Alternative Map Projections Using Cost Function Distortion
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Solution Overview
Problem
Conventional map projections distort or lose geographical information, making them unsuitable for modern use patterns that require consideration of cost functions such as time, scenic value, terrain difficulty, or economic incentives, and fail to highlight regions of economic activity.
Innovation Solution
A map projection system that provides alternative projections based on user-selectable cost functions or spatial functions, optimizing geographical information for specific user needs by displaying vectors with angular relationships and magnitudes corresponding to cost functions or region expansions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If conventional map projections are used to represent geographical information on a two-dimensional plane, then the map can be displayed and used for basic navigation, but geographical information is lost or distorted and cannot account for cost functions such as time, scenic value, terrain difficulty, or economic incentives
Solution Approach 1:
The patent segments geographical information representation by creating multiple specialized projection systems, each optimized for specific cost functions (time, scenery, terrain, economics). Instead of using a single conventional projection that loses information across all dimensions, the system divides the mapping function into specialized segments that preserve different types of geographical information according to user needs.
Solution Approach 2:
The patent adds functional dimensions to traditional two-dimensional map projections by incorporating cost function values as additional representation layers. This allows the map to encode not only spatial position but also temporal, aesthetic, topographic, and economic dimensions, effectively transforming the information density without proportionally increasing visual complexity.
2Adaptability or versatility
If conventional map projections preserve basic spatial relationships, then navigation is possible, but they fail to highlight regions of economic activity and provide user-specific relevant information
Solution Approach 1:
The patent implements dynamic adaptability by allowing users to select different cost functions and having the map projection dynamically reconfigure to emphasize relevant information. The system transitions from static conventional projections to dynamic projections that adapt their information prioritization based on user-selected criteria such as minimizing travel time, maximizing scenic value, avoiding difficult terrain, or highlighting economic incentives.
Solution Approach 2:
The patent applies local quality by allowing different regions of the map to be projected with different priorities based on user-selected cost functions. Regions with high economic activity, scenic value, or terrain difficulty can be locally optimized in the projection to highlight their specific characteristics, rather than applying a uniform projection across the entire map.
3Ease of operation
If traditional map projections are used, then the system is simple and easy to understand, but they distort geographical information and are not suitable for modern use patterns requiring cost function consideration
Solution Approach 1:
The patent creates simplified visual copies or representations of complex cost function data overlaid on traditional map projections. By using visual encodings such as color gradients, contour lines, or symbolic representations for cost function values, the system maintains the familiar and easy-to-understand base map while copying additional layers of reliable, accurate information that accounts for time, scenery, terrain, and economics.
Data Source
AI summary
A method is provided for determining angular relationships from a point of interest to a plurality of peripheral points of interest on a map. One or more cost functions from the point of interest to the plurality of the peripheral points of interest on the map are analyzed. A plurality of vectors emanating from the point of interest to the plurality of the peripheral points of interest on a different representation of the map are displayed. Another method is provided for identifying points of interest on a map. Regions of high interest are identified on the map. Regions of low interest are identified on the map. The regions of high interest are expanded on a different representation of the map. The regions of low interest are contracted by an amount proportional to an amount the regions of high interest are expanded on the different representation of the map.