Polygonal Obstacle Path Routing via Vertex Labeling
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Solution Overview
Problem
Existing methods for determining non-intersecting paths between two points in a field of polygonal obstacles often result in intersecting paths and unnecessary CPU usage due to repeated checks and incorrect vertex ordering, leading to inefficiencies and resource-intensive comparisons.
Innovation Solution
The method involves offsetting initial paths to form adjusted paths, labeling vertices, and sorting them to reconstruct non-intersecting paths by creating offset regions and subdividing segments to avoid new intersections, while using a labeling system to correctly order paths and prevent unnecessary crossings.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If paths are offset from obstacles to avoid intersections, then path clearance from obstacles is improved, but new intersections may occur between offset paths and obstacles or other offset paths
Solution Approach 1:
The patent applies preliminary action by performing offset operations on paths before final routing determination. By offsetting paths from obstacles in advance and pre-identifying potential intersection points, the system prepares the path data structure to avoid intersections during the actual routing process, rather than detecting and correcting them afterward.
Solution Approach 2:
The patent implements feedback by continuously checking offset paths for new intersections with obstacles and other paths. When intersections are detected, the system feeds this information back into the routing algorithm to compute corrected paths, creating an iterative process that refines path clearance until no intersections remain.
2Manufacturing precision
If conventional comparison methods are used to order paths at common vertices, then path ordering can be achieved, but significant CPU usage and time are required due to comparing each path to every other path
Solution Approach 1:
The patent applies segmentation by dividing the path comparison task into smaller units. Instead of comparing each path to every other path in the entire set, the system segments the comparison to only paths that share common vertices, and further segments by processing vertices individually. This reduces the computational complexity from O(n²) to a much smaller subset of comparisons.
Solution Approach 2:
The patent implements local quality by applying different ordering strategies to different vertices based on their local characteristics. At each common vertex, the system analyzes the specific geometric configuration and applies ordering rules tailored to that local context, rather than using a uniform global ordering approach. This improves ordering accuracy while reducing unnecessary comparisons.
Data Source
AI summary
The present invention provides a method, system and computer program product for routing multiple paths through polygonal obstacles. In a preferred embodiment, the method begins by offsetting the initial paths through the obstacles from the obstacles to form adjusted paths. If it is determined that any adjusted path encounters a new intersection, the adjusted path or paths are modified to form revised paths. The vertices of each obstacle are labeled. All the revised and all the adjusted paths are sorted. Then, according to their sorted order, the revised and the adjusted paths are reconstructed to form offset paths.