Weighted Voronoi Diagrams in Biology

This page describes the program that constructs weighted Euclidean and power diagram for computer simulation and analysis of the system of growing plants. It also demonstrates application of power diagram to a problem from the fields of biology and ecology. The permission to use the program for scientific or commercial purposes should be obtained from the author:

Marina Gavrilova
Department of Computer Science
University of Calgary, Calgary, Alberta, Canada
e-mail: marina@cpsc.ucalgary.ca

The program and several sample input files can be obtained from: vpplants.zip.

Problem description

The biological model is defined as follows:

Given a set of plants in the plane. The plants are characterized by their coordinates, radii and the type of species. Different species have different rules according to which they grow and that define, in particular, the ratio between the size of the area it can occupy and the volume of the plant.

The problem is to study the size-distance and size-area relationships as measures of plant interactions in the densely packed system of growing plants.

The application of the Voronoi diagrams, particularly weighted Euclidean Voronoi diagram and power diagram for circles and spheres, provides easy representation and efficient approach to problem solution. Such weighted Voronoi diagrams are constructed for plant community by incremental method. The area occupied by a plant is computed as the area of the Euclidean or power region corresponding to this plant. A linear regression of area of the power region with plant volume is computed and is used for spatial analysis of plant communities.

The software is currently used for research purposes at the University of California, Santa-Barbara, Department of Ecology, Evolution and Marine Biology. For more information on this research contact Jochen Schenk: schenk@lifesci.lscf.ucsb.edu.



Sample screenshot


Program description

The program is in the file VPPlants.exe. It is written in Delphi and runs under Windows 95. The input data set is imported from an input file (menu File/Open). The choice of metric (Euclidean or power) and the diagram to be constructed (Voronoi diagram or Delaunay triangulation) is provided to the user. The Process! menu constructs and displays the resulting diagram. The results can be saved (menu File/Save). On-line Help provides the description of the format of input and output file.

Input file format

1st line is for comments (it is always ignored)

Each other line contains the description of a plant:

X, Y, Number, Edge, Species, Radius, and the rest is ignored

Output file format

1st line contains comment

Each other line contains information similar to the input:

X, Y, Number, Edge, Species, Radius, Voronoi area, Power area

The output file can be used as an input file.

Please note that in the case of intersecting circles some power areas might be zeros or negative. The areas of the edge plants are also somewhat arbitrary.

Example of the input file:

X,Y,Number,Edge,Species,Radius
17.57,17.99,16,e,P,0.77
16.5,19.16,17,e,P,0.745
16.04,17.99,25,c,P,0.55
16.01,18.32,26,c,O,0.07
16.42,16.48,28,c,O,0.18
15.11,15.3,29,c,A,1.255
15.09,15.98,30,c,P,0.67
14.21,14.63,31,c,A,1.21
13.92,17.89,33,e,A,1.025
11.98,19.18,35,e,A,0.7
11.05,19.25,36,c,A,0.755
9.74,19.94,38,e,A,0.88
10.3,16.93,40,c,A,1.085
9.83,15.73,41,c,A,1.13
11.64,14.83,42,c,A,0.555