An incremental construction algorithm for Venn diagrams
نویسندگان
چکیده
The drawing of Venn diagrams have traditionally served as an aid to analyze the characteristics exhibited by the diagram and its underlying Venn graph. Little attention has hitherto been given to the presentation, construction and way in which a Venn diagram conveys information. We present a new algorithm for the construction and layout of a Venn diagram based on an incremental technique. The algorithm constructs the Venn diagram by incrementally deriving new intersections from previously placed ones on a grid. We also propose criteria which can be applied to analyze a Venn diagram’s drawing and layout. Our algorithm aims to generate an aesthetically pleasing layout by satisfying the proposed criteria.
منابع مشابه
Analysis of Venn Diagrams Using Cycles in Graphs
This paper is the last in a series by the authors on the use of graph theory to analyze Venn diagrams on few curves (see [1,2,6,7]). We complete the construction (and hence the enumeration) of spherical Venn diagrams on five curves, which yields additional results about conjectures of Grünbaum concerning which Venn diagrams are convex, which are exposed, and which can be drawn with congruent el...
متن کاملDrawing Area-Proportional Venn and Euler Diagrams
We consider the problem of drawing Venn diagrams for which each region’s area is proportional to some weight (e.g., population or percentage) assigned to that region. These area-proportional Venn diagrams have an enhanced ability over traditional Venn diagrams to visually convey information about data sets with interacting characteristics. We develop algorithms for drawing area-proportional Ven...
متن کاملNew Roses: Simple Symmetric Venn Diagrams with 11 and 13 Curves
A symmetric n-Venn diagram is one that is invariant under n-fold rotation, up to a relabeling of curves. A simple n-Venn diagram is an n-Venn diagram in which at most two curves intersect at any point. In this paper, we introduce a new property of Venn diagrams called crosscut symmetry, which is related to dihedral symmetry. Utilizing a computer search restricted to diagrams with crosscut symme...
متن کاملHalf-Simple Symmetric Venn Diagrams
A Venn diagram is simple if at most two curves intersect at any given point. A recent paper of Griggs, Killian, and Savage [Elec. J. Combinatorics, Research Paper 2, 2004] shows how to construct rotationally symmetric Venn diagrams for any prime number of curves. However, the resulting diagrams contain only ( n bn/2c ) intersection points, whereas a simple Venn diagram contains 2n − 2 intersect...
متن کاملSpherical Venn Diagrams with Involutory Isometries
In this paper we give a construction, for any n, of an n-Venn diagram on the sphere that has antipodal symmetry; that is, the diagram is fixed by the map that takes a point on the sphere to the corresponding antipodal point. Thus, along with certain diagrams due to Anthony Edwards which can be drawn with rotational and reflective symmetry, for any isometry of the sphere that is an involution, t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- South African Computer Journal
دوره 26 شماره
صفحات -
تاریخ انتشار 2000