U.S.O.A. Forest Service Research Note

PSW-180

ABSTRACT: Th e terrain visibl e from a gi ven po i nt can be determined quickly and effic i ently by a computer. A FOR­TRAN subp rogram--called VIEWIT--has been deve loped for this purpose . I npu t consists of data on elevations, by coo rdi nat es, which can be obtained from maps or ae rial photos. The com­puter will p roduc e an ove rlay that shows the maximum area vi sible from an obse rvation point. Both the ob­se rvation po i nt and the len~th of line-o f- sight are variable. Th1s new techni que makes it unnecessary to draw over l ays manually . RETRIEVAL TERMS : view areas; scene area ana lysis ; computer programs . OXFORD: 907 . 1 : U712 . 2- -U681.3.

Delineating Landscape View Areas

a computer approach

Elliot l. Amidon Gary H. Elsner

Whether viewed from an observation point or a moving vehicle, a forest landscape has distinctive esthetic value. Wildland manag­ers have begun to delineate the boundaries

· .. of views as a step toward protecting scenic ,. : . ·values. Delineating maximum visible areas can have other benefits, as for example, in evaluating alternative sites for locating fire towers or scenic overlooks.

To identify view areas, the forester must go out in the field. He can outline a bound­ary on a map, as seen from one or more van­tage points. Boundaries will vary--depend­ing on the observer's particular position, surrounding topography, visibility, and the observer himself. Field work will always be required to · determine final boundaries. But a map overlay displaying the maximum area visible for the particular topography would reduce field work .

An overlay can be drawn manually by con­structing terrain profiles. 1 The cost of constructing hundreds of profiles would, how­ever, be prohibitive. The military services have encountered similar problems in calcula­ting line-of-sight and low-altitude flight paths. Our review of military algorithms suggested that a digital computer program would offer an economically feasible proce­dure for delineating view areas. 2 But exist­ing computer programs were not directly suited for delineating visible areas. A new program was called for.

We have developed a FORTRAN subprogram-­called VIEWIT--to compute the area visible from an observer's position. Computations of observations of 1-1/2-mile radius requir­ed only 1 second on a UNIVAC 1108 computer (fig . 1). The radius of the view area can be varied to allow for analyzing different size areas from the same vantage point . Com­putation time using the new procedure was 50 times faster than that with other com­puter programs . And it is no longer nec­essary to draw overlays manually.

(Reaffirmed and reprinted, 1976. See also General Technical Report PSW-11 and Research Paper PSW-91 issued by this Station.)

Figure 1.--Area vi s ibl e within 1-1 / 2 miles of the observer ' s position for the hypoth e tical data shown in Figure 2. The number 11 designates visible points .

SCALIN S IZE! SIZEJ RADIUS lOBS JOBS KARDS 316Bo.oo s. o o 6.oo 1.so 18 28 52

B88888888888888888888888888888888888888888888888888888888888888886888B88 888888888888888888888888888888888888888888888888888888888888888888888888 888888888888ij8888888888888888888888888888B888888888888888888888888888888 888888888888888888888888888888888B88888888888888888888888888888888888888 8888B8888888888888888888888888888888888888888888888888888888888888888888 8888888888888888888B8888888888888B88888888888888888888888888888888888888 88888B888888888888888888888888888888888888888888888888A88888888888888888 888888888888888888888B88888888888888888888888888888888888888888888888888 888888888888888888888888888888888888888888888888888888888888888888888888 8888888888888888888888888888888888 0888888888888888888888888888888888888 888888888888ij8888888888888 0 0 0 0 0 0 0 0 08888888888888888888888888888 8888888888888888888888 0 0 0 0 0 0 0 0 0 0 0 0 0888888888888888888888888 888888888888888888 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 088888888888888888888 8888888888888888 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0888888888888888888 88888888888888 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08888888888888888 ij88888888888 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 088888888888888 888888888888 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01188888888888888 8888888888 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 0 0888888888888 8888888888 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0888888888888 88888888 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08888888888 88888888 0 0 0 0111111 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08888888888 888888 0 0 0 0 0 0 0 011 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 088888888 ij88888 0 0 0 0 0 0 0 01111 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 088888888 888888 0 0 0 0 0 0 0 01111 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 088888888 888888 0 0 0 0 0 0 0111111 011 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 088888888 888888 0 0 0 011 011111111111111 0 0 011 0 0 0 0 0 0 0 0 0 0 0 088888888 888888 0 0 011 0 0111111111111111111 l 0 0 0 0 0 0 0 0 088888888 8888 o 011 o o 0111111111111111111. Obssrvsr 1 o o o o o o o o o 0888888 888888 0 011 0 0111111 0111111111111 l 0 0 0 0 0 0 0 0 088888888 888888 011 0 0 01111 01111111111 0111111 0 0 0 0 0 0 0 0 0 0 0 088888888 888888 011 0 011 0 0 011 0 011 0 0 0111111 0 0 0 0 0 0 0 0 0 0 088888888 888888 0 0 01111 0 0 0 0 0 0 0 0 0111111 0 0 0 0 0 0 0 0 0 0 0 088888888 888888 01111111111 0 0 0 0 0 0 01111111111 0 0 0 0 0 0 0 0 0 0 088888888 888888 011111111 0 0 0 0 0 01111 0 0 0 011 0 0 0 0 0 0 0 0 0 0 088888888 8888888811 011 0 0 0 0 0 011 011 0 011 0 0 0 0 011 0 0 0 0 0 08888888888 8888888811 0 0 0 011 0 0 011 0 01111 0 011 0 0 0 011 0 0 0 0 08888888888 888888888811 0 0 011111111 0 011111111 0 0 0 0 01111 0 0 0 0888888888888 888888888811 01111 011111111111111111111 0 0 0 01111 011 0 0888888888888 8888888888881111 011 0 011111111111111111111 0 0 0 0 011 088888888888888 88888888888811 0 0111111 011111111111111111111 0 0 011 0 088888888888888 88888888888888 0 0 0111111 0111111111111111111 0 0 0 0118888888888888888 8888888888888888 0 0111111111111111111 011 01111 0 0 0888888888888888888 8ij8888888888888888 01111111111111111111111111111 0 088888888888888888888 88888888888888888888881111111111 0 0 01111 0 011888888888888888888888888 88888888888888888888888d881111 0 0 0 0 0 0 08888888888888888888888888888 88888888ij8888888888888888888888888 0888888888888888888888888888A8888888A 8888888888888888888888888888888888888888888888888888888888888888888888AA 8888888888888888888~8888888888888888888888888888888888888888888888888888 888888888888888888888888888888888888888888888888888888888888888888888888 888888888888888888888888888888888888888888888888888888888888888888888888 8888888888888888888888888888e8888888888888888888888888888888888888888888 868888888888888888888888888888888888888888888888888888888888888888888888

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• 5 G 7 8 ~

an II 12 ll 10 15 1G 11 18

I' 20 21 Z2 21 z• 25 26 27 28 2~

30 ll 32 n l• 35 36 37 38 l~

•o 01 02 •l

•• 05 .6 01 08 ., 50 51 52

Figure 2. --Hypothetical data on terrain, with elevations shown in hundreds of feet. Th ey are the input to the VIEWIT subprogram for deter­mining areas visible from given points.

-2-

The basic data required to compute visible areas--elevations, by coordi­nates--are simple but voluminous (fig. 2) . They may be read directly from topographic maps or interpreted stereo­scopically from aerial photographs. For a given data matrix of elevations and radius, VIEWIT will compute the

ii fOR VIEWIToVIEWIT

visible area from a specified observa­tion point. The user must write a mainline program to call VIEWIT and to specify input and output for his par­ticular data set.

The complete VIEWIT subprogram is as follows:

SUBROUTINE VIEWITISCALINoSIZEioSIZEJoRAOIUSoiOBS•JOBSoKARDSolEVEL• liNRIMoMOJMI

c c

VTfWlT SELECTS THE CELLS LYING ON A CIRCLE Of ANY GIVEN RADIUS WITH

C TOBS C JOBS C TNIHM r c

CENTER AT IOBSoJOBS. I COORDINATE Of OBSERVER J COORDINATE Of OBSERVER OUTPUT MATRIX. WHEN CELL !oJ IS OUTSIDE VISIBILITY RANGE• INRTMIIoJI=B8 • WHEN IoJ IS VISIBLE fROM IOBSoJOBS• INRIM ~11 • WHEN IoJ IS NOT VISIBLE• INIHM = 0 •

C LEVEL INPUT MATRIX Of ELEVATIONS TN HUNDREDS OF fEET • C Kf I DTMENSION DIRECTION COEFFICIENT • WHEN KF=-1 • I IS DECREMENT C ED fROM JOBS • WHEN Kf = 1 • I IS INCREMENTED fROM lOBS • C J<SITI J DIMENSION DIRECTTON COEFFICIENT. KSfll DECREMENTS J FROM JOBS·o C KSIZI INCREMENTS J FROM JOBS C SCALIN RECIPROCAL Of MAP REPRESENTATIVE FRACTIONoE.G.o''3168D''• C SIZE! NO. Of CELLS PER INCHo MEASURED HORIZONTALLY C SIZEJ NO. Of CELLS PER INCH, MEASURED VERTICALLY C RADIUS RANGE OF VISIBILITY IN HILES C JRADlM RADIUS IN J CELL DIMENSION • C RAOIH SQUARE Of THE RADIUS fHYPOTENUSE OF RT TRIANGLE WHOSE VERTirES c c c c c

JM RM Tll

c u t: TML C !M

r.

ARE IJOBSoJOBSio fTOBSoJMiofToJMI • DECREMENTED BASE OF TRIANGLE IN J CELL DIMENSION DECREMENTED BASE Of TRIANGLE IN MILES • LEfT-MOST CELL IN LINE OF SELLS THROUGH WHICH CIRCLE PASSES TO LEFT Of IOBS • AT A GIVEN RM. Rir.HT-MOST CELL IN THAT LINE • LEfT - MOST CELL IN THAT LINE o TO RIGHl Of JOBS RIGHT- MOST CELL IN THAT LINE • TO RIGHT OF JOBS

. OIMENSIO~ KSIZlolNRIMIHOJMolloLEVELIHDIMoll KSill=-1 KSI21=1 SCALIN=63360/SCALTN JRADJH =SIZEJ • SCALIN • RADlUS SIZEI= SIZEI•SCALTN SIZEJ = SIZEJ•SCALIN RAOIM = RAOIUS••Z JMIN = JOBS-JRADTH TL=IOBS-1 IH=IOBS+l RM=RADTUS JM=RH•SJ2'E.J FTRST SPECIAL CASEoPERFOPMED ONCEoAVOIDING DIVISION BY ZERO M= JOBS Kf=O

• DO ZZ L = lo 2 N=JOBS+KS!LI•JM CALL GENRAYIIOBSoJOSStMoNoKFol•KSoiNRIMoLEVELoHO!H)

22 CONTINUE JBEG=JMIN+l DO 30 JY =JBEGoJOBS JH=JH-] RM = RM - 1./SJZEJ

-3-

RADCAL =RADIH-PJ RIH=SORTfRADCALJ LIH = RIH•SIZEI Ill = Tl Il = IOBS - LTH TML = TH JH:IOBS+LIH DO 28 l = lo 2 N=JOBS+KSILJ•JH KF=-l DO 2~ H::Tlolll CALL . GENRAYC lOBS oJ08So MoNo KF oLoKSo INRIMo LEVEloKDIHJ

2~ CONTINUE KF=l DO 26 M::THLoiH CALL GENRAYIIOBSoJOBSoHoNoKFoLoKSoiNRIHoLEVELoMDIHJ

2& CONTINUE Z8 CONTINUE 30 CONTJNUE

RETURN END

il FOR GENRAYoGENRAY SUBROUT I NE GENRAYfl08SoJ08SoloJoKFoL•KSoiNRIMoLEVEloHDIHJ

C GENRAY GENER ATES a RAY OF CELLS FROM JOB So JOBS TO EACH I oJ ON THE C CIRCLE • THE RAY CONSISTS or All AND ONLY THOSE CELLS THROUG~ C WHICH A LINE FROM THE OBSERVER TO A RJH P9INT PASSES • C AN6MAX MAXIMAL ANGLE SETWEfN OBSERVER AND ANY CELL ON THE RAY WHICH C HAS BEEN TESTEO FOR VISIBILITY • C U~fR MUST CHOOSE INITIAL VALUE OF ANGMAX. SELECT ZERO IF THE CENTER C CELL IS TREATED AS A PLANE WITH THE OBSERVER FIXED AT ITS CENTER. ALL C TERRAIN AT A LESSER ELEVATION WILL BE INVISIBLE. OTHERWISE SELECT A C LARGE NEGATTVE VALUECEGo-9'3'3J WHICH TREATS THE CELL AS A POI1'4T. C JLtG NUMBER OF CELLS BETWEEN JOBS AND J • C lLEG NUMBER OF CELLS BETWEEN JOBS AND I •

DTHENSION KSC2JoiNRIMIM01MolJolEVELCMDIHol) ANGMAX=-999 JLEG:IABSfJ-JOBSJ JFCIOBS.EO.IJ GO TO 35 ILEG=IABSfi-IOBSJ JFCILEG.LT.JLEGJ GO TO 20 I::IOBS DO 10 K=l•ILEG J::J+KF J :JOBS•KSCLJ•JLEG•KITLEG RSPAN:JABSCIOBS-JJ CALL VTSTRYiloJoiOBSoANGHAXolNRIHoLEVELoRSPANoJOBSoHOIHJ

10 CONTINUE GO TO ~0

20 J=J08S DO 30 K=l•JLEG J :: J•KSILJ J :JOBS+KF•ILEG•KIJLEG RSPAN=IABSfJOBS- JJ CALL VlSTRYIJoJoiOBSoANGMAXolNRIHoLEVELo~SPANoJOBSoHDIMJ

30 CONTINUE GO TO ItO

C SPECIAL CASE !VERTICAL RAYJ AVOIDING DIVISION BY ZERO J5 KF=KSIL J

J=JOBS DO 3 8 K = 1 • Jl E G J=J+KF RSPAN::TABSCJOBS-JJ CALL VJSTRYIIoJolOBSoANGMAXolNRI"•lEVELoRSPANoJOBSoHDIMJ

l8 CONTINUE -.o RETURN

END

-4-

ar FOR VJSTRYoVIST~Y

SUBROUTINE VTSTRYfloJoiOBStANGMAXtiNRIMtlEVEltRSPANtJOBStHOIHI C VISTRY OETERHJN£S VISIBILITY OF SUCCESSIVE CELLS ALONG THE RAY • C ANGNEX ANGLE BETWEEN OBSERVER AND IoJ •

DIMENSION JNRTHfHOIMolJtl(VELfHOTHo11 ANGNEX=fLEVELfltJI-LEVELfiOBSoJOBSII/RSPAN JFfANGNEX.GE.ANGHIXI GO TO 10 TNRJH(J,JI=O GO T 0 ZO

10 INRJHCI oJI =1 J ANGHU=ANGNEX

20 RETURN END

FOOTNOTES

1Spurr, Stephen H. Photogrammetry and photo­interpretation . Ed. 2. New York: Ronald Press Co. 472 p. , illus. 1960.

2Bardoll, Ivnn H., III Comput e riz ed · visibility calculations maximum si ~hting range program. San Diego : Univ . of Caltf . 121 p. Jul. 1967 . Boehne, R. C. Digital simul Ation o f environmental 1 imita ti ons of int c rvi s ibili ty. In, Digital simulation in operational res earch. S.H. Ho1lingdale, ed. New York : ~ne rican Elsevier Publ. Co. p. 227-238, illus . 1967 . Ford, Les t e r R. , Jr., Isaacson , H. S., and Pethel, F . C. Computer t errain simulation for line-of-sight ca l culations. Ope r. Res. J. 4:478-482, illus. 1959. McGrath, James J. , ed. Aeron auti cal charts and map display . Goleta, Calif.: Human Fac­tors Research, Inc. 237 p., illus. Aug. 1967.

Th e Authors---------------------------------­ELLIOT L. AMIDON, an economist, is conducting for est economics studies, with particular em­phasis on multipl e -use problems. He earned B.S . (1954), in for est management at Colorado Agri cultural and Mechanical College, and M.S . de gr ees (1960), in agricultural economics at_ th e Unive rsity of California . He has be en w1th th e Be rke ley station staff since 1959. GARY H. ELSNER is studying quantitative planning probl ems in for est r ecreation. He earned a B.S. degr ee (1962) in agricultural economics at the Unive rsity of Arkansas, and M.S. (1964) and Ph . D. (1966) degrees a t the University of Cali­fornia, Be rkeley.

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