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.

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

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.

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

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.

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