Alternative Map Projections Using Cost Function Vectors
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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 or spatial functions, such as travel time, scenic value, terrain difficulty, or economic incentives, which are not adequately represented.
Innovation Solution
A map projection system that provides alternative projections based on user-selectable cost functions or spatial functions, using engines to determine angular relationships, estimate cost functions, and display vectors representing these functions, allowing users to make informed decisions based on optimized geographical information.
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 navigated, but geographical information is lost or distorted
Solution Approach 1:
The system dynamically generates multiple map projections based on different cost functions (time, scenic value, terrain difficulty, economic incentive) rather than using a fixed conventional projection. This allows the map to adapt and transform according to different user needs and priorities, resolving the contradiction by making the projection flexible rather than static.
Solution Approach 2:
The system changes the parameters of map projection by incorporating multiple cost functions as weighting factors. Instead of using standard projection parameters alone, the system adjusts projection characteristics based on user-selected criteria such as travel time, scenic value, terrain difficulty, or economic incentive, thereby reducing information loss while maintaining navigability.
2Adaptability or versatility
If traditional map projections are used, then the map structure remains simple, but it cannot adequately represent modern use patterns requiring cost functions and spatial functions
Solution Approach 1:
The system provides multi-functionality by enabling users to select different cost functions (time, scenic value, terrain difficulty, economic incentive) to generate various types of optimized routes and regional representations from a single unified platform. This universal approach allows one system to serve multiple purposes that previously required separate specialized tools.
Solution Approach 2:
The map projection system dynamically adapts to different user needs by allowing selection of various cost functions and spatial functions. The system transforms the static map into a dynamic representation that can be reconfigured based on user priorities, thereby enhancing adaptability without requiring multiple separate systems.
3Measurement precision
If vectors are displayed to represent angular relationships and cost functions, then users can make informed decisions, but the visualization complexity increases
Solution Approach 1:
The system adds a visual dimension by representing angular relationships and cost functions through vectors on the map. This dimensional enhancement allows users to perceive directional information and cost metrics simultaneously, improving measurement precision while the vector representation keeps the visualization manageable through intuitive graphical elements.
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.