Polygon Boolean Operation and Topology Correction for Map Rendering

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Solution Overview

Problem

Existing polygon Boolean operation algorithms fail to accurately handle edge cases such as self-intersecting polygons, overlapping polygons, and complex intersections, leading to the generation of invalid polygons in electronic maps.

Innovation Solution

A polygon Boolean operation and topology correction algorithm that combines a variation of the Vatti algorithm with a topology correction algorithm to identify and correct 'hot pixels' and ensure proper winding order, generating valid polygons by snap-rounding into an integer coordinate system.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If existing polygon Boolean operation algorithms are used, then basic polygon operations can be performed, but they fail to handle edge cases (self-intersecting polygons, overlapping polygons, complex intersections) leading to invalid polygons

Engineering Contradiction:

Improvepolygon validityVSAvoidedge case handling

Core Design Contradiction:

ReliabilityVSAdaptability or versatility

Solution Approach 1:

The algorithm performs preliminary detection of edge cases (self-intersections, overlaps, complex intersections) before executing Boolean operations. By identifying and flagging problematic polygons in advance, the system can apply specialized correction procedures only where needed, ensuring valid output without compromising overall processing efficiency.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The invention modifies the standard Vatti algorithm by introducing additional parameters and checks specifically for edge case detection. It changes the processing parameters to accommodate complex scenarios such as self-intersecting polygons and chains of holes, transforming the algorithm from handling only simple cases to managing comprehensive polygon complexities while maintaining reliability.

Inventive Principle:

Principle #35Parameter changes

2Adaptability or versatility

If polygon Boolean operation algorithms process complex intersections, then more comprehensive map areas can be represented, but precision errors occur leading to invalid polygons

Engineering Contradiction:

Improvecomplex intersection processingVSAvoidpolygon precision

Core Design Contradiction:

Adaptability or versatilityVSManufacturing precision

Solution Approach 1:

The algorithm incorporates feedback mechanisms that continuously monitor the polygon processing state. When detecting precision-critical situations during Boolean operations on complex intersections, the system adjusts its calculations dynamically, applying corrective measures to maintain precision while handling complex geometries.

Inventive Principle:

Principle #23Feedback

Solution Approach 2:

The invention segments complex intersection problems into smaller, manageable components. By breaking down complex polygons into simpler sub-polygons and processing them individually through the Boolean operation, the algorithm maintains precision in each segment while collectively representing comprehensive map areas accurately.

Inventive Principle:

Principle #1Segmentation

3Productivity

If standard Vatti algorithm is used, then Boolean operations can be performed, but it produces invalid polygons for self-intersecting and overlapping polygons

Engineering Contradiction:

Improveprocessing speedVSAvoidpolygon correctness

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The enhanced algorithm performs preliminary classification of polygons into standard and edge-case categories before processing. This allows the system to apply the efficient standard Vatti algorithm to simple polygons while reserving specialized correction procedures only for problematic cases, thereby maintaining high processing speed overall while ensuring correctness where needed.

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The invention applies different processing qualities to different parts of the input data. Standard polygons receive rapid processing using the original Vatti algorithm, while edge-case polygons receive more thorough, correctness-focused processing. This local differentiation optimizes the balance between productivity and reliability across the entire dataset.

Inventive Principle:

Principle #3Local quality

Data Source

PatentUS11049297B2Generating valid polygon data based on input data with errors

Publication Date: 2021.06.29 MAPBOX INC

AI summary

A polygon Boolean operation and topology correction algorithm generates valid polygons despite polygon data containing self-intersecting polygons, overlapping polygons, polygons including a chain of holes, and/or polygons including complex intersections. A polygon Boolean operation and topology correction algorithm uses two variants of the Vatti algorithm along with a topology correction algorithm to address problematic areas within input data, such as the overlapping area shared between one or more polygons or a polygon having no area at all. Upon performing a variant of the Vatti algorithm to identify hot pixels within an arrangement of polygons, the polygon Boolean operation and topology correction algorithm runs a second variant of the Vatti algorithm to generate polygons within an integer coordinate system using snap-rounding. Snap-rounded polygons are then analyzed by a topology correction algorithm that ensures the proper winding order is followed to render valid polygons for display in an electronic map.