ramp: a computer system for mapping regional areas

8/8/2019 RAMP: a computer system for mapping regional areas

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D E P A R T M E N T O F A G R I C U LT U R E245, B E R K EL E Y , C A L I F O R N I A 94701

USDA FOREST SERVICEGENERAL TECHNICALREPORT PSW-12 11975

RAMP: a computer system formapping regional areas

Bradley B. N ickey


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CONTENTSPage

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Individual Fire Re ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 RAMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Digitization Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Computer Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Com puter Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Converting Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Aligning Coordina tes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Mapping Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Literature Cited . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. 9


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Nickey, Bradley B.19 75 . RAMP: a compu ter system for mapping regional areas. USDAForest Serv. Gen. T ech. R ep. PSW-12, 9 p., i llus. Pacific SouthwestForest and Range Exp. Stn., Berkeley, Calif.Until 1972, the U.S. Forest Service's Individual Fire Reports recorded

locations by the section-township-range system..These earlier fire reports,therefore, lacked c ongruen t locations. RAMP (Regional Area Mapping Pro-cedure) was designed to make the reports more useful for quantitativeanalysis. This comp uter-based techn ique converts locatio ns expressed insection-township-range notations into lati tude-longitude coordinates. Twosubsystems make up RAMP. The technique can be applied to other typesof land-management problems.Oxford: 439: 582 : U681 .4Retrieval Terms: fire case histories; burn pattern; mapping systems; coor-dinates; locations; computer programs; RAMP; Regional Area MappingProcedure.

T h o A n t h n ~

BRADL EY B. NICKEY is an operations research analyst with the Station'sfire mana geme nt systems research unit , headq uartered at the Forest FireLaboratory, Riverside, Calif . He was graduated from San Diego StateCollege (B.S. deg ree in general engineering, 1 96 1; M.S. degree in businessadministration, 196 6). Before joining the Fores t Service in 1967, heworked as an industrial engineer at Norto n Air Force Base, in California.


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M u c h n fo rmation use fu l fo r l and-use p lann ing re-mains untapped by computerized retrieval systemsbecause of the cost of correcting inadequate land 10-cators. A typical example of this problem is found inth e U. S. Forest Service's Individual Fire Report(Form 5 100-29). In 1972 , the form was revised torecord fire locations in degrees and minutes of lati-tude and longitude. But until then, the section, town-ship, and range in which the fire started were re-corded. This location is appropriate for statisticaltabulations, but is not suitable for quantitative ana-lysis. Therefore, much of the information in theseearlier reports is not available to the fire manager andplanner.

To tap this reservoir of historical information, acomputer-based technique called the Regional AreaMapping Procedure (RAMP) was developed. RAMP isdesigned to provide longitude and latitude values ofsection corners and m idpoints from digitized map 10-cations of townships.

This report describes RAMP, its characteristics,digitization requirements, and computer software,and suggests how the system could be used in solvingother types of land management problems.

Instructions on how to prepare input for the com-puter system are found in the Procedural Guide forth e RAMP Quantization and Coding Process. Th eGuide is available upon request to: Director, PacificSouthwest Forest and Range Experiment Station, P.0. Box 245, Berkeley, California 94701, Attention:Com puter Services Librarian.

INDIVIDUAL FIRE REPORTSThe individual Fire R eports are a primary source

of wildfire information used in fire prevention, fueltreatment, and fire planning. Generally, the planningtechniques currently used require manual processingof this information. But computer-produced tabu-lations and summary reports are available by usingkeypunched copies of the form.

Analyzing the spatial information in the IndividualFire Reports by advanced quantitative techniqueswould require a computer. However, such work hasbeen hampered by the format of the report-partic-ularly its location of the fire by the use of the sec-t ion-township-range system. The township andsection pattern of the Deschutes National Forest, in

Oregon, illustrates the complexity of the problem@g. 1).Sectio ns are nominally 1 mile square ; townshipsare 6 miles by 6 miles and contain 36 sections. Thehalf townships (T.25 1/2S.)?however, contain six sec-tions, and one of them is much smaller than theothers (see section 31, fig. I ) . Irregularities such asthese preclude the use of the existing locator for com-puter analysis.Spatial analysis of the Individual Fire Reports ar-chives requires a change to a congruent loc ator , suchas degrees latitude and longitude. Highly accuratecomputer-based mapping systems that use legal landdescriptors, least-square error techniques, and othersophisticated methods are available, but are costly(Swann and others 1970). For many jobs a high de-gree of locator accuracy is not critical.

Figure 1-The township configuration found on theDeschutes National Forest, Oregon, includes halftownships (6sections) as well as full ones (36 sec-tions). Some of the sections may be much smaller thanothers.


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RA MPRAMP (Regional Area Mapping Procedure) accepts

the e r ror s inherent in a map , and conver ts the sec t ion-corner projections int o degrees lat i tude and longi-tude. Briefly, the system involves digitizing the loca-t ions o f the corners of a few sections in each town-ship. Variations from nominal size are identified anddistr ibuted among the s ections, by procedures similar. to the General Land O ff ice survey rules for handlingerrors. Finally, the locations of all remaining sectionsand the cent roid of each sec t ion a re com puted. Withthis system, digit izing one township can result in asmany as 35 section locations being calculated auto-mat ica l ly by the com puter . Loca t ions by la t i-tudellongitude and section/range/township are thencross-referenced.

RAMP consists of tw o interrelated subsystems: oneconver ts sec t ion corner loca t ions on a m ap t o a digitalrecording of an x-y coordinate in a form compatiblefor computer processing; the other provides instruc-t ions th at take advantage o f townsh ip surveying prin-ciples a nd section num bering configuration s to mini-mize the am ou nt o f digit izing.

DIGITIZATION REQUIREMENTSMany different character ist ics exist on commer-

cially available digitizers. Some of the more criticaldifferences are (a) fixed versus variable length digitalrecords-a record is the unit of data to be transmittedto t he c ompute r, (b ) nu ~n be r f x-y coordina te pointsthat can be entered on a record, (c) availabil i ty orl imi ta tions or b oth on keying informat ion in to a rec -or d, and (d) co ordinate al ignment procedures. Eachdifference affects the digit izing and coding proce-dures. In turn, each procedure inf luences the com-puter program used to process the digit ized infor-mat ion.

In RAMP, nine d ifferent digitized records are used.They provide the essential information for (a) devel-opment of scale coeff icients for conversion of x-ycorner locations to degrees lat i tude and long itude, (b)alignment o f th e x axis of the digit izer coordinatesystem with the long itude axis of the map, (c) identi-f ication of the lat i tude and longitude at the or igin ofthe digit izer coordinate system, (d) determination ofthe lat i tude and longitude of the corn er points andcentroid o f a section(s), and (e) comp arison of knownmap coordinate locations with calculated values. An80-column punchcard, l imited to three sets of digit-ized x-y coordinate points and 41 columns of keyedinfor mati on, provides th e means for l inking these rec-o r ds t o t he c om pute r subsyst em.

The time required for digitizing is a function ofthe nu mber of townships wi thin a fores t, the amou ntof key informat ion requi red, and the number of non-rectangular sections i t contains. For example, on theClearwater National F orest , in Ida ho, i t was necessaryto digit ize 463 records to cover 3646 sections. Manyof these records were required t o process an extraor-dinar i ly large num ber of nonrectangular sections.This work took about 3-112 hours . On the otherhand, only 1 16 records were needed to cover 54 1 1sections in the Tonto National Forest in Arizona. Inthis case, ab ou t 2 hou rs were needed to digit ize themaps.

The average numb er o f sections calculated for ea chdigitized record for seven forests is 15.4 (table I).However, considerable differences from the averageexisted for different forests.

ACCURACYAnalysis of the magnitude and direction of calcu-lated locations for 53 points, taken from nine dif-

ferent forest maps, showed no systematic errors overthe range of lat i tude and longitude examined. Thecomputed standard error for lat i tude was 252 feetand 43 7 feet for longitude ( table 2) .

The scale of al l of the maps digit ized was % inchto 1 mile. The smallest line digitized on these mapswas clearly legible at a viewing d istance of 5 feet. Thiswould indicate that the l ines were at least 0.03 inchwide (Robinson and Sale 1969) . A l ine of this widthis equivalent to a distance of 316 feet on the mapsanalyzed. One of the more accurate computer-basedsystems accepts calculated points which have an errorof less than 200 feet at the lat i tude/longitude inter-sections (Swann and others 1970) . I t would appearfrom this comparison that the errors associated withRAMP are reasonable-especially for ma ps of thescale used in the study.

COMPUTER SOFTWAREMany commercially available digitizers have built-

in fu nctions to insure the al ignment of the coordinatesystem with a map system that covers a small geo-graphic area. When this capability is not available, asin RAMP, the com pute r sof tware mu st perform thesefunctions. A closely related item is the ability to in-terrupt a digitized session, remove the map from thedigitizer, and then later restart the process so that allnew records are adjusted to the original initial origin.

Somew hat less com mo n is a buil t-in function forthe conversion of x-y coordinates developed by digit-izing ma p points to coordinates of lat i tude and longi-


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t u d e . W i t h i n W P , conversion to latitude isachieved by using a constant scale factor for eachmap. However, this factor may change between maps.Because the distance between two latitude lines de-creases rapidly as they approach the earth's poles, theconversion to longitude is a variable scale factor de-pending upo n th e lat i tude of the point .

To relate congru ent location dimension t o a sec-tion-township-range locator, three different sets ofcomputer instructions are used in W P : a) one de-termines the latitude and longitude of the fourcorners and the midpoint of a single rectangularshaped section; (b) another performs similar calcula-tions for triangular or qu adrilateral sections; and (c)the third provides latitude and longitude locations foreach section within a township. Both of the first twotechnique s have an efficiency of I ; that is, for eachdigitized record, one section is provided with latitudeand longitude locations. The third technique can re-sult in an efficiency of up to 36. Lower efficienciesthan this are due to the existence of irregular town-ships.

Table 1-Efficiency of RAMP, as measured by the average number of sectionsprocessed by on e digitized recordForest Digitized Sections EfficiencyUnit records processed (sections/record)Deschutes N.F.T ont o N. F.Pike N. F.Sequoia N. F.Mendocino C.D.F.R.U.Sierra N.F.Clearwater N. F.

T ot a l 1 1555 23915Average 222.1 3416.4 15.4

Table 2-Know n and calcu~ ated coordinates of latitude and longitude for 53points from nine forest maps (scale: 112 inch - I mile)

Coordinates11 LMean atitude1 Standarddeviation Lo1 Mean ngitude1 Standarddeviation

KnownCalculatedError

I11

40.227140.2272

0.0001

4.61164.6103

-0.001 3

Degrees111.09281 1 1.0929

0.0001

11 632011.6311-0.0009

A full township consists of 36 sections (fig.1).Less than full townships may occur (T.25 1/2S.,R.6E., for ex ample). In those instances, generally oneor more of the northern rows or western columns ofthe township or both are absent. Each digitized rec-ord must contain three digitized points-coded infor-mation containing the unique township and rangeaddress-and the number of the section which servesas the intersection of the most western column andthe most northern row of the township.

To illustrate, a record for T.25S., R.6E. (fig. 1)would contain the digitized northwest and southeastcorner points of section 6 and the southeast cornerpoint of section 36. It would also contain the codesT.25S., R.6E., and 6. T h s inform ation would resultin th e development of latitude and longitude for eachcorner and m idpoint for all 36 sections. If the recordcontained an 8 instead of th e section number 6 , 25sections would be processed. The section num bers eli-minated would be 1-7, 18, 19, 30, and 31. In addi-tion, any oversized or fractional section dimensions inthe northern row or western column of the township


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or bo th would be noted by the computer, and appro-priate ad justments made in all other sections withinthe same row or column or both.The RAMP computer program consists of about1300 statement l ines, wri t ten in FORTRAN IV lan-guage fo r an IBM 360150 O perating S ys tem 1, and re-quires appro ximately 130 K of core to execute. Directtransfer of this program t o other systems is limitedbecause of design effects resulting from the interfacewith the R SS 40 0 Graphic Quanti tizer.

COMPUTER OPERATIONSThree major categories of calculations are required

b y W P . t pro vid es a lg orith ms t o ( a) d ete rm in eand correct for the nonalignment that may exist be-tween the X axis of the digitizer coordinate systemand the longitude axis of the map ; (b) develop scalingcoefficients for converting digitizer coordinates tospherical coordinates of longitude and latitude; and(c) calculate th e latitude and longitude of th e cornersand th e midpoints of sections.

Converting CoordinatesTwo scaling operations are used by RAh4P. Ade-

quate precision is achieved by treating the conversionof Y digitized units to latitude values as a constantwithin a given National Forest, but it may change invalue for a different forest. Two widely separate butknown latitude points, selected from one of the twolatitude scales on either side of a map, are digitized.The basic F OR TRA N equation used to develop the Yconversion coefficient is

in which:SCALE(3) = Y conversion coefficientYDELTA = Difference between the two Y coor-

dinates, resulting from the digiti-zation of kno wn latitude values.

IRANGE = Difference between the two knownlatitude coordinates digitized forYDELTA,

Because latitudes converge quickly at the earth'spoles, the conversion of X digitized units to longitudevalues is treated as a variable, depending upon thelatitude of the point being transformed. Two widelyseparate but known longitude points are digitized

' ~ r a d e a m es a n d c o m m e rc i al e n te r p ri s es o r p r o d u ct s a rementioned solely for necessary information. No endorsementby the U.S. Dep artme nt of Agricul ture is implied.

from the longitude scale on the to p of the map. Thesame operation is repeated on the bottom longitudescale of the map. The X conversion coeff icient, beinga variable value, is calculated for every point beingtransformed by incorporating Equation I into a con-version coefficient fu nction . The num ber of X digiti-zation units within a degree of longitude at the to p ofa map will be less than the equivalent degree mea-sured at the bottom of the map. RAMP uses linearinterpolation to approximate this change in dimen-sions within a National Forest.

The X conversion coefficient function isSCALE(J) = SCALEX(1) - SCALEX(2) (2 )*(LATTOP - SCALE(3)*LAT(J))

/ (LATTOP-LATBOT)and

in whichSCALE(J) = X conversion coefficient at Lati-

tude J.SCALEX(1) = X conversion coefficient at the

t op ( I= l ) a nd a t t he bo t t om (1 ~ 2 )longitude scales of the maps.

LATTOP = Approximate latitude of the toplongitude scale, expressed in deci-mal degrees of latitude.

LATBOT = Approximate lati tude of the bot-tom longitude scale, expressed indecimal degrees of latitude.

LAT(J) = Y Coordinate of the point (J)being converted to spherical coor-dinates. This variable should beexpressed in units measured bythe digitizer.

XDELTA(1) = Difference between the two X co-ordinates, resul t ing from thedigitization of known latitudevalues at I.

JRANGE(1) = Di f fe re nc e be t we e n t he t woknown longitude coordinates di-gitized at I.

Aligning Coo rdinatesIf the digitizer coordinate system originated ex-

actly at the center of a 3 6-inch wide map (scale: %inch = 1 mile), an alignment error of 15 minu tes be-tween the two coordinate systems would result in aconversion error of about 82 8 feet for locations near


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the m ap edge. A nd if maps are larger tha n 36 inches,they would be subjected to even greater errors. Inaddition, a digitizer operator would be hard pressedto k eep alignment errors close to 15 minutes. Manydigitizers allow the ope rato r to establish the origin ofits coord inate system at any convenient map point. Aseldom used but more universal requirement is theability to perform rectangular coordinate axis trans-lation or rotations, or both. This procedure wouldallow the interruption of a digitization process, re-moval of the map from the eq uipm ent, and continu-ation of the digitization with all measures trans-formed to the initial coordinate system. The RAMPcomputer program provides for all of these pro-cedures.

The most simple alignment correction problemexists when the longitude and latitude at the origin ofthe rectangular coordinate system is known. The angleof rotation between the X axis and the longitude axisis found b y

THETA = ARSIN(D/(SCALE(l)*SCALE(2) (4)*(YY 1*XX2-W2*XX1)))

andD = XX2*SCALE(2)*(LZERO-LONE) (5)

+ XX l *SCALE(l)*(LTWO-LZERO)in which

THETA = Angle separating the X axis of thedigitizer with a longitude line on themap.

LZERO = Longitude at the origin of the rec-tangular coord inate sys tem, ex-pressed in decimal degrees of longi-tude.

LONE = Longitude at a known point on themap. This point should be located tothe right of LZERO and have aknown value less than LZERO, andbe expressed in decimal degrees oflongitude.

LTWO = Longitude at a known point on themap which has a value greater thanLZERO, expressed in decimal de-grees of longitude.

XXI ,YY I = X and Y digitization value of LONE,expressed in rectangular coordinateunits.XX2,YY2 = X and Y digitization value of LTWO,expressed in rectangular coordinateunits.

SCALE(K) = Equation 2 solved for point YYl(K=l) and YY2 (K=2), respectively.

When the map coordinates at the origin of thedigitizer are unknown, a much more complex pro-blem exists. Finding the angle of rotation and thelongitude and latitude at the origin requires the solu-tion of two transcendental equations containing threeunknowns. Since the number of unknowns exceedsthe nu mbe r of available expressions, an iterative pro-cess for finding the solution is required. Fortunately,the range over which the iteration must be performedis small. Most "unassisted" digitizer operat ors canalign the two coordinate systems within a range ofseveral degrees. The tw o equations that need t o besolved are

XFUN = ABS(L0NE-LTWO) (6)-ABS((SCALE(2)*XX2-SCALE(l)*XXl)*COS(ARG)-(SCALE(l )*YY 1-SCALE(2)* YY2)*SIN(ARG)

andYFUN = ABS(LAT0NE -LATWO)-ABS (7)

(((YY2-YY I )*COS(ARG)-(XX2-XXl)*SIN(ARG)*SCALE(3)))in which

XFUN, YFUN = Conditional transcendentalequations containing the un-known angle of rotation.

ARG = An assumed angle of rota-tion between the X axis ofthe d ig i t i ze r coo rd ina tesystem and a longitude lineon the map.

LATON E, LATWO = Known latitudes at LONEand LTWO respectively, ex-pressed in decimal degreesof latitude.

If the two coordin ate axes have been closelyaligned before digitizations, only one angle of rota-tion will exist between 510 degrees that will yieldequivalent solutions for Equations 6 and 7. If bothequatio ns are equal, ARG is nearly equal to THE TA.The map coordinates at the origin of the rectangularcoordinate system are now found by:

LZERO = LONE + XX 1*SCALE( I) (8)and

LATO = LATONE - YY I *SCALE(3) (9)in which


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LATO = Latitude at the origin of the rectan-gular coordinate system, expressed indecimal degrees of longitude.

An interrupted digitization effort-one that re-quires establishmen t of a new origin-will normallyrequire both a t ranslat ion and rotat ion t rans-forma tion t o align the new origin with the initial ori-gin. This allows all the digitized records of a map tobe .processed during a single computer run. Twoflagged points digitized during the initial effort areredigitized. The angle of rotation between the old andthe new is found by

THETAN =ARCOS((C*C - A* A - B*B) (10)/ (-2.*A*B)in which

an dC = (X2NEW + XlOLD - X20LD)**2 (13)+ (Y2NEW + YIOLD - Y20LD)**2

in whichTHETAN = Rotation angle required to

align the current rectan-gular coo rdinate system ofthe digitizer to the originalr e c t a n g u l a r c o o r d i n a t esystem.Rectangular coordina tesfrom the ini t i a l d igi t i -zation effort. Each pointwas previously marked as apotential future referencelocation.

XINEW, YINEW Rec tang ular coordina tes{XINEW, Y2NEW) = from the new digitizationeffort of the above flaggedlocations.

The translation constants for X and Y axes are, re-spectively

XADJ = XlOLD and YADJ = Y 1OLD (14),(15)

Methods to perform the actual translation or rota-tion, or b oth , utilizing the results from Equ ations 4to 15 are available in most mathematical handbooks(Selby and others 1965).

Mapping SectionsA section is considered mapped when all corners

of the boundary and the centroid of the area withinthe bou ndary are described b y longitude and latitudecoordinates. Attachment of the section-township-range label to the coo rdinates creates a suitable cross-reference index record for the individual Fire Re-ports.

Three methods exist within RAMP for mappingsections: (a) one provides latitu de and longitude loca-tions of the four corners and midpoint of each sec-tion within a township; (b) another performs similarcalculations for a triangular or quadrilateral section;and (c) the last procedure determines the latitude andlongitude for a single rectangular section.

The first method reduces the number of digitizedpoints required to process a township by taking ad-vantage of the surveying and identity coding stand-ards of sections within a township.Three sets of digitized points, the township andrange codes, and at least one but not more than twosection numbers are needed to process a township.The northwest corner of the section that serves as theintersection of the top row and leftmost column ofthe township is digitized and referred to as X1 andY 1. The southeas t corn er of this same section is digit-ized and referred to as X2 and Y2. The number ofthis section, (ISECT) is also recorded. The last pointdigitized-X3, Y3-is the southeast corner of the sec-tion that occupies the intersection of the rightmostcolumn and bottom row of the township. If anyrighthand columns or southern rows of the townshipare missing, the section number (JSECT) is alsorecorded.

In RAMP, all townsh ips are initially assumed to b emade up of 36 sections. Each row and column in afull township also has a reference number associatedwith it . For example, section number 6 is defined as amember of column 1, row 1. Section number 5 is amember of column 2, row 1. The intersection of col-umn 1, row 2 w ould then be occupied by sectionnumber 7. Thus, the origin of the reference system isconsidered to be section number 6. Columns movingto the east increase in number as they move awayfrom the origin. Rows increase as they move southfrom the origin. With this reference system, the a ctualnumber of sections and their configuration in thetownship can be determined from values of ISECTand JSECT.

The reference number of the most no rthern row ofthe township can be found by

LY = (ISECT - 1) / 6 + 1 (1 6)


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and the m ost western column is

If JSECT- is no t presen t o n the digitized reco rd, theprogram assumes that no eastern columns and south-ern rows of the tow nship are missing. Modification ofEquations 16 and 17 provide the means to determinewhat columns or rows, or both , are absent. Thenumber of the first southern row missing from atownship is found by

LYY = (JSECT - 1 ) / 6 + 2 (18)and the first eastern colum n missing is

LX X = ABS(FLOAT(MOD(JSECT-1 ,I 2)) (1 9)- 5.5) + 0.6Given the num ber of rows and columns in a town-

ship, the dimensions of all sections except those inthe most northern row and the most western columnare assumed t o have equal widths and heights. Thewidth of the section is

XDELTA = (ABS(X2 - X3)) / (LXX - LX (20)- 1)and the height is

Many of t he sections within a township haveboundaries and corner points in com mo n with othersections of the township. A full township contains 36sections and thus has 49 uniquely located sectioncorners. RAM P uses two 7-by -7 matrices t o define theX and Y coordinates of th e corner po ints. The Xcoordinate of the f irs t tw o columns of the matrix(using standard matrix algebra notation) are

Xi .L = XL and Xi .LX + I = X2 (2% (23)and for the remaining columns of the matrix are

X i , j= Xi , j - , + XDELTA (24)in which, LY 5 i 5 LLY-I and LX+ 25 5 LX X-1.

In a similar manner, the coordinates of the firsttwo rows of th e Y ma trix are

and for the remaining rowsY iJ = Yi., , j - YDELTA (27)

i n w h i c h L Y + 2 < i < L W - 1 a n d L X < j < L X X - 1 .With all elements of the two coordinate matrices

known, Equations 1 and 3 can then be used to de-velop the latitude and longitude of each sectionpoint.

The second me thod is used to m ap a quadrilateralsection that has one 90-degree internal angle. The90-degree angle is required in RAMP because of thehardware limitation of no more than three digitizedpoints on a record. This angle is used as a referencepoint in the algorithm. Its coordinates are calculatedfrom information gained in the digitization of thethree other corners of the quadrilateral. A simpleralgorithm can be developed which does not requirethe 90-degree internal angle when four points can bedigitized per record. Moving clockwise from the refer-ence point, the operator digitizes the first corner (re-ferred to as X1 and Y1 here). T hen he digitizes thenext c orner (known as X2 and Y2). And then hedigitizes the last corner (called X3 and Y3) beforereturning to th e reference point.

RAMP assumes that the right angle of the quadri-lateral section is located at the origin of a rectangularsystem of axes. The quadrant which contains the sec-tion is found by logical analysis of the first and lastpoints digitized. Thus

X 3 > X 1 and Y1 > Y 3 = Q u a d r a n t 1 .X 3 > X1 and Y1 < Y 3 = Quadrant 2X3 < X1 and Y1 < Y3 = Quadrant 3X3 < X1 and Y1 > Y3 = Quadrant 4

For sections located in Quadran ts 1 and 3 , the coo rdi-nates of the origin areX 4 = X1 and Y4 = Y3 (28),(29)

and for Quadrants 2 and 4, the coordinates are:X 4 = X 2 and Y 4 = Y 1 (30),(3 1)

A quadrilateral section containing one 90-degreeinternal angle can have two "basic" shapes (fig. 2). I tis always possible to partition such a section into anoblique triangle and a right triangle. Location of thecentroid in this section requires identifying a fifthpoint, called X5 and Y5. The coordinates of the un-known point are located on a straight line passingthrough the points X I, Y1 and X3, Y3. The equationof this line is

in whichA = Y 2 - Y 3 , B = X 1 - X 3 (33),(34)


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an d

The point X5,Y5 is also a member of a straightline passing through point X2,Y2. By requiring thisline to be perpendicular to Equation 32, the coordi-nates of the point X5,Y5 can be found by the fol-lowing expression

an d

The centroid of the quadrilateral section can nowbe obtained by the use of the principle of moments(Higdon and others 1955). Logical check of thepoints X5,Y5 and X2,Y2, along with the quadrantposition of the section will determine if the area ofth e obliqu e triangle, called A 2, must be removed oradded t o the area of the right triangle (A l). Thu s

Quadrant 1 or 4 , and X2 < X5 = - A 2Quadrant 2 or 3 , and X2 > X5 =- A 2The moments of the areas around the X and Y

axes for sect ions located in quadrants 1 or 3 areXBAR = (A1 *X3 + A2*(X3 + X2)) (38)/ (3 .*(A1 + A2))

an dYEAR = (A1 *Y 1 + A2*(Y 1 + Y2)) (39)/ (3.*(Al + A2))

respectively. For sections located in quadrants 2 and4, the mom ents of the areas around the X and Y axesare

XBAR = (A1 *X1 + A2*(X1 + X2)) (40)/ (3.*(Al + A2))and

YBAR = (A1 *Y3 + A2*(Y3 + Y2)) (41)( 3 . * ( A l + A 2 ) )respectively. The intersection of the XBAR andYEAR is the location of the midpoint of the quadri-lateral section, expressed in the rectangular coordi-nates of the digitizer. Equations 1 and 3 can be usedto develop the latitude and longitude of corners ofthe section and its midpoint.

A modification of the above process is used tdigitize a right-triangular section. In this si tuat ion , thethird digitized point (X3,Y3) is the corner of the internal 90-degree angle. Equations 28 to 37 are notrequired in this situation. RAMP uses a logical comparison of the three digitized points to differentiate aright triangle from a quadrilateral section. Infor-mation on the quadrant position of the section willdetermine the equations to use for solution of XBARand YBAR. When A2 is given a zero value, Equations38 to 41 are then applicable for locating the m idpo intof the section.

The third method is used to map a single rectan-gular section. Only two digitized points are required.The problem is easily solved by RAMP.

Figure 2-A quadrilateral section that contains an in-ternal 90-deg ree angle can have tw o "basic" shapes.Dashed lines illustrate how the section can be viewedas an oblique triangle added ( A ) or subtracted ( B )fro m a r ight tr iangle.

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APPLICATION

RAMP was designed originally to provide a usefulspatial variable that could be associated with datafrom the Individual Fire Reports for the FOCU S pro-gram. FOCUS (Fire Operational Characteristics UsingSimulation) is a model being developed at the PacificSouthwest Forest and Range Experiment Station'sForest Fire Labo ratory , Riverside, California, to sirrt-ulate the probable consequences of available alterna-tives in fire planning (Storey 1972). T o dat e, a cross-reference catalogue has been produced within thecom pu ter for 12 National F orests and one CaliforniaDivision of Forestry Ranger Unit by RAMP.

The techniques and procedures used in RAMP canbe applied by land-use planners to tap many othersources of useful spatial information. As an example,a brief investigation shows that it could be applied tothe following U. S. Forest Service reports: (a) BridgeInventory, R5 -770 0-24 ; (b) Rep ort of Suspected


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Timb er Trespass, R5-65 00-129 ; (c) Record of Sale,Land or Easement, R5-5 400-11 ; (d) Animal DamageSurvey, R5 -520 0-39 ; (e) Prescribed Bum Repo rt,R5-5100-199; (0Archaelogical Site Survey Record,RS-2700-3 1; an d (g) Tree Seed Crop Condition Re-port, R5-2400-58.

LITERATURE CITEDHigdon, Archie, and William B. Stiles.

1955. Engineering mechanics. p. 12-14, 62-77. Prentice-Hall Inc., New York

Robinson, Arthur H., and Randall D. Sale.1969. Elements of cartography. p. 251-252. Joh n Wileyand Sons, New York.

Selby, Samuel M., and Brian Girling.1965. Standard mathematical tables. p. 515. The Chem-ical Rubber Co., Cleveland.Storey, Theodore G.1972. FOCUS: a computer simulation model for f i econtrol planning. Fire Tech. 8(2):91-103.Swann, D. H., P. B. DuMontelle, R. F. Mast, and L. H. VanDyke.1970. ILLIMAP-a computer-based mapping system forIllinois. 111 State Geol. Sum. Circ. 45 1:1-24.

ramp: a computer system for mapping regional areas

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