Low Ink Graph Drawing Using Shared Edge Segments
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Solution Overview
Problem
Dense graph drawing methods face challenges such as edge overlaps, ambiguity in connectivity, and labeling difficulties due to high node degrees, especially in straight-line and orthogonal drawing styles, leading to poor readability.
Innovation Solution
A low-ink graph drawing method that assigns nodes to grid points and routes edges with one bend point, using horizontal and vertical line segments, and represents bend points with short line segments or arcs, while compacting the drawing to reduce complexity and maintain connectivity clarity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If straight-line force-directed graph drawing methods are used, then the drawing process is simple, but edge overlaps and node obstruction occur frequently
Solution Approach 1:
The patent segments each edge into multiple linear segments connected by bend points. Instead of drawing straight lines, edges are divided into segments that route around nodes, preventing overlap and obstruction while maintaining the overall connectivity information.
Solution Approach 2:
The patent introduces an additional routing dimension by adding bend points at strategic locations. Edges are no longer confined to straight-line paths but can navigate through the 2D space by bending at intermediate points, allowing them to pass above or below nodes without obstruction.
2Reliability
If orthogonal or arbitrary polyline edge routing is used, then node obstruction is reduced, but individual edges become hard to follow due to multiple bend points
Solution Approach 1:
The patent applies different routing strategies to different parts of the graph based on local density. In high-density regions, edges use more bend points to navigate around nodes, while in sparse regions, simpler routing is used. This local adaptation optimizes both node visibility and edge traceability.
Solution Approach 2:
The patent uses a limited number of bend points per edge rather than allowing arbitrary numbers. By constraining the maximum number of bend points and using them strategically only where necessary, the method prevents edges from becoming overly complex while still achieving node obstruction avoidance.
3Reliability
If nodes are enlarged to ensure minimum separation of incident edges, then edge separation is improved, but node size becomes enormous
Solution Approach 1:
Instead of enlarging nodes to create separation space, the patent segments edges into multiple segments with bend points positioned between nodes. This creates separation through the routing path rather than through node size, keeping nodes compact while maintaining edge distinguishability.
Solution Approach 2:
The patent introduces bend points as intermediary elements between nodes. These bend points act as mediators that create separation and routing control without requiring the nodes themselves to be enlarged. The bend points provide the necessary spacing while keeping node sizes appropriate.
4Reliability
If edges are routed to avoid node overlap, then readability improves, but the drawing space requires more area
Solution Approach 1:
The patent merges the routing paths of multiple edges by sharing common bend points and linear segments. Instead of giving each edge its own unique path, adjacent edges share routing infrastructure, which reduces the total drawing space while maintaining individual edge distinguishability through labeling and segment differentiation.
Solution Approach 2:
The patent creates universal routing structures that serve multiple edges simultaneously. Common bend points and linear segments function as shared infrastructure for multiple edges, reducing redundant space consumption while maintaining the ability to distinguish individual edges through labels and segment characteristics.
Data Source
AI summary
A computer-implemented method of drawing an undirected graph in which multiple nodes are connected by multiple edges is provided using a computer system in which a computer is coupled to the computer display. The computer includes a processor and memory. A representation is received of a graph having multiple nodes and multiple edges, in which positions of the nodes relative to one another have been previously determined. The representation is modified so as to: 1) preserve the positions of the nodes relative to one another; and 2) simplify the visual representation of the graph by sharing drawn lines between different distinct edges in such a way as to enable the different distinct edges, despite such sharing, to still be recognized by a user. In one embodiment, the processor places the nodes in unique positions with integer coordinates.