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For a Venn diagram, enter the number of sets. For an Euler diagram, enter a space-seperated list of regions defined by alphabetically-labelled curves. For example, the input a b c ac bc abc would create an Euler diagram that results from removing region ab from 3-Venn.
The drop-down list specifies which method to use for generating the structure of the Euler diagram:
- Edwards
- Anthony Edwards' general n-Venn diagram generator. This is usually the most suitable generator since it maximizes the number of vertices.
- AignerSCD
- The Boolean lattice is decomposed into symmetric chains which are arranged radially to produce an Euler diagram. The unwanted regions are then removed from each chain.
- AignerModSCD
- The unwanted regions are removed from the Boolean lattice before the chains are produced. The chains are then arranged radially to produce an Euler diagram.
The drop-down list specifies how the free path of each face expands to create the required area:
- Differential Growth
- The amount of expansion along each ray defined by the fixed path can vary. The goal is to produce as smooth (i.e., convex) a free path as possible while achieving the required area.
- Uniform Growth
- The distance of the free path from the fixed path along each ray is the same. The result is that the free path has the same shape as the fixed path except for the segments at the endpoints. This tends to make the diagram most jagged than necessary.
- Convex Static
- An implementation of Differential Growth where the area of each region is chosen so as to make the free path convex. This is an experimental way of drawing standard Euler diagrams without concern for area-proportionality.
This window shows an area-proportinal Euler diagram where each region has equal area (i.e., each region has an area of 50 units).
If you left-click on a bounded region, it will be hilighted and the frame on the right will show the region's labels and size:
The slider can be used to adjust the selected region's size according to the layout algorithm you selected (e.g., Differential Growth). After adjusting a region's size, the diagram is rescaled to fit the window:
To remove the selected region, set its size to 0 or, preferablly, press Delete which will update the underlying Euler Graph:
As shown in the above screenshot, the concurrent edges that result from deleting a region are shown by interlacing the constituent curves' colours.
Once a region is deleted, you can press Compress which will attempt to remove the concurrent edges by bringing the curves at the endpoints together:
Depending on which regions have been removed, it may be impossible to remove all concurrent edges:
However, if more regions are removed and the compression is performed again, the result may improve:
Initially, the rays are uniformly distributed. You can left-click and drag the endpoint of ray in order to alter its position:
By moving the rays, the resulting diagram maintains its area-proportionality, but can have an altered shape:
