based on at least one of an original hole of the to-be-corrected polygon and a second simple polygon; and generating each corrected polygon based on each first simple polygon and the internal hole respectively corresponding to each first simple polygon.