Delineating Landscape View Areas
a computer approach
Elliot l. Amidon
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 r di nat e s, which can be obtained
fr om maps or a e rial photos. The computer will p r oduc e an ove rlay that
shows t he maximum area vi sible from
Both the oban obse rvation point.
se rvati on 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.
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 IZ E!
SIZEJ RADIUS lOBS JOBS KARDS
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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
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8888 o 011 o o 0111111111111111111. Obssrvsr 1 o o o o o o o o o 0888888
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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
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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.
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
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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:
fOR VIEWIToVIEWIT
SUBROUTINE VIEWITISCALINoSIZEioSIZEJoRAOIUSoiOBS•JOBSoKARDSolEVEL•
liNRIMoMOJMI
VTfWlT SELECTS THE CELLS LYING ON A CIRCLE Of ANY GIVEN RADIUS WITH
CENTER AT IOBSoJOBS.
TOBS
I COORDINATE Of OBSERVER
J COORDINATE Of OBSERVER
JOBS
TNIHM 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 •
LEVEL INPUT MATRIX Of ELEVATIONS TN HUNDREDS OF fEET •
Kf
I DTMENSION DIRECTION COEFFICIENT • WHEN KF=-1 • I IS DECREMENT
ED fROM JOBS • WHEN Kf = 1 • I IS INCREMENTED fROM lOBS •
J<SITI J DIMENSION DIRECTTON COEFFICIENT. KSfll DECREMENTS J FROM JOBS ·o
KSIZI INCREMENTS J FROM JOBS
SCALIN RECIPROCAL Of MAP REPRESENTATIVE FRACTIONoE.G.o''3168D''•
SIZE! NO. Of CELLS PER INCHo MEASURED HORIZONTALLY
SIZEJ NO. Of CELLS PER INCH, MEASURED VERTICALLY
RADIUS RANGE OF VISIBILITY IN HILES
JRADlM RADIUS IN J CELL DIMENSION •
RAOIH SQUARE Of THE RADIUS fHYPOTENUSE OF RT TRIANGLE WHOSE VERTirES
ARE IJOBSoJOBSio fTOBSoJMiofToJMI •
DECREMENTED BASE OF TRIANGLE IN J CELL DIMENSION
JM
DECREMENTED BASE Of TRIANGLE IN MILES •
RM
LEfT-MOST CELL IN LINE OF SELLS THROUGH WHICH CIRCLE PASSES TO
Tll
LEFT Of IOBS • AT A GIVEN RM.
Rir.HT-MOST CELL IN THAT LINE •
u
LEfT - MOST CELL IN THAT LINE o TO RIGHl Of JOBS
TML
RIGHT- MOST CELL IN THAT LINE • TO RIGHT OF JOBS
!M
. 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
i l 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
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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
1
Spurr, 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 e rrain 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 e st economics studies, with particular emphasis on multipl e -use problems. He earned
B.S . (1954), in for e st management at Colorado
Agri cultural and Mechanical College, and M.S .
de gr e es (1960), in agricultural economics at_
th e Unive rsity of California . He has be en w1th
th e Be rk e ley station staff since 1959. GARY
H. ELSNER is studying quantitative planning
probl ems in for e st r e creation. He earned a B.S.
de gr ee (1962) in agricultural economics at the
Unive rsity of Arkansas, and M.S. (1964) and
Ph . D. (1966) de grees a t the University of California, Be rkeley.
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