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Drawing road networks with focus regions.

Jan-Henrik Haunert¹, Leon Sering

¹Chair for Computer Science I, University of Würzburg, Am Hubland, D-97074 Würzburg, Germany. jan.haunert@uni-wuerzburg.de

IEEE Transactions on Visualization and Computer Graphics

|October 29, 2011

Summary

This study introduces a graph-based optimization for map projections, minimizing distortion in sparse road networks. The novel approach significantly reduces map distortion compared to traditional fish-eye projections.

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Area of Science:

Cartography
Computer Graphics
Computational Geometry

Background:

Mobile map users require detailed local information and contextual remote data.
Map density is managed using mapping functions like fish-eye projections, which enlarge focus regions by distorting other areas.
Existing methods lack control over distortion placement, often distorting important road network areas.

Purpose of the Study:

To develop a novel spatial mapping method for road networks that minimizes distortion in sparse areas.
To create a graph-based optimization approach for generating less distorted maps.
To implement and evaluate a method that avoids predefined mapping functions.

Main Methods:

Representing road networks as graphs with edges as road segments.
Employing a graph-based optimization approach to compute a new spatial mapping.
Minimizing the square sum of distortions at edges using a convex quadratic program (CQP).
Incorporating constraints such as forbidding edge crossings via linear inequalities.

Main Results:

The proposed method generated maps with significantly less distortion than predefined fish-eye projections.
The convex quadratic programming approach efficiently solves the optimization problem.
The method successfully incorporates constraints like preventing edge crossings.

Conclusions:

Graph-based optimization offers a superior approach to spatial mapping for road networks compared to traditional methods.
The technique effectively minimizes distortion by concentrating it in sparse network regions.
Further research will focus on automating road selection and developing real-time heuristics.