Browse Prior Art Database

Venn Diagram Circle Creation Algorithm

IP.com Disclosure Number: IPCOM000105895D
Original Publication Date: 1993-Sep-01
Included in the Prior Art Database: 2005-Mar-20
Document File: 4 page(s) / 160K

Publishing Venue

IBM

Related People

Arthurson, D: AUTHOR [+2]

Abstract

Disclosed is an algorithm for determining the distance between two overlapping circles based on the information on their areas and the overlap areas. It also shows how it is used to create Venn diagrams with up to three proportionally drawn circles. The implementation relates to IBM Application System. (Note that overlap of three circles in a 3-circle Venn diagram is a result of three pairs of overlaps which although each is correct the 'overlap of 3-overlaps' can be drawn but not in proportion).

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Venn Diagram Circle Creation Algorithm

      Disclosed is an algorithm for determining the distance between
two overlapping circles based on the information on their areas and
the overlap areas.  It also shows how it is used to create Venn
diagrams with up to three proportionally drawn circles.  The
implementation relates to IBM Application System.  (Note that overlap
of three circles in a 3-circle Venn diagram is a result of three
pairs of overlaps which although each is correct the 'overlap of
3-overlaps' can be drawn but not in proportion).

     Rules for data usage which are suitable for Venn representation
should be clearly understood.  EG, data (items, objects, things)
shown by the overlap value must be the same data; i.e. contained in
both C1 and C2.  If C1 was to include all males and C2 was to include
all females then there could be no way of analysing the data to
produce an overlap.  But what if the overlap was to show those who
are married?  This is invalid because any married males included in
the overlap cannot possibly be any of the females in C2.  If C1 was
to include all males and C2 was to include all employees in
department 10 then the overlap would be the males in department 10.
These are the same people and is therefore a valid analysis.

     Fig. 1 shows a Venn consisting of two circles which overlap.
Three pieces of information are needed for it to be drawn; C1, C2 &
C12.  If it was drawn proportionally then the area of the circles and
that of the overlap would be in proportion to values provided for C1,
C2 & C12.  Note that C12 cannot be larger than the minimum value of
C1 and C2.  The overlap area must be linked to the total area of both
circles.  When drawn proportionally the area of overlap is calculated
as a fraction of the total area of the two circles or C12/(C1+C2) is
the area of overlap.  It is the same rule as applied by the IBM*
product GDDM/PGF 2 circle Venn.  This disclosure extends the theory
to more than 2 circles.  The following example fig. 2 shows a 3
circle Venn with overlaps.  A 3 circle Venn can be considered to be 3
X 2 circles.  Each pair of circles is processed as for a 2 circle
Venn.  The complete diagram is a composite of each of the 3 pairs so
that each pair satisfies the rules discussed previously for 2
circles.  The overlap of all 3 circles, C123, cannot be drawn in
proportion.  It is the result of 3 pairs of overlaps.  Each overlap
is correct for the 2 circles to which it relates.  This is important
to remember otherwise any diagram drawn may be misunderstood.

     Described now is the method and formula for calculating the
overlap area.  Consider Fig. 3.  It shows two different examples of 2
circles overlapping.  In the first example, type 1, only part of
circle 1 is overlapping circle 2.  Note that the CHORD, line joining
the 2  points of overlap, is to the right of the centre of circle 1.
In type 2, the overlap is much larger and that the chord...