United States 

Department of New Methods, Algorithms, and 

Agriculture 

Forest Service 

Software for Rapid Mapping of 

Tree Positions in Coordinate 

Forest Plots 

Southern 

Research Station A.D. Wilson 

Research Paper 

SRS-19 
New Methods, Algorithms, and Software 

for Rapid Mapping of Tree Positions in 

Coordinate Forest Plots 

A.D. Wilson 
Contents 

Introduction ....................................................... 1 

Materials and Methods .............................................. 2 

General Methodology ............................................... 2 

Sequential-Target Mapping Method .................................... 5 

Plot-Origin Radial Mapping Method ................................... 12 

Three-Dimensional Mapping ........................................ 16 

Results .......................................................... 16 

Test Plot Orientation .............................................. 16 

Sequential-Target Mapping Method ................................... 16 

Plot-Origin Radial Mapping Method ................................... 19 

Mapping Plot-Center Coordinates ..................................... 21 

Methods Accuracy and Performance ................................... 21 

Discussion ........................................................ 23 

Forest Management Implications ..................................... 24 

Acknowledgment .................................................. 24 

Literaturecited ................................................... 25 

Appendix: Definitions of Terms ....................................... 26 
New Methods, Algorithms, and Software 

for Rapid Mapping of Tree Positions in 

Coordinate Forest Plots 

A.D. Wilson 

Abstract 

The theories and methodologies for two new tree mapping methods, 

the Sequential-target method and the Plot-origin radial method, are 

described. The methods accommodate the use of any conventional 

distance measuring device and compass to collect horizontal distance 

and azimuth data between source or reference positions (origins) and 

target trees. Conversion equations are presented to convert fieldderived azimuth coordinates to plot-center coordinates, permitting 

plots of all tree positions relative to the geometric center of the plot. 

Plot rotation algorithms for Polar X and Polar Y plotting methods 

allow the rotation of all plotted positions to any orientation within a 

rectangular mapping fiame and permit corrections for magnetic 

declination. Additional algorithms are provided to calculate horizontal 

distance and azimuth between plotted trees and plot-center or between 

any two tree positions in the plot. All algorithms were incorporated 

into TreeMapper, a computer program for DO§. The methods and 

software were tested on a forested plot. Low mean differences 

between actual and calculated values indicated the accuracy of the 

methods. The mapping methods and software, originally developed to 

map trees in research plots for spatial and epidemiological studies of 

oak wilt disease, have wide applications in forest inventory, 

management, ecology, spatial-modeling, and other field activities and 

tasks that require accurate information about tree positions and 

spatial distribution patterns and ways to keep track of tree attributes 

and treatments over time. More detailed explanations of the 

methodologies for downloading data and running TreeEvlapper will be 

provided in a second paper. 

Keywords: Ceratocystis fagacearum, field plotting, oak wilt, spatial 

structure, stem mapping, tree inventory surveys, tree mapping. 

The construction of accurate maps of forest stands and 

woodland plots is required for many aspects of forest 

management, inventory, and research. Natural resource 

managers use forest maps for inventory analysis, timber 

sales, harvest plans, best management practices (BMP) 

reports, soil and range conservation management, timber 

management, wildlife management, and many other natural 

resource applications. Many applied fields of land 

management, including forestry, use cartographic surveys of 

objects in the landscape to plan, develop, and manage landuse areas. The construction of accurate maps is a 

prerequisite for planning and executing most types of 

activities carried out by USDA Forest Service personnel in 

forested areas within and outside of the national forests. 

Timber industry personnel in the State and private sectors 

also need accurate maps of forest stands to conduct work 

activities associated with timber management and harvesting 

on State and private forests. 

Research scientists in forestry and related sciences 

commonly install field plots in order to evaluate forest 

management practices, test new pest suppression 

alternatives, investigate ecosystem functions, conduct 

forest health and inventory analyses, and facilitate studies in 

many other related disciplines. The task of installing 

research field plots often requires that the treatments applied 

or attributes of individual trees are recorded in map form. 

Consequently, labeling and mapping trees ir, the research 

plots are often the first tasks when establishing new field 

plots. Maps of field plots allow one to keep track of the 

locations of trees receiving specific treatments so they can 

be found repeatedly during subsequent data collection visits 

to the plots. 

Many algorithms and variations of protocols for mapping 

forest plots have been used for numerous forestry 

applications, ranging from ecological investigations of 

spatial patterns for development of management-oriented 

(growth and yield) models to analysis of biotic interactions 

(competit ion) and spatial structure (Baskent and Jordan 

1995, Glitzenstein and others 1986, Moeur 1993, Platt and 

Hermann 1986). Methods for mapping field plots have used a 

variety of approaches to determine the locations of static 

objects in the landscape, including triangulation (Quigley 

and Slater 1994), double right-angle prism (Reed and others 

1989), distance-bearing (Moeur 1993), and least-squares 

mapping methods (Hall 199 1, Rohlf and Archie 1978). Some 

of these methods require teams of two or more field workers, 

several distance measurements, or both to determine tree 

positions within each plot. Other methods are limited in 

application to plots of specific shapes. The standard 

mapping convention, commonly used for many forestry 

applications, employs a rectangular coordinate system with 

the origin in the lower left corner of the plot (Warren and 

Cook 1984). This convention places all plotted trees into 

Quadrant I of a typical two-dimensional Cartesian plot, 

making all x- and y-coordinate values positive for each 
position. All of these methods vary considerably in 

accwacy, time consumption, and difficulty of execution. 

The Sequential-target mapping method and the Plot-origin 

radial mapping method were developed to overcome the 

limitations of current mapping options. These new methods 

improve the ease and flexibility of mapping methods and 

equipment needed for tree plot surveys; minimize the time 

needed by foresters, private land owners, and researchers to 

produce maps of tree plots to scale; and eliminate the need 

for expensive and complicated global positioning system 

(GPS) equipment for mapping small-area plots. They can be 

applied to two-dimensional (planar) or three-dimensional 

(topographic) mapping of forest plots that are smaller than 

most geographic infomation system (GIs)-scale plots, 

generally < 1 square mile (mi2). The methods offer procedures 

for surveying trees in the two most common field situations: 

(1) closed or dense stands where substantial physical 

obstruction occurs among trees to be surveyed and (2) 

relatively small open stands where all trees of interest are 

visible from a central reference position (origin). Although 

these mapping methds originally were developed to 

facilitate the establishment of field research plots for studies 

of oak wilt disease, they can be used on any forested plot. A 

preliminary report has been published (Wilson 1993). 

The objectives of this research follow: (1) devise two new 

methods for rapidly mapping tree positions in twodimensional and three-dimensional coordinate field plots; (2) 

develop methods for rotating mapped positions to any 

desired orientation relative to the plotting axes to 

accommodate all positions in the mapping field, correct for 

magnetic declination, or both; (3) derive new algorithms 

required for mathematically transforming field coordinates in 

the two mapping methods, for map rotations, and for 

calculating horizontal distance and azimuth values between 

any two trees in the plot as well as between plotted trees and 

plot-center; and (4) develop software to efficiently execute 

the algorithms described in this paper and provide output in 

the form of readil y weable and printable mo-dimensional 

maps and suppo"ting spatial data on trees in forested plots, 

This paper is the first of two describing new tree-mapping 

methods. It explains how to survey and collect mapping data 

in the field; gives details on the theory behind the mapping 

methods, algorithms, and software; demonstrates their use in 

a small sample; evaluates their accuracy; and explores 

management implications. The second paper will explain how 

to domload, edit, and input the field data into specially 

designed mapping software (TreeMapper) that utilizes the 

algorithms described here to create maps and other desired 

outputs. Terms used to describe the mechanics of the 

mapping methods are defined in the appendix. 

Materials and Methods 

Field data-The sample field data used to demonstrate the 

mechanics ofthe tree mapping methods were taken from 20 

trees in an oak wilt research plot near Lampasas, TX. The 

plot was located in a stand of live oaks (&uercusJirsiformis 

Small) positioned adjacent to the expanding edge of an oak 

wilt infection center caused by Ceratocystis fagacearum. 

The plot originally was established to examine the rate 

disease symptoms spread through the stand relative to the 

rate toxic hgal metabolites move in advance of the hgus. 

Field survey met hodolw-Most forest-plot mapping 

methods in forestry-related applications use either Cartesian 

rectangular coordinates (x, y) or geopositional coordinates 

(latitude, longitude) collected fiom field surveys as input 

data for mapping algorithms. The data generally are collected 

with compass, theodolite, electronic measuring devices 

(EMD's), or GPS equipment-which depends on telemetry 

data from orbiting satellites. The methods described in this 

paper use vector data acquired between reference and target 

positions during field surveys. These data are used to 

calculate spatial information on relative tree positions from 

plot-center coordinates and to generate a two-dimensional 

map of the forest plot that may be printed for field use. An 

initial scout of the forested plot area is recommended before 

the field survey to determine the general distribution of trees 

that will be included in the plot. This preview provides an 

opportunity to determine the most appropriate survey 

method and the best path for traversing the plot to 

systematically cover the plot area. A11 trees to be included in 

the survey should be marked and numbered before the 

survey to facilitate the accurate identification of individual 

trees during and after the survey. Simple conventional metal 

tags to more elaborate bar code labels with encoded 

infomation may be used for this purpose. Site attributes, 

tree characteristics, and treatments for individual trees 

should be recorded during the mapping survey. 

Azimuth coordinates (horizontal vector), consisting of 

horizontal distance ( WD) and azimuth (AZ), are the only 

measurements that must be recorded during the field survey 

for two-dimensional mapping with these methods. Slope 

angle (SA) also must be recorded for three-dimensional 

mapping. Azimuth may be taken relative to either magnetic 

north or true north. Compasses should be set with the 
appropriate declination when true north values are desired. 

Magnetic declination values may be obtained from a United 

States Geological Survey (USGS) iwgonic chart or 

topographic qmdrangIe map of the locality containing the 

survey area of interest. If declination is 

field survey, the final plot map may be rotated later to correct 

for declination when this infomat ion is known. Horizontal 

vector data from field surveys are converted into rectangular 

coordinates relative to plot center by using a series of 

coordinate conversion algorithms to construct the final plot 

map* 

The specific field techniques used to collect azimuth 

coordinates during field surveys depend on the mapping 

method chosen for the survey. The criteria used to decide 

which mapping method is most appropriate and applicable to 

the survey task will be discussed in more detail under 

'Methodology and Theory' in the sections describing each 

mapping method. Once the survey method has been chosen, 

field measuremen& may begin. 

The Foresight-inline survey method is used with the 

Sequential-target mapping procedure. With this survey 

method, azimuth coordinates are taken sequentially among 

trees included in the survey. All measurements must be made 

in precisely the same way to avoid cumulative plotting errors 

on the final plot map. For example, all azimuth coordinates 

from reference trees (origins) to target trees must be taken on 

all target trees at the same height above the ground as the 

surveyor instrument. Several other techniques may be used 

to ensure that all measurements are precise and consistent. 

One technique involves always measuring from the center of 

the reference tree to the near face of the target tree by 

resting the surveyor device against the bark of the reference 

tree with the front of the device in the center of the reference 

tree and perpendicular to the line of sight in the direction of 

the target tree. Then, the radius of the target tree is added to 

the distance. The recorded distance is the HD between the 

center of the reference tree and the center of the target tree. 

In a simpler technique, the surveyor device is positioned 

behind the reference tree; the front of the device is aligned 

with the near face of the reference tree; and the HD to the 

face of the target tree is measured. Some error will occur if 

the trees differ significantly in diameter. To minimize A2 

errors with these techniques, the surveyor instmment can be 

aimed on target trees near the edge of the bole on the same 

side from which measurements are taken on the reference 

tree. This approach is useful if either the reference tree or the 

target tree has a large diameter or if the trees are close 

together. Alternatively, a measurement can be taken from 

both sides of the reference tree, aiming at the center of the 

target tree, then averaging the measurements to obtain the 

best AZ measurement. Horizontal distance and AZ 

components of azimuth coordinates also may be taken in 

sqarate measurements. Finally, HD could be measured 

using one of the techniques described above, while the AZ 

component could be taken at a position direct1 y between the 

reference and target tree. Regardless of the technique 

selected, one technique should be used throughout the 

survey. 

Radial surveys are used with the Plot-origin radial mapping 

method in which all azimuth coordinates are taken fiom a 

central fixed location (origin) within the plot. A surveyor 

device should be mounted onto a sturdy tripod directly over 

this marked, fixed position. The surveyor device may be 

positioned over the stake using a surveyor's plumb. The 

tripod should rotate 360" to allow measurements in all 

directions. 

Equipment requirements-A wide range of surveying 

equipment from simple compass, steel tape, and clinometers 

to theodolites and sophisticated EMD's may be used with 

the tree mapping methods described in this paper. Horizontal 

distance and AZ measurements may be written down and 

entered into a spreadsheet or recorded with a data logger 

and downloaded to a computer. Laser survey instruments 

were found to be very quick and accurate. Hundreds of trees 

can be surveyed in just a few hours with these instruments. 

The Criterion 400 Survey Laser (Laser Technology Inc., 

Englewood, GO) was used in this research. This infrared 

survey laser gives distance measurements to 0.1 meters (m) 

(accuracy k 9.4 centimeters [cm]) and measures distances 

from 3.7 to 457 m without a reflective prism (Anonymous 

1992). Shorter distances may be measured by taking the 

difference between HD measurements to the target and 

source tree from a position behind the source and in line 

with the target tree or by using the optional engineering 

diode that measures distances less than 3 m. The instrument 

records angular measurements (AZ and vertical angle) to 0. I O 

(6 minutes) with an accuracy of * 0.2 to 0.3O and a range of 0 

k 60O of vertical angle using a tilt sensor encoder and 

fluxgate compass. Horizontal distance is calculated 

automatically in sloping terrain from slope distance and 

vertical angle, eliminating the need for clinometric 

measurements. 

The specific procedures used to record and store azimuth 

coordinates on various survey lasers during field surveys 

may vary considerably. The following sequence of steps 

used for recording data in this study applies to the Criterion 

400 Survey Laser. These steps merely serve as an example of 

the protocols that may be required for this process. The 

Criterion 400 Survey Laser provides two separate submenus 
under the Survey Menu in its built-in instrument software 

that permit data acquisition during field surveys 

(Anonymous 1992). The Basic Measurements submenu 

provides horizontal vector data (HD and M) or azimuth 

coordinates, on one screen. The user may scroll through 

subsequent screens that show these values individually 

along with slope distance, percent slope, and inclination 

(vertical angle in degrees). The horizontal vector data screen 

provides all the infomation needed for two-dimensional 

planar mapping. Data collected on the Basic Measurements 

submenu must be downloaded through the battery port into 

a data logger or field computer immediately after a valid 

measurement is taken because the programming does not 

allow direct storage into the memory of the instrument. The 

data are downloaded using the Enter button on the 

instrument keypad. The accuracy of the data should be 

checked before storage. Horizontal vector data also may be 

gathered by using the Unit Survey submenu. This submenu 

requires selection of initial setting options, such as survey 

number, unit (measurement number), point generat ion (for 

auto numbering sequence of foresight or backsight 

surveys), survey reference (point from another survey or 

coordinate reference), and choice of foresight or user 

defined survey methods, before horizontal vector data can 

be acquired. All data collected are stored in the laser 

surveyor's memory. A foresight-only survey with inline 

generated values and coordinate type reference must be 

selected as options for open surveys with the Sequentialtarget mapping method. The User defined numbering system 

option should be used with the Plot-origin radial mapping 

method. The FromlTo screen must be edited for the proper 

origin-target numbering sequence before each measurement 

when using the User defined numbering system, but the 

Foresight-inline numbering system automatically generates 

the proper numbering sequence. The horizontal vector 

screen is reached by scrolling through the x-, y-, and zcoordinate screens or using the Review button. Values may 

be edited using the Delete or Clear buttons on the keypad 

before a replacement measurement is taken. The next 

measurement is taken by editing the FromlTo screen as 

needed and using Review to reaccess the horizontal vector 

screen. 

Software requirements-TreeMapper 1.0 for DOS is anewly 

developed computer program written in Visual Basic that 

incorporates the algorithms described in this paper to 

produce two-dimensional maps of forest plots from azimuth 

coordinates collected during the field survey (Lester and 

Wilson 1995). The program converts azimuth coordinates to 

plot-center coordinates and graphically plots tree positions 

(to scale) on screen. Figure 1 provides a comparison of the 

overall sequence of coordinate conversions used in the 

program to calculate plot-center coordinates for the 

Sequential-target and Plot-origin radial mapping methods. 

Input data may be entered in the program manually or 

imported from a data logger or EMD. Dodoaded data from 

the data logger or survey laser must be edited to eliminate all 

data except origin-reference, HI), and AZ values. Because a 

single computer screen pixel at 640 x 480 video graphics 

adapter (VGA) monitor-resolution is used as the mapping 

unit, the maximum dimensions of the mapping field are 

limited to plots of 640 x 480 units (feet, meters, chains) in size 

at 1 x scale factor. Higher resolution screens will display the 

I Sequential- / target method 

Plot-origin 

radial method 

Figure I-Flowchart illustrating the sequence of coordinate conversions 

used by TreeMapper to calculate plot-center coordinates for the 

Sequential-target and Plot-origin radial mapping methods. 
plot maps at the same resolution and size and will not fill the 

entire screen. Large forest plots may be mapped after 

reduction with small-scale factors. The program allows for 

reduction and magnification of the plot fkom 0.1 up to 

lox-scale factor. Map sizing allows plot adjjustments to fit all 

plotted points into the map frame and to improve the 

resolution of plotted tree positions in small plots. Plots of 

tree positions may be rotated up to 90' in two directions 

using Polar X or Polar Y plotting methods to improve fit 

within the map fkame. Horizontal distance and AZ between 

any two positions not directly measured may be calculated. 

Maps may be printed using high resolution, LaserJetcompatible printers or may be saved to disk in graphics file 

formats (e.g., PCX files) that are easily imported into other 

computer graphics software. The program requires a 386 or 

higher International Business Machines (IBM) compatible 

computer, VGA monitor, a minimum of 2 megabytes (MB) of 

random access memory (RAM), and 2 MB of free hard disk 

space. 

Sequential-Target Mapping Method 

Methodology and theory-The Sequential-target method is 

useful for mapping irregularly shaped or elongated forest 

plots with dense stands or stands containing abundant 

obstructions between trees. The method may be used in 

open surveys to map the locations of individual trees (or 

other static objects) within a plot or in closed surveys to 

map the boundaries of plots, timber stands, or property lines. 

Survey data for the Sequential-target method are collected 

between source and target trees in sequential numerical 

order as marked during the presurvey tree-labeling process. 

This survey method, referred to as a Foresight-inline survey, 

considers the source tree as the origin. The azimuth 

coordinates refer to the position of the target tree relative to 

the source tree. The target tree becomes the new origin 

(source tree) from which azimuth coordinates are taken for 

each subsequent target tree. Consequently, the sequence of 

(source-to-target) azimuth coordinate measurements taken 

using the Foresight-inline survey method correspond to tree 

combinations [(I-2), (2-3), (3-4) . . .] and represent relative 

coordinates. Backsight azimuth coordinates may be taken 

fkom target to source trees as needed to check the precision 

of HD and AZ in foresight data, but backsight data are not 

used for mapping. Figure 2 shows a comparison of the 

spatial orientation of the data-acquisition sequence used 

with the Foresight-inline survey method in Sequential-target 

mapping to the orientation used with the Radial survey 

method in Plot-origin radial mapping. 

Survey data stored in the memory of an EMD or data logger 

may be downloaded to a computer for conversion into a 

format that can be plotted. The Sequential-target mapping 

method converts field-derived azimuth coordinates into 

polar, rectangular, tree- 1 reference, and finally plot-center 

coordinates through a series of algorithms for each 

conversion. Condition formulas define which equations are 

used based on the input values of coordinates under 

Figure 2-Sequence of measurements for acquisition of azimuth coordinates (HD, AZ) during field surveys using the (a) Foresight-inline 

survey method and (b) Radial survey method. 
Table 1-Incremental data showing the relationship between azimuth 

bearings and polar bearings using polar X and polar Y tree plotting 

meth 

Azimuth Polar X Polar Y uth Polar X PolarY 

"Bearing values (in degrees). Azimuth (compass) bearings (a) increase in the clockwise 

direction from a variable reference position either on the positive x-axis (polar X) or 

on the positive y-axis (polar Y), while polar bearings (8) increase in the counterclockwise 

direction from a fixed reference position on the positive x-axis. 

conversion. Polar coordinates (r, 0) and rectangular 

coordinates (x, y), like azimuth coordinates, are relative 

coordinates that only indicate the position of target trees 

relative to the previous source tree. However, tree- 1 

reference coordinates and plot-center coordinates are 

absolute coordinates that tie all tree positions together 

relative to a common reference point. Tree-1 reference 

coordinates indicate the positions of trees relative to tree- 1. 

Plot-center coordinates indicate the positions of trees 

relative to the geometric center ofthe plot. Plot-center 

coordinates are used to produce the final plot map. 

Forest plots are produced from plot-center coordinates using 

either Polar X or Polar Y plotting methods. Polar X and Polar 

Y plotting methods produce plots whose positive x-axis or 

positive y-axis rays point to north when no plot rotation is 

used. In addition to Polar X and Polar Y plots, plot axis 

rotations allow all plotted positions to be rotated through 

any desired angle (a) up to 90" in either a clockwise 

(eastward) or counterclockwise (westward) direction. The 

maximum angular rotation is 90" because a 90" westward 

rotation of a Polar X plot is equivalent to a Polar Y plot with 

no rotation. Conversely, a Polar Y plot rotated 90" eastward 

is equivalent to a Polar X plot with no angular rotation, and a 

45" eastward rotation of a Polar Y plot is equivalent to a 45" 

westward rotation of a Polar X plot. When plots are rotated, 

the direction of north rotates with the points to maintain the 

proper orientation of points relative to north. Consequently, 

the rays of the positive x-axis or y-axis no longer point to 

north. Hence, the strict definition of a Polar X or Y plot no 

longer exists. 

Azimuth to polar coordinate conversioneThe initial step in 

the Sequential-target mapping method employs algorithms 

that take horizontal vector or azimuth coordinates (HD, AZ) 

as input data and convert them to polar coordinates (r, 8). 

The polar coordinate system is based on the vector 

quantities of radial distance or magnitude (r) and polar angle 

or direction (8). It provides a constant or standardized 

format for expressing coordinates in relation to a fixed 

orientation relative to the positive x-axis, from which 

bearings are measured in a counterclockwise direction. 

Azimuth coordinates, by comparison, are based relative to 

north on the x-axis, or more commonly y-axis, and have 

bearings that progress clockwise from the respective 

reference axis. Horizontal distance and radial distance are 

equivalent, but bearing values change in this coordinate 

conversion. Table 1 shows the relationship between AZ and 

polar bearings for the Polar X and Polar Y plotting methods. 

Conversion of azimuth coordinates to polar coordinates 

increases the flexibility of the potential mapping 

manipulations that are possible by allowing: (1) a choice of 
plotting methods to produce different map orientations 

relative to north on the x- or y-axis, (2) rotations of plots 

(plotted positions) up to 90° clockwise or counterclo~kwise 

for any orientation relative to these axes, and (3) corrections 

for magnetic declination from true north. 

A direct conversion of azimuth coordinates to rectangular 

coordinates would preclude the ability to easily select the 

axis desiwated as north or to rotate plots by requiring that 

separate case-specific condition formulas be used for 

calculating the positions of trees for every possible mapping 

orientation selected relative to the plotting axes. This would 

complicate the mapping process and create difficult logistic 

problems in developing computer code in software designed 

to instruct the production of plot maps by the computer. 

Two procedures, the Polar X and Polar Y plotting methods, 

were developed to increase the versatility of mapping 

orientations. The method used to convert azimuth 

coordinates to polar coordinates depends on the onientation 

chosen for the plot with respect to the axis selected (as 

magnetic or true north) and whether plot rotation is required. 

The Polar X method (without plot rotation) considers the 

positive x-axis ray to point to magnetic north, while the Polar 

Y method considers the positive y-axis ray to indicate 

magnetic north. These axes indicate true north when the 

plots are rotated to correct for declination (fig. 3). Plot 

rotations through an angle (a) permit map orientations 

relative to north that are not fixed on the x- or y-axis, which 

can be demonstrated in a typical clockwise (eastward) polar 

X plot rotation of 45" (fig. 4). Figure 5 illustrates how rotation 

of all plotted points in an eastward axes rotation would 

appear. A plot axes rotation may be necessary if the longaxis of the plot varies significantly &om the long axis ofthe 

f~ed mapping area or if all plotted points will not fit 

completely within the map frame. A plot also may be rotated 

to provide a different map orientation relative to the mapping 

field. A rotation of the plot in an appropriate direction and 

angle ensures that all of the trees present in the forest plot 

are represented in the final plot map. In addition, plot 

rotations may be necessay to correct input data for 

declination or to reotient the map to designate an axis as true 

north. The data may be corrected for declination before 

mapping or the plot may be rotated by the declination 

amount. In the former case, data converted fiorn magnetic to 

true north before input into a mapping algorithm would 

result in a map with N indicating true north. In the latter case, 

a rotation of the plot through an axis rotation angle 

(equivalent to the declination) would result in a map in which 

the positive x- or y-axis ray points to true north, and N 

rotates with the plotted points and indicates magnetic north. 

An eastward plot rotation would be required for correction 

of an east declination of equivalent magnitude and a 

westward plot rotation would be necessary to correct a west 

declination. 

Table 2 provides equations used to convert azimuth 

coordinates to polar coordinates, with or without plot 

rotations, using the Polar X and Polar Y plotting methods. 

Polar X plots use Equations 1 through 5 and Polar Y plots 

use Equations 6 though 1 1. Condition formulas are used to 

determine which corresponding conversion equation to use 

to derive polar bearings. Axes rotation angles (a) only apply 

to conditions and conversion equations when plots are 

rotated. 

Polar to rectangular coordinate conversion~onversion 

of polar coordinates (r, 0) to rectangular coordinates (x, y) is 

required for two-dimensional mapping with the Cartesian 

coordinate system. Because azimuth coordinates of target 

tree positions are taken sequentially relative to the last 

reference point (source tree or position) using the Foresightinline survey method, all azimuth coordinates as well as 

calculated polar and rectangular coordinates are relative 

coordinates. Hence, the origin is redesignated with each new 

measurement. An initial plot of all relative tree positions 

must be constructed before the absolute positions of trees 

relative to a common origin can be calculated. The 

TreeMapper software plots the positions using a series of 

offsets that redesignate the new origin each time until all 

positions are plotted. The accumulated positions of trees 

then are stored as an array in screen coordinates for 

subsequent conversions. 

The equations used for converting polar coordinates to 

rectangular coordinates depend on the plotting quadrant 

within which the target position will be plotted. The plotting 

quadrant indicates the polarity of the resulting x and y 

coordinates and is determined by the magnitude of the polar 

angle bearing as indicated by the condition formulas (table 

3). The conversion equations for quadrants II-IV (Equations 

14 through 19) are equivalent to Equations 12 and 13 in 

quadrant I, because the sine and cosine functions take into 

account quadrant positions for difTerent polar bearing 

magnitudes. However, the equations appear in this 

alternative form for future comparison with conversion 

equations 106 through 12 1. 

Rectangular to tree-1 reference coordinate conversions 

The screen coordinates saved in computer memory as an 

array following polar to rectangular coordinate conversions 

are essentially tree- 1 reference coordinates. Tree- 1 reference 

coordinates are determined by designating tree- 1 as the 

origin with coordinates (0,O) and adding the relative 

rectangular coordinates of each successive target tree to the 

coordinates of the source tree to generate the accumulative 
Figure 3-Relationship of azimuth to polar bearings and the orientation of north with respect to plot axes using the 

(a) Polar X plotting method and (b) Polar Y plotting method. 
Polar X plot rotation 

Figure 4--Typical 45' east (clockwise) axes rotation of a Polar X plot with concomitant changes in azimuth and polar bearings. 

Figure 5-Angular displacement of plotted positions associated with a 45O east (clockwise) rotation of a Polar X plot. Positions are 

indicated (a) before rotation and (b) after rotation. 
Table %Equations for converting field-derived azimuth coordinates (HD, A.2) to polar coordinates (r, 8) 

for Sequential-brget mapping of trees using polar X and polar Y plotting methals 

Plotting Plot Condition 

methods rotat iona formulas 

Conversion 

equat ionsb 

Equation 

number 

Polar Y 

Polar X None All azimuth values 

West AZ <a 

AZ >a 

East kzs360-a 

AZ >360-a 

None Us90 

AZ>90 

West U<90+a 

AZ>90+a 

East AZs90-a 

AZ>9O-a 

a West = counterclockwise rotation of points (positions) within plot (relative to the fixed plot frame); East = clockwise 

rotation of points within plot. 

'Symbols: 0 = polar coordinate angle (bearing) between the positive x-axis and the ray from the origin (source position) to 

the target tree position measured in the counterclockwise direction; AZ = zaimuth; a = axis rotation angle of plotted points. 

Table %Equations for converting polar coordinates (r, 0) to rectangular 

coordinates (x, y) with the Sequen tial-target mapping method 

Plotting Condition Conversion Equation 

quadranta formulas equationsb number 

I O<0<90 x=rcose 

y = r sin 0 

II 90< 011 180 x=-rcos(180-0) 

y= rsin (180-0) 

III 180<0~270 x=-rcos(0- 180) 

y=-rsin(0- 180) 

IV 270<0<360 x= rcos(360-0) 

y=-rsin(360-0) 

"The polarity of x-coordinate (abscissa) and y-coordinate (ordinate) for points in each 

quadrant (quafter-plane) follow: Quadrant I: x > 0, y > 0; Quadrant 11: x < 0, y > 0; Quadrant 

111: x < 0, y < 0; Quadrant IV: x > 0, y < 0. 

Conversion of polar coordinates (r, 0) to rectangular coordinates (x, y); r = radial distance 

or magnitude; 0 = polar angle or direction (bearing). 
coordinates of each tree in the plot relative to tree-1. The 

conversion of rectanplar coordinates of each sequential 

tree position in the plot into tree- 1 reference coordinates 

provides absolute coordinates that tie together all tree 

positions in the plot relative to a common reference position 

(tree- 1 ). 

Tree-1 reference to plot-center coordinate conversioneA 

plot of tree- 1 reference coordinates using coordinate 

summing results in a tree-1 reference map in which tree-1 is 

the origin positioned at the center of the mapping field. The 

distribution of tree positions on a tree- 1 reference map is 

typically skewed to one side of the plotting area (fig. 6A). 

The skewed distribution may result in the plotting of some 

points outside the mapping frame, This condition is 

corrected by converting tree- 1 reference coordinates into 

plot-center coordinates. Plot-center coordinates are tree 

positions relative to the plot's geometric center (fig. 6B). The 

conversion involves calculating the geometric center of all 

tree positions in the tree- 1 reference plot followed by 

repositioning the geometric center along with all plotted 

points to the origin at the center of the mapping field. 

The geometric center of a tree-1 reference plot is found by 

searching through all of the coordinates in the tree- 1 

reference plot to find the highest (maximum) and lowest 

(minimum) x and y values. These extreme values of x and y 

are usually found in the coordinates of several different 

trees. TreeMapper instructs the computer to determine these 

maximum and minimum values using a bubble-sort 

procedure. The midpoint between the extreme x and extreme 

y values in the plot data set identifies the coordinates of the 

geometric center (GC) . The coordinates of the GC are 

calculated by using the following formula: 

The GC coordinates then are used to determine the 

correctional offset needed to reposition all plotted positions 

to the center of the mapping field. Correctional ofEset values, 

obtained by multiplying the GC coordinates (x and y values) 

by (-I), are added to each corresponding x- and y-coordinate 

of the tree- 1 reference plot to obtain plot-center coordinates. 

This equation is applicable only when the plot survey 

contains more than three trees because calculations with 

less than four trees may result in coordinates that are not in 

the center of the plot. 

Algorithms for A2 and intertree HD calculations-Forest 

management and modeling studies investigating correlations 

and interpretations of spatial patterns, structure, or density 

of forest stands with respect to environmental conditions, 

growth and yield, productivity, ecosystem fhctions, and 

interaction dynamics often require information on the 

positions of trees relative to each other and to plot-center. In 

addition, movement within plots is facilitated by knowledge 

of the bearing and HD from a reference position near a 

current position to a target position where subsequent work 

tasks are planned. The Criterion 400 Survey Laser has a 

navigation function that will steer the operator to the target 

with an audible beep or tone when the operator enters the 

coordinates of the origin and target positions. 

Figure 6-Positional offset of plotted positions during conversion from (A) tree-1 reference coordinates to (B) plot-center 

coordinates. 
Ubown WD's between plotted positions may be 

detemined using the Pythagorean theorem with plot-center 

absolute coordinates. TreeMapper calculates 

between any two points of interest in a Distance Calculator 

submenu. Horizontal distance between trees in the plot also 

may be calculated directly from polar coordinates using the 

following equation derived Erom the law of cosines: 

d = \i r,' + r,' - 2 r, r, cos (02 - 0,) 9 

where 

d = HD between any two plotted tree positions, 

r = radial distance or magnitude, and 

8 = polar angle or direction (bearing), the vector components 

of polar coordinates acquired fiom a common origin. 

However, this equation only may be used when all azimuth 

coordinates (fiom which all polar coordinates are calculated) 

are taken from the same reference position (origin) as in the 

Plot-origin radial mapping method Consequently, this 

method for calculating HD between trees does not apply to 

the Sequential-target mapping method because the reference 

position is not fixed but moves with each new measurement. 

This equation is noted as an alternative to show that HD's 

could be derived by other means. However, this equation is 

not used here because it would add inefficiency to the 

software program that calculates both tree positions and 

HD's between trees Erom plot-center coordinates in both 

mapping methods. In addition, tree coordinates derived fiom 

sequential mapping using the Foresight-inline survey 

method cannot be determined directly Erom the law of 

cosines. 

Azimuth calculations are somewhat more complex because 

they must take into account plotting methods, plot rotations, 

and the relative magnitude of x and y plot-center 

coordinates. Table 4 presents equations for calculating the 

AZ of target trees from plot-center for Sequential-target 

mapping with Polar X equations 20 through 42) and Polar Y 

(Equations 43 through 65) plotting methods, with or without 

plot rotations. Computers calculate trigonometric functions 

in radians. Consequently, the TreeMapper software must 

multiply the results of the conversion equations by the 

constant 180in (57.29577) to convert radians to degrees. 

Table 5 provides analogous equations for calculating the AZ 

of targets trees from any tree position in the plot using Polar 

X (Equations 66-85) and Polar Y equations 86 tkrough 1 05) 

plotting methods. Condition formulas that determine which 

azimuth equation to use to calculate the AZ between any 

two tree positions in the plot are selected on the basis of the 

relative magnitude of x and y coordinates of the source and 

target tree positions. 

P1ot-O-n Radial Mapping Method 

Methodology and theory-The Plot-origin radial method is 

usehl for mapping relatively small, roughly circular plots, 

such as variable-radius plots, in generally open stands 

where all trees of interest are in clear view from a central 

location. Survey data for this method are collected at a 

suitable fixed position near the center of the plot using the 

Radial survey method. This central reference position, 

referred to as the reference origin or Plot-origin, is the 

position from which azimuth coordinates of all target tree 

positions are measured. Horizontal vector data may be taken 

in either a clwkwise or a counterclockwise direction. 

Azimuth coordinates taken in sequence with the Radial 

survey method correspond to tree combinations [(O- I), (04, 

(0-3), . . .] and represent absolute coordinates because all 

positions are determined relative to a futed reference point 

(see fig. 2). The futed reference point is the origin, but not 

necessarily the geometric center and plot-center. 

Azimuth to rectangular coordinate conversionsCoordinate conversions fiom azimuth coordinates to polar 

and rectangular coordinates may be executed with the same 

algorithms used in the Sequential-target method (Equations 

1 through 19). These algorithms allow plot rotations of plotorigin radial plots. However, in this method the TreeMapper 

software plots rectangular coordinates relative to the 

common reference origin. Hence, all conversion coordinates, 

including azimuth, polar, and rectangular, are absolute 

coordinates because the reference origin is a static position 

fiom which all field coordinates are recorded. Commonreference plotting in the TreeMapper software is achieved 

by offsets back to the reference origin after each tree 

position is plotted. 

Alternatively, rectangular coordinates of Polar X and Polar Y 

plots (by strict definition) without plot rotations may be 

calculated using the equations presented in table 6. 

However, the plots may not be rotated. Unlike Equations 14 

through 19, Equations 106 through 12 1 cannot be reduced to 

a pair of equations (for x and y coordinates) applicable to all 

plotting quadrants, because the condition fomulas have 

changed with respect to the quadrants with which they are 

applicable. These changes result from a shift in the position 

of north associated with the use of Polar X and Polar Y 

plotting methods; consequently, A2 values are shifted 

accordingly. 
Table &Equations for ealcdating azimuth of target trees from plot-center with the Sequential-target mapping method 

using polar X and polar Y plotting methods with and vvithout plot rotation 

Plotting Plot 

methods rotationa 

Condition 

fomdas 

Azimuth 

equationsb 

Equation 

number 

AZ= 0 

AZ= 90 

AZ = 270 

AZ=360-arctan1 y/xl 

AZ= 180+arctan/ y~ I 

AZf180-;lrctan i /y/x 1 

AZ-arctan ylx 

AZ= 0 

AZ= 90+a 

AZ = 270 +a 

Polar X None x=O and y=O 

x=O and y<O 

x=O and y>O 

x>O and y>O 

x<O and y~0 

x<O and y<O 

x>O and y<O 

West x=O and y=O 

x=0 and y<O 

x=O and y>O 

x>O and y~ 

AZ=360-arct ylxl+a 

AZ=a -arctan 7' ylx I 

AZ= 180+arctanl y/xI+a 

AZ= 180- ;lrct~I~~l~~+~ 

AZ=arctan yfx +a 

AZ= 0 

AZ = 90 -a 

AZ = 270 -a 

AZ=360-arctanl y/xl-a 

AZ= 180+arctanl y/ 1-a 

AZ= 180-arctan 11 ylx -a 

when a < arctan 

when a > arctan 

AZ = arctan l y / x / 

AZ=360-(a -arctan1 y/xl) 

AZ= 0 

AZ = 180 

AZ= 0 

AZ= 90-arctanl y/xl 

AZ=27o+arctanl yl I 

AZ=270-arctan I ylx 1 

AZ= 90+arctan/ y/x/ 

AZ= 0 

AZ= 180+a 

AZ=a 

AZ= (90-arctanl y/xl)+a 

y / XI 

1 x 1 

"West = counterclockwise rotation of points within plot (relative to grid frame); East = clockwise rotation of points within plot. 

Symbols: AZ = azimuth; a = plot-rotation angle. Computer calculations must include a correction factor consisting of multiplying the values 

resulting fiom arctan functions by the constant 1801x (57.29577) to convert radians to degrees because computers calculate trigonometric 

functions in radians. 

x<O and y>O 

x<O and y<O 

x>O and y<O 

East x=0 and y=O 

x=O and y<O 

x=O and y>O 

x>O and y2O 

x<O and y20 

x<O and y<O 

x>O and y<O 

when a 5 arctan y 1 x 

when a > arctan y / x 

Polar Y None x=O and y=O 

I I 

x=O and y<O 

x=O and y>O 

x>O and y>O 

x<O and yrO 

x<O and y<O 

x>O and y<O 

West x=O and y=O 

x=O and y<O 

x=O and y>O 

x>O and y>O 

x<O and y20 

when a < arctan y 1 x 

when a > arctan y / x 

x<O and y<O 

i I 

x>O and y<O 

East x=O and y=O 

x=O and y<O 

x=O and y>O 

x>O and y>O 

when u 5 90 - arctan 

when a > 90 - arctan 

x<O and y>O 

x<O and y<O 

x>O and y<O 
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Table +Equations for converGon of Geldderived uth coordinates @D, AZ) to rectangular @lotcenter) 

coordinates (x, y) without plot rotations using P1ot-o-n radial mapping with polar X and polar Y plotting methods 

Plotting Plotting Condition 

quadranta method6 fomulas 

Conversion 

equationsc 

Equation 

number 

Polar X 270<AZ<360 

180<AZs270 

90<AZs180 

OrAZs90 

Polar Y OrAZs90 

270<AZs360 

180<AZr270 

90<AZs180 

x= ~COS(~~O-BZ) 

y= HDsin (360 -AZ) 

x=-mcos(M - 180) 

y= HDsin (AZ- 180) 

x=-HDcos(180-AZ) 

y=-HD~in(l80-AZ) 

x= HDcosAZ 

y=-HDsinAZ 

x= HDcos(90-AZ) 

y = HD sin (90 - AZ) 

x = - HD cos (AZ - 270) 

y= HDsin (AZ-270) 

X=-HDCOS(~~O-AZ) 

y=-HDsin (270 -AZ) 

x= HDcos(AZ-90) 

y=-HDsin(AZ-90) 

a The polarity of x-coordinate (abscissa) and y-coordinate (ordinate) for points in each quadrant (quarter-plane) follow: Quadrant I: 

x > 0, y > 0; Quadrant 11: x < 0, y > 0; Quadrant 111: x < 0, y < 0; Quadrant IV: x > 0, y < 0. 

Polar X plotting designates the positive x-axis ray as magnetic north; Polar Y plotting designates the positive y-axis ray as magnetic 

north. 

"Conversion of Azimuth coordinates (HD, AZ) to rectangular (plot-center) coordinates (x, y); HD = horizontal distance between 

source (origin) or plot-center and target tree; AZ = azimuth (bearing). 

Rectangular to plotcenter coordinate conversionsBecause rectangular coordinates indicate tree positions 

relative to the reference origin, which is rarely at the 

geometric center of the plot, rectangular to plot-center 

conversions are needed to offset the plotted positions from 

the reference origin to plot-center. These conversions are 

achieved using the same methods for calculating the 

geometric center of a Sequential-target plot, with a 

correctional offset to reposition all plotted positions to the 

center of the mapping field. Orientation of Plot-origin radial 

maps in the field, like Sequential-target maps, requires that 

the geometric center of the plot is located and marked as plot 

center. Horizontal vector survey data may be input into the 

TreeMapper software on a notebook computer while in the 

field to determine plot-center coordinates; this reference 

position then can be marked before leaving the plot. 

The geometric center of the plot can be located easily in the 

field by using an EMD near the reference origin to take 

repeated horizontal vector readings to targets of known plotcenter coordinates and moving the reference position until it 

matches these plot-center coordinates. The process is 

facilitated by first identifying the physical position required 

to meet the proper AZ bearing to a target with horizontal 

vector readings taken in a circular path around the target, 

followed by a straight line correction on that bearing to 

identify the proper HD. Additional conformat ional readings 

to other targets of known plot-center coordinates should 

confirm the position ofplot-center. Alternatively, plots could 

be set up using rectangular coordinates relative to the 

reference origin fkom which azimuth coordinates were taken, 

but all plotted positions would not necessarily fit within the 

mapping frame unlike plot-center maps, which position 

plotted points around the center of the mapping field. 

Azimuth and intertree distance calculations-Horizontal 

distance of plotted points from plot-center and intertree 

HD's between any two plotted positions in the pIot may be 

calculated from plot-center absolute coordinates using the 

distance calculator in TreeMapper. Azimuth from plot-center 

to plotted positions can be determined using equations 20 

through 65 and AZ between plotted positions can be 

calculated using equations 66 through 105, depending on 

the plotting method and rotation used. 
Three-Dimensional Mapping 

Topographic maps of forest plots are needed where slope or 

elevation have significant effects on forest inventory 

assessments, management and harvesting decisions, 

constfuction activities, and research. The Sequential-target 

and Plot-origin radial mapping methods for two-dimensional 

plotting may be extended to three-dimensional plotting to 

create topogaphic maps. The theory and me tho do lo^ for 

applying these mapping methods to topographic mapping 

are explained here to show that this is not a limitation ofthe 

methods. However, TreeMapper for the disk operating 

system (DOS) does not have topographic mapping 

capability due to the memory limitations of the DOS 

environment. Application ofthis capability will require 

development of comparable sohare in the memory-rich 

Windows environment. 

The addition of a Z-coordinate to indicate an elevation 

change (AZ) between the source position and the target 

position is required to generate (x, y, z) rectangular 

coordinates necessary for three-dimensional mapping. 

Measuring SA, HD, and AZ with the EMD during field 

surveys provides three-dimensional azimuth coordinates 

(HD, AZ, SA) as input data for mapping. The change in 

elevation (AZ) then may be calculated frorn the SA using the 

following equation: 

AZ = HD tan SA 

where 

SA = slope angle equivalent to the arctan of percent slope 

(expressed as a decimal fraction). 

The z-coordinate then is determined by adding the AZ to the 

z-coordinate of the source (reference) position from which 

the measurements were taken. If the source position is the 

reference origin, as in the Plot-origin radial method, the zcoordinate will be the same as the AZ because the reference 

origin is the base elevation from which all plotted positions 

are referenced. Although there is an offset of x- and ycoordinates to plot center, the z-coordinate does not change. 

When the Sequential-target method is used, the AZ must be 

added to the z-value of each successive reference position 

to determine the cumulative z-coordinate of each successive 

target position relative to tree- 1 (the relative base elevation). 

An absolute plot-center z-coordinate for each position then 

may be calculated by determining the midpoint in the two 

extreme (highest and lowest) tree- 1 reference z-values and 

adding a correctional offset to each tree- I z-coordinate to 

arrive at plot-center z-coordinates for each plotted position. 

The coordinates of plot center with the z-coordinate added 

become (O,0,0) for three-dimensional mapping, in which the 

elevation geometric center, located at plot-center, is defined 

as the base elevation where Z = 0. 

Slope distance (SD) is useful and necessary information for 

certain field mensuration tasks requiring actual distance 

measurements between plotted points on a slope. Slope 

distance, the actual distance between two plotted positions 

with an elevation change, may be calculated with the 

following equation: 

Results demonstrating three-dimensional mapping 

algorithms are not included because the sample data set was 

not obtained from a location that had significant relief. 

Results 

Test Plot Orientation 

Field sample data taken from the small, relatively open oak 

wilt research plot near Lampasas, TX were used to illustrate 

data inputs, conversions, and outputs from algorithms used 

to produce maps with the Sequential-target and Plot-origin 

radial mapping methods. Most of the research trees in this 

plot were oriented along a north-south axis. Thus, the Polar 

X plotting method without axes rotation was selected for 

both mapping methods because the x-axis is the long axis of 

the mapping field 

Sequential-Target Mapping Method 

Table 7 presents the results of data conversions for 20 trees 

in this plot. Relative azimuth, polar, and rectangular 

coordinates between origin and target trees are listed in the 

same sequential order as that of the horizontal vector data 

recorded in the field. The HD component in azimuth 

coordinates and the r component in polar coordinates were 

equivalent, but A2 to 0 polar bearing conversions changed. 

Azimuth to rectangular coordinate conversions-kzimu& 

coordinates were converted into a standardized polar 

coordinate format to permit plot rotations and then Cartesian 

rectangular coordinates to permit plotting. Comparisons of 

azimuth and polar coordinate data demonstrate that only the 

angular bearing component of the azimuth coordinate 

changes with this conversion, while HD to target is 

unaffected. No other changes occur in the conversion 

because the polar coordinate system has a fixed reference 
Table 7Xonversion of dmuth coordinates to polar and rectangular coordinates using Sequential-target 

mapping with the Polar X plotting method without plot rotation 

Relative coordinatesd 

Tree Equations Azimuthc 

origin-targeta usedb @A m) 

Polar 

(r7 0) 

Rectangular 

(x, Y) 

"Survey data for 20 trees were taken sequentially between source and target trees with each target tree becoming the source tree 

for each successive azimuth coordinate measurement. 

Equation number (in order) for conversions of: 1) azimuth to polar coordinates and 2) polar to rectangular coordinates (x and y 

values). 

'Azimuth coordinates were taken in the field between source trees (origin) and target trees using the Sequential-target survey method. 

*~~mbols: HI3 = horizontal distance; AZ = azimuth; r = radial distance (magnitude) equivalent to horizontal distance; 8 = polar 

bearing (direction); x, y = Cartesian coordinates. 

starting point (the positive x-axis) fkom which all bearings 

were measured. The fixed reference point allows one to 

define a polar coordinate equivalent for any AZ, regardless 

of the reference point chosen for the azimuth coordinate. 

The use of polar coordinates allows the standardization of 

azimuth coordinates regardless ofplotting orientation. The 

polar-to-rectangular conversion transforms polar vector data 

into the Cartesian coordinate format. This rectangular 

coordinate format greatly facilitates computer plotting and 

HD calculations by allowing the use of trigonometric 

functions, grid plotting, and the Pythagorean theorem. 

Rectangular to plot-center coordinate conversion~Al1 

relative tree positions in the plot must be tied together by a 

common reference position to obtain absolute coordinates 

by which any two positions can be directly compared. The 

conversion to absolute coordinates by assigning tree-1 as 

the reference origin (0,O) and adding the relative rectangular 

coordinates of each successive target coordinate resulted in 

a sum positional change relative to tree- 1. Tree- 1 coordinates 

are absolute because all points are based on a single 

reference position (tree- 1). The midpoint between the 

extremes of the x- and y-coordinates among all coordinates 

in the tree-1 reference data set determine the geometric 

center. In the sample data set, the geometric center of the 

tree- 1 refaence plot was determined to be (-44.2,12.2). 

Hence, the correctional oEset values (44.2, -12.2) were added 

to each corresponding x- and y-coordinate in the data set to 

arrive at plot-center coordinates (table 8). Absolute plotcenter coordinates allowed calculations of HD and AZ of 

each tree fkom plot-center. 
Table &-Conversion of rectanmlar coordinates to tree-1 reference and plot-center coordinates using 

Sequential-target mapping with polar X plo~ng, no plot rotation, and with wociated horizontal distance 

and dmuth of target trees from plot center 

Tree Tree- 1 reference Plot-cerrter Equations Distance from Azimuth firom 

no. coordinates" coordinatesb usedC plot-cente8 plot-center 

- -- 

" Tree-1 reference coordinates were determined by accumulative summing of relative rectangular coordinates starting with 

tree-2 (tree-1 becomes the new origin). 

* Plot-center coordinates were obtained by adding the correctional offset (44.2, -12.2) to the coordinates of each tree in 

the tree-1 reference plot. The coordinates of the geometric center of the tree-1 reference plot was (-44.2, 12.2). 

'Equation number for calculation of azimuth to target tree from plot center. 

d~arget distance was calculated using the Pythagorean theorem: d = d [(x, - x,)Z + (y, - y,)Z]. The numbers indicate the 

reference equations used to determine the tree azimuth fiom plot-center. 

Relative and absolute coordinates with plot-rotation-Use of 

polar coordinates provides the flexibility of rotating the axes 

of a plot to any desired orientation. However, the process for 

conversion of relative azimuth coordinates to rectangular 

coordinates changes slightly when plot-rotations are 

employed. A correctional adjustment in the polar bearing 

(directional) component (8) of the polar coordinate 

accommctdates the necessary change to allow detemination 

of the new rectangular coordinates of each point after 

rotation. The data set was divided into two parts (table 9): 

(1) trees 1 through 10 were rotated 45" westward 

(counterclochise), and (2) trees 1 1 through 20 were rotated 

45" eastward (clockwise). This division was done to show 

the effects of plot rotations in opposite directions on 

conversion coordinates. The rectangular coordinates reflect 

the change in the polar bearing as the points were rotated in 

an arc of magnitude and direction equivalent to the angular 

rotation indicated by the plot rotation. 

The conversion process from rectangular to tree- 1 reference 

and plot-center coordinates with rotated plots was identical 

to the process used when no plot-rotation was applied. The 

only exception was that tree- 10 (not tree- 1 ) was used as the 

reference origin (0,O) for trees 1 1-20 from which tree- 1 

reference coordinates were detemined. There were two 

correctional oRsets, one for each part of the divided data set, 

because each part was essentially treated as a separate plot. 

Table 10 shows the position of each tree relative to the 

geometric center for each of two subplots. 
Table Mmrdinate-plot conversion data generated by polar X plo~ng method using Sequential-target mapping 

with axes robtion of plot 

Relative coordinatesb 

Tree Plot rotation Equations Azimuth Polar Rectangular 

origin-target Degrees Direction useda @a m) (r, 0 ) (x, Y) 

45 West 3,16,17 

3,16,17 

3,16,17 

3,18,19 

3,14,15 

3,16,17 

3,14,15 

3,12,13 

3,16,17 

45 East 4,12,13 

4,16,17 

4,18,19 

4,16,17 

4,16,17 

4,14,15 

4,14,15 

4,16,17 

4,16, 17 

4,16,17 

"Numbers indicate (in order) the equation number used for (1) azimuth to polar coordinate conversions and (2) polar to rectangular 

coordinate conversions. 

Target coordinates relative to origin; Azimuth (HD, AZ), Polar (r, 8), Rectangular and plot-center (x, y). 

Intertree distance and azimuth calculations-The HD and 

AZ from one tree to another can be calculated fiom plotcenter coordinates of the source (reference position) and the 

target position. The distance-azimuth caIculator utility in the 

TreeMapper software serves this function. Table 1 1 lists this 

spatial information between different combinations of source 

and target positions. Once the HD and AZ are known, an 

EMD can be used to locate the desired position. 

Plot-Ori@n Radial Mapping Method 

Azimuth to rectangular coordinate conversion+~e 

results of converting field-derived azimuth coordinates to 

plot-center coordinates using the Plot-origin radial mapping 

method were very similar to results with the Sequentialtarget method, but with a few noted exceptions. Unlike the 

Sequential-target mapping method, all coordinates in the 

Plot-origin radial conversion process are absolute 

coordinates from the beginning because all azimuth 

coordinates were recorded relative to a common, static 

reference origin during the Radial field survey. The use of a 

common reference origin (position 0) from which all azimuth 

coordinates were recorded is reflected in the origin-target 

column of table 12. Because all conversion coordinates are 

plotted with respect to the reference origin, there is no need 

for tree- 1 reference coordinates. The conversion to polar 

coordinates permits plot rotations with this mapping 

method; however, examples of plot rotation and calculations 

of intertree FD and AZ were not included here. 

Rectangular to plot-center coordinate conversion~Plotcenter coordinates derived fiom the Plot-origin radial 

mapping method were identical to those calculated using the 

Sequential-target mapping method (see table 8). The HD and 

AZ values from plot-center for each plotted position also 

were in agreement between the two methods because these 

calculations were based on identical plot-center coordinates. 
Table lWonversion of rectangular coordinates to plotcenter coordinates using the 

polar X ploning method and Sequential-target mapping with plot rotation 

Tree Plot rotation Tree- 1 reference Pfot-center 

no. Degrees Direction coordinatesu coordinatesb 

East 

45 West (0.0,O.O) 

(-2.5, -8.2) 

(- 10.8, -9.9) 

(-1 3.3, -10.5) 

(-8.4, -2 1.3) 

(- 1 0.0, -20.5) 

(- 1 6.8, -2 1.4) 

(- 1 7.2, -2 1.4) 

(- 1 6.4, -8.0) 

(-38.3, -14.4) 

(2.3,3.1) 

(-6.5, -3.6) 

(-6.0, -4.9) 

(-12.0, -14.3) 

(-12.1, -16.1) 

(-26.3,33.5) 

(-30.3,36.1) 

(-32.4,12.2) 

(-34.4,l. 7) 

(-35.0,1.3) 

" Tree- 1 reference coordinates were determined by accumulative summing of relative rectangular 

coordinates starting with tree-2 (for trees 1-10) and tree 11 (for trees 1 1-20) with trees 1 and 10, 

respectively, as the new origins in this split data set. 

Plot-center coordinates were obtained by adding the correctional offsets: (19.2, 10.7) for trees 1-10 

and (16.4, -10.0) for trees 11-20 to the coordinates of each tree in the tree-1 reference plot. The 

coordinates of the geometric centers of each tree-1 reference split-plot data set are (-19.2, -10.7) and 

(- 16.4, 10.0), respectively. 

Table 11-Determinations of intertree distance and azimuth between tree positions using plotcenter coordinates for a 

plot created with polar X plotting and Sequential-target mapping with no plot rotation 

Plot-center coordinates 

Tree Source Target Equations Target distance Target azimuth 

source-target (x, ,Y, (x2 9 Y, used" Erom source tree from source tree 

1 -4 (44.2, -12.2) (27.3, -10.2) 69 17.0 186.7 

2-8 (36.6, -16.2) (12.8, -3.7) 69 26.9 207.7 

3-7 (29.5, -1 1.5) (1 3.1, -4.0) 69 18.0 204.6 

5-14 (23.1,-21.3) (4.4, -2.3) 69 26.7 225.5 

7-10 (1 3.1, -4.0) (2.8, 16.1) 69 22.6 242.9 

9-1 5 (22.8,5.2) (5.6, -3.7) 70 19.4 152.6 

11-19 (2.2,20.0) (-22.8, -6.9) 70 36.7 132.9 

12-17 (0.7,9.0) (-44.2,20.3) 69 46.3 194.1 

13-18 (2.0,8.5) (-28.8, 1.9) 70 3 1.5 167.9 

14-20 (4.4, -2.3) (-22.9, -7.6) 70 27.8 169.0 

15-12 (5.6, -3.7) (0.7,9.0) 69 13.6 246.5 

17-13 (-44.2,20.3) (2.0,8.5) 7 1 47.7 14.3 

1 8-4 (-28.8, 1.9) (27.3, -10.2) 7 1 57.4 12.2 

19-16 (-22.8, -6.9) (-39.5,21.3) 69 32.8 239.4 

20-6 (-22.9, -7.6) (1 8.6, -8.2) 7 1 41.5 0.8 

16-8 (-39.5,21.3) (12.8, -3.7) 7 1 58.0 25.5 

1 4-9 (4.4, -2.3) (22.8,5.2) 68 19.9 337.8 

17-7 (-44.2,20.3) (13.1, -4.0) 7 1 62.2 23 .O 

10-3 (2.8, 16.1) (29.5, -1 1.5) 7 1 38.4 45.9 

"Target distance was calculated using the Pythagorean theorem: d = 4 [(x, - x,P + (y, - y,)Z]. The numbers indicate the equations used to 

determine the target azimuth from the source tree. 

20 
Table lZ--Conversion of azimuth coordinates to polar and rectangular coordinates using the 

Plot-o*n radial mapping method with polar X plotting and no plot rotation 

- - 

Absolute coordinatesc 

Tree Equations 

origin-target useda 0-n 

Polar 

(r, 0) 

"Numbers indicate (in order) the equation number for conversions of (1) azimuth to polar coordinate 

conversions, and (2) polar to rectangular coordinate conversions (x and y values). 

Azimuth coordinates were taken in the field at plot-center (origin) using the Plot-center radial survey 

method. 

"Symbols: ID = horizontal distance; AZ = azimuth; r = radial distance (magnitude) equivalent to horizontal 

distance; 8 = polar bearing (direction); x, y = x-coordinate and y-coordinate, respectively, in the Cartesian 

coordinate system. 

dRectangular coordinates are equivalent to plot-center coordinates (although not necessarily the geometric 

center) because all survey azimuth coordinates were taken from a single central reference position in the plot. 

Mapping Plot-Center Coordinates 

Absolute plot-center coordinates were used to construct the 

finaI plot maps for both Sequential-target and Plot-origin 

radial mapping methods. Figure 7 presents the Polar X plot 

map for the 20 sample trees. The map displays a plot of live 

oak trees that was located in an open stand on the 

expanding edge of an oak wilt infection center. 

Asymptomatic healthy trees were threatened by imminent 

infection through root grafts and common root systems with 

symptomatic diseased trees. The positions of the 20 trees in 

the sample data set were numbered in the order surveyed. 

The map was produced at a scale factor of 1.6x to improve 

resolution between trees, yet maintain all plotted positions in 

the mapping frame. A scale-bar was provided to indicate a 

measure of HD. Plot-center is indicated by the cross hairs in 

the center of the mapping field. Magnetic north was placed 

on the positive x-axis because the plot used the Polar X 

plotting method with no plot rotation. The orientation could 

have been corrected for true north using a plot rotation of 

approximately 10" east (the declination for Lampasas, TX). 

The arrow to north would still indicate magnetic north, but it 

would be rotated 10' eastward (clockvvise) away from the 

positive x-axis, and the positive x-axis would then point to 

and indicate true north. All plotted positions would be 

rotated clockwise with the plotting axes and magnetic north 

bearing to maintain the proper orientation. 

Methods Accuracy and Performance 

The accuracy and performance of the two mapping methods 

were tested by directly measuring azimuth coordinates 

between different combinations of tree positions not 

measured during the initial field survey and comparing these 
Oak Wilt Research Plot-Lampasas, Texas 

$. Asymptomatic 

Figure 7-Map of oak wilt research plot @ampasas, TX) constructed from identical plot-center coordinates derived from the Sequential-target and Piotorigin radial mapping methods. The first 20 trees included in the sample data set were numbered. Scale factor = 1.6x, Scale bar = 10 meters. 

values to calculated values derived from TreeMapper using 

the original survey data. The Sequential-target and Plotorigin radial mapping methods essentially produced identical 

plot-center coordinates and thus had comparable 

performance. Mean differences between actual and 

calculated values were 1.25 f 1.63 m (* 1 SEM) for HD 

measurements and 1.76 f 2.5' (f 1 SEM) for AZ 

measurements, indicating the overall accuracy of the 

mapping methods. 

The major sources of error in the methods occurred during 

field measurements. The magnitude of error depended on the 

precision of the data acquisition methods, the diligence in 

using proper and consistent technique, and the recognition 

of obviously bad field readings due to obstacles interfering 

with the transmission path ofthe EMD. The variability in 

tree diameters introduced error in both HD and AZ. 

Measurements taken on the side of the tree at a tangential 

position perpendicular to the target caused an error in AZ of 

f 1 to 2' depending on tree diameter and target distance. This 

error was corrected in this study by taking AZ readings in 

the direct line between each source and target tree. Target 

distance from the reference position did not significantly 

affect AZ readings from the EMD because laser beam 

divergence on this instrument is very small; as low as 3 

milliradians (mmd) or 0.17 19', which represents an error of 

only 1.37 m over a maximum range shot of 457 m without a 

reflective prism. Azimuth readings to the center of the bole 

on the target tree were preferred because target width can 

vary considerably depending on tree diameter and HD from 

the source tree, 

Tree diameters also affect HD measurements depending on 

where the EMD is positioned relative to the center of the 

source tree. The ideal measurement reflects the HD from the 

center of the source tree to the center of the target tree. This 

measurement was achieved in this study by taking HD 

readings from the near face of the reference tree to the near 

face of the target tree. Horizontal distance measurements 

also were affected significantly when the target tree leaned 

heavily, a common occurrence with live oaks, preventing an 

accurate measure to the position where the tree emerges 
from the ground. The EMD was aimed low at the base of the 

target tree when taking HD readings to reflect the ground 

position at the center of the tmk. When the source and 

target tree are spaced by a distance shorter than the range of 

operation of the EMD, the HD can be determined by taking 

two distance measurements. The operator takes a position 

behind the source tree directly opposite the target tree 

within the operating range of the instrument and then takes a 

HD measurement to the source tree, A slight offset to one 

side allows a shot to the target tree. The HD then can be 

detemined by subtraction. A similar method without the 

offset can be used to acquire A.Z readings between source 

and target trees that are too close together for operation of 

the EMD. The accuracy of HD and AZ values often can be 

improved when these measurements are acquired from two 

separate laser shots, sometimes at different locations on the 

reference tree depending on its growth characteristics. 

Errors from field measurements were theoretically cumulative 

with the Sequential-target method because azimuth 

coordinates were taken from tree to tree with a moving 

source or origin for each measurement. By contrast, errors 

were not cumulative with the Plot-origin radial method 

because the reference origin was a fixed position fiom which 

all azimuth coordinates in the survey were recorded. 

Nevertheless, no significant difference was found in the 

accuracy of the two methods (P < 0.00 1). The errors 

generated with the Sequential-target method using the 

Foresight-inline survey method were generally small and 

tended to be insignificant due to the precision and accuracy 

provided by the survey laser and to the use of consistently 

applied surveying methods. 

The final ground resolution of tree locations relative to each 

other, as reflected by the plot map and supporting 

coordinates, primarily depends on the word-length of the 

computer as detemined by the progammer's capability for 

extending precision, which is limited by the computer 

language used. The magnitude of ground resolution also is 

affected by the units of measure. Large units of measure 

would result in the same proportional ground resolution as a 

smaller unit of measure, but the absolute resolution in terms 

of physical distance would be smaller resulting in greater 

absolute resolution for smaller units of measure. However, 

larger units of measure often are required for very large plot 

areas to ensure all ploned positions fit within the mapping 

.firame. 

The Sequential-target and Plot-origin radial mapping 

methods provide a means for rapidly producing accurate 

maps of forest plots to scale and for quantifLing the 

positions and spatial distributions of trees in those plots. 

These methods do not require as many direct field 

meascvements as other mapping methods and thus allow 

more trees to be mapped faster with fewer personnel. They 

only require azimuth coordinates from each sweyed tree 

using appropriate survey equipment. This horizontal vector 

data, recorded either fiom a static reference origin or 

between individual plot positions, then can be converted 

into plot-center coordinates to map the plot in the center of 

the mapping field. Queries about the spatial relationships 

between individual tree positions, plot center, or both then 

are possible using the vector calculator utility in the 

TreeMapper software. 

These mapping methods are versatile for several reasons: 

(1) the variety of instruments that may be used to acquire the 

input data; (2) the use of surveying methods for data 

acquisition that do not require expensive and complicated 

GPS equipment; (3) the rapidity of map construction and 

coordinate output; (4) the polar coordinate conversion step 

with two plotting methods (Polar X and Y); (5) the capability 

of interpositional HD and AZ caleulatisns; (4) the 

accommodation of two forest plot survey methods, the 

Foresight-inline and Radial survey methods, to cover the 

two most common field survey situations encountered 

during field surveys; and (7) plot rotations that allow one to 

rotate the plot in any direction to customize the orientation 

with respect to the mapping field. Plot rotations are useful in 

making sure all plotted positions are included in the fixedarea rectangular mapping fiame, especially for irregularly 

shaped or elongated plots. They allow plotting corrections 

for declination and provide the ability to select unique map 

orientations to achieve perspectives relative to specific 

features that will be emphasized on the map. They also 

provide the ability to calculate interpositional azimuth 

coordinates between any two positions in the plot and are 

useful for supplying the information needed to guide 

movements between positions during routine work tasks in 

the field. 

The TreeMapper software for DOS, developed to rapidly 

execute the algorithms of each mapping method, enables the 

rapid acquisition of accurate spatial data about individual 

tree positions in a plot and provides this information with 

the plot map output. A number of features have been 

included in the software to facilitate the mapping process. 

Mapping parameter options include sequential or radial 

mapping, polar X or polar Y plotting, axes rotations up to 90' 

in two directions, correction for declination, map scale factor 

adjustment for enlargements or reductions, and English, 

chain, or metric scale units. The map label options are 
position numbering, symbol type, and title or headings. 

Wnting options include support for 185 printer drivers, 

landscape or portrait printing orientation, and normal or 

reverse color. The vector calculator utility permits 

calculations of HD and AZ between any two positions, plot 

center, or both. TreeMapper, in addition to mapping 

capabilities, provides optional printouts of the output data 

of all coordinate conversions along with the map. The map 

and supporting coordinate data may be used in the field to 

locate the geometric plot-center and individual trees in the 

plot and to keep track of treatments, attributes, and 

responses of individual trees for research and management 

applications. The software also can be loaded onto a laptop 

computer to permit acquisition of this information when the 

field plot is originally constructed. 

The use of vector data from EMD's in these mapping 

methods provides several advantages over the use of 

telemetry data from satellites via GPS instruments. Although 

GPS instruments may be used to determine the latitudelongitude (lat-lon) coordinates of any position in a forest 

plot, geopositional coordinates generally do not provide 

sufficient resolution to separate the positions of individual 

trees within small-area plots, especially when the trees are 

spaced close together. Lat-lon values to 0.01 seconds are 

needed to achieve 1 -m accuracy. However, most GPS 

equipment does not measure positions with that level of 

accuracy. By comparison, Em's with submeter accuracy 

easily allow unequivocal resolution of individual trees. The 

dificulty is further compounded by the common inability to 

obtain geopositional readings under a dense canopy. When 

GIs maps are required (e.g., for very large plots) coordinates 

are usually obtained by using an EMD and converting these 

coordinates to geopositional coordinates using GIs software 

to solve the accuracy problem. The output from vector data 

usually will provide higher resolution than telemetry data, 

but a printed map of stands with high tree density often will 

require enlargements by increasing the scale factor to 

provide adequate resolution to distinguish closely spaced 

trees. 

Forest Management Implicabions 

The mapping methods described have been useful in 

numerous oak wilt studies including work on early 

diagnosis, epidemiology, disease suppression, and others 

outlined for future research (see Wilson 1995). They have 

been used to set up research plots, keep track of treatments 

for data collection over time, and to measure the rate of 

movement of fungal pathogens through forest stands. These 

mapping methods are applicable to other work tasks that 

require accurate information about tree positions, intertree 

HD's, and spatial patterns and distributions and the ability 

to keep track of tree attributes over time. These tasks include 

forest inventory surveys, management operations, research 

studies of spatial models and forest dynamics, road building, 

timber hanresting, wildlife management, and recreation 

planning. Some specific applications of the types of spatial 

information provided by the mapping methods may be found 

in growth and physiological modeling studies investigating 

the effects of intertree shading on stand dynamics (see 

Kuuluvainen and Pukkala 1989, Urban and others 199 1, 

Wang and Jarvis 1 990), predicting individual tree 

characteristics from intertree interactions (see Reed and 

Burkhart 1985, Sarnra and others 1989), and estimating the 

influences of site characteristics, tree distribution, and 

canopy structure on physiological processes to simulate tree 

growth and primary production (see Leemans and Prentice 

1987, Mohren and others 1984, Sieviinen and others 1988). 

The methods also could be particularly useful in repeated 

horizontal-point and plot survey sampling for estimating 

stand components of growth and developing volume growth 

estimation models (see Eriksson 1995, Gregoire 1993, May 

1988, Roesch and others 1989, Schreuder and others 1993, 

Van Deusen and others 1986). Even wider applications of 

these methods extend to the mapping of positions for any 

stationary objects in the landscape, including buildings, 

towers, landmarks, signs, road intersections, and any other 

objects with a definable position. 

The USDA Forest Service is now beginning to keep track of 

individual trees in forest inventory surveys in the Western 

States to prevent the theft, harvest, and illegal sale of highvalue trees. This trend will continue as increasing demand 

for forest products greatly augments the value of standing 

timber. The increasing need to produce maps of forest 

stands and keep track of individual trees demonstrates the 

need for these new, easy-to-use mapping algorithms and 

methods with versatile software that use data directly from 

an EMD or other surveyor device to rapidly produce maps 

and spatial output data on trees and other objects in the 

forested landscape. 

Acknowledgment 

The author gtatehlly acknowledges Drs. Ted D. Leininger 

and Nathan M. Schiff for reviewing drafts of the manuscript 

and Don G. Lester for writing the computer code for the 

TreeMapper 1.0 software for DOS and double checking the 

values presented. 
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Appendix 

Definitions of Terms 

Angle of rotation. The angle (a) through which a plot is 

rotated in a clockwise (eastward) or counterclockwise 

(westward) direction, 

Azimuth (U), The magnetic compass direction from a 

reference position to a target position. 

Azimuth coordinates. Field-derived horizontal vector 

measurements of an attribute (target tree) position relative to 

a reference point (source), often the origin, given as 

horizontal distance and azimuth (ED, AZ). 

Elevation distance (ED). The vertical rise or fall in elevation 

between a reference and target position indicated by 

changes in the z-coordinate in three-dimensional mapping; 

equivalent to SD sin SA. 

Foresight-inline survey. A sequential field survey method 

that utilizes each consecutive target position as the reference 

origin from which the coordinate position of a subsequent 

target is recorded. 

Geometric center. The position within a tree-1 reference plot 

that represents the midpoint between the extreme x and y 

(maxima and minima) values among all tree- 1 reference 

coordinates for positions included in the plot. 

Horizontal distance (HD). The level distance, equivalent to 

SD cos SA, between two geographic positions plotted on a 

horizontal plane passing between the two points at a 

constant elevation; most apparent from an aerial viewpoint 

above both positions. 

Horizontal vector. Field data equivalent to buth 

coordinates. 

Inclination. Slope angle or angle of slope. 

Plot center. Plot geometric center and origin, or position fiom 

which plot-center coordinates of all plot positions are 

referenced, to be distinguished fiom plot reference origin. 

Plot-center coordinates. Coordinates of a plotted position 

relative to the plot geometric center, which is located at the 

plot origin in the center of the mapping field. 

Plot-origin radial mapping. Plot mapping method that 

utilizes Radial survey data from a common reference origin to 

calculate and map tree positions. 

Plot-reference origin. Reference position from which all 

field coordinate data is acquired using the Radial survey 

method, to be distinguished from the plot-center position. 

Plot rotation. The rotation of all plotted positions on the 

plot map through an angle (a) for the purpose of adjusting 

or customizing the orientation of the plot relative to the 

mapping frame. 

Polar coordinates (r, 0). Vector-type coordinates of a tree or 

object position indicated in terns of a radial or 

horizontal distance (magnitude) and counterclockwise 

angular displacement (direction) relative to the positive xaxis. 

Polar X plotting. Method for plotting tree or object 

positions by designating the positive x-axis ray to indicate 

the direction of magnetic or true north as a base plotorientation, allowing plot rotations relative to this map 

orientation. 

Polar I' plotting. Method for plotting tree or object 

positions by designating the positive y-axis ray to indicate 

the direction of magnetic or true north as a base plotorientation, allowing plot rotations relative to this map 

orientation. 

Radial distance (r). Magnitude (distance) component of 

polar coordinates. 

Radial survey. Field survey method employed in the Plotorigin radial mapping procedure that takes all tree or object 

coordinates relative to a common position (the plot reference 

origin). 

Rectangular coordinates. Cartesian coordinates that define 

an object position relative to a reference origin at the 

intersection of two or three mutually perpendicular plotting 

axes (x, y, andlor z) with positive or negative values to 

indicate opposing directions on each axis. 
Sequential-target nnapping. Plot mapping method that 

utilizes Foresi@t-iniine survey data from sequential 

reference origins to calculate and map tree positions. 

Slope angle (SA). Angle of slope between reference position 

and target position, also called vertical angle or inclination. 

Slope distance (ST)). The direct distance between two object 

positions at different elevations measured on an inclined 

(sloping) line through the two positions. 

Theta (@). Directional component ofpolar coordinates 

indicating counterclmkwise angular displacement relative to 

the positive x-axis. 

Tree-1 reference coordinates. The relative coordinates of 

a target position relative to a common reference position 

(tree- I) determined by coordinate summing of rectangular 

coordinates using Sequential-target mapping methods. 
Wilson, A.D. 2000. New methods, algorithms, and software for rapid mapping of tree positions in 

coordinate forest plots. Res. Pap. SRS-19. Asheville, NC: U.S. Department of Agriculture, Forest 

Service, Southern Research Station. 27 p. 

The theories and methodologies for two new tree mapping methods, the Sequential-target method and 

the Plot-origin radial method, are described. The methods accommodate the use of any conventional 

distance measuring device and compass to collect horizontal distance and azimuth data between source 

or reference positions (origins) and target trees. Conversion equations are presented to convert fieldderived azimuth coordinates to plot-center coordinates, permitting plots of all tree positions relative to 

the geometric center of the plot. Plot rotation algorithms for Polar X and Polar Y plotting methods 

allow the rotation of all plotted positions to any orientation within a rectangular niapping frame and 

permit corrections for magnetic declination. Additional algorithms are provided to calculate horizontal 

distance and azimuth between plotted trees and plot-center or between any two tree positions in the 

plot. All algorithms were incorporated into TreeMapper, a computer program for DOS. The methods 

and software were tested on a forested plot. Low mean differences between actual and calculated values 

indicated the accuracy of the methods. The mapping methods and software, originally developed to 

map trees in research plots for spatial and epidemiological studies of oak wilt disease, have wide 

applications in forest inventory, management, ecology, spatial-modeling, and other field activities and 

tasks that require accurate information about tree positions and spatial distribution patterns and ways to 

keep track of tree attributes and treatments over time. More detailed explanations of the 

methodologies for downloading data and running TreeMapper will be provided in a second paper. 

Keywords: Ceratocystis fagacearum, field plotting, oak wilt, spatial structure, stem mapping, tree 

inventory surveys, tree mapping. 

1