Polyline Vertex Reduction via Flatness Ratio Segmentation
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Solution Overview
Problem
Current systems lack efficient methods for processing and rendering polylines, which often have many vertices and are computationally expensive, making it desirable to reduce the number of vertices while maintaining rendering quality.
Innovation Solution
A recursive process that uses a flatness ratio and distance threshold to identify and remove vertices from polylines, splitting the polyline into segments and recursively applying these criteria to reduce the number of vertices without significantly degrading the polyline's representation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the number of vertices in a polyline is reduced, then processing and rendering efficiency is improved, but the accuracy of the polyline representation deteriorates
Solution Approach 1:
The polyline is divided into multiple segments by identifying pivot vertices that maximize the distance from the estimation line. Each segment is processed independently through recursive application of the flatness ratio test, allowing localized optimization while preserving overall shape fidelity. This segmentation enables efficient processing of large polylines while maintaining accuracy in critical regions.
Solution Approach 2:
The patent introduces a flatness ratio parameter (combining distance threshold and segment length) to dynamically determine vertex removal criteria. By changing the parameter from a simple distance threshold to a ratio that considers both distance and segment length, the system adapts the reduction criteria to local geometric characteristics, preserving accuracy in curved regions while aggressively reducing vertices in straight sections.
2Speed
If a simple distance threshold is used to remove vertices, then processing speed is improved, but the quality of the reduced polyline deteriorates
Solution Approach 1:
Before applying the flatness ratio test, the algorithm performs preliminary actions by identifying and marking pivot vertices that define critical segments. This preliminary segmentation allows the subsequent vertex removal test to focus only on relevant vertices within each segment, improving processing speed while ensuring that vertices defining the polyline's essential shape are preserved through the recursive application of the flatness ratio criterion.
Data Source
AI summary
Data is received that describes a polyline having a first endpoint, a second endpoint, and a plurality of intermediate vertices, each of the intermediate vertices lying between the first endpoint and the second endpoint. An estimation line segment is drawn between the first endpoint and the second endpoint. An intermediate vertex is identifies as a pivot vertex from the plurality of intermediate vertices that is a greatest distance from the estimation line segment. A flatness ratio is calculated by dividing a distance of the pivot vertex from the estimation line segment by a length of the estimation line segment In a computer, the flatness ratio is compared to a predetermined threshold value. If the flatness ratio does not exceed the predetermined threshold value, the intermediate vertices are discarded, thereby modifying the polyline.