The Digital Terrain Model­Theory & Application*

C. L. MILLER, Asst. Prof. of SurveyingDirector, Photogrammetry Lab.

AND

R. A. LAFLAMME, Research Asst.Dept. of Civil & Sanitary Engineering,

Massachusetts Inst. of TechnologyCambridge, Mass.

ABSTRACT: In order to realize the full potential value of an integratedsystem of photogrammetry and electronic computers as applied to en­gineering problems, the concept of a digital terrain model has been de­veloped oy the Photogrammetry Laboratory at the Nlassachusetts Instituteof Technology. A band or area of terrain is represented in numerical ordigital form from data taken from a contour map, or directly from thestereoplotter and stored on computer input material. The stored digitalterrain model may be used to obtain numerical solutions to many typesof terrain analysis problems by processing through an electronic digital com­puter according to programmed instructions. Such an approach enablesthe engineer to numerically evaluate an unlimited number of possiblelocation, design, and other geometric solutions to the problem presented.

INTRODUCTION

T HE electronic digital computer can beapplied to two major areas of applica­

tion important to the photogrammetricengineer. The first is concerned with thereduction of the raw data (the photograph)to obtain the basic photogrammetric out­put (the spatial location of points). Thecomputations associated with analyticalspace resection and intersection, aero­triangulation, transformations, and adjust­ments would be examples of the first areaof computer application.

The second area of application concernsthe computations associated with the solu­tion of engineering, scientific, and militaryproblems which involve the use of photo­grammetric output data. The determina­tion of highway earthwork, the determina­tion of the change in the shape of a glacier,and the supplying of guidance instructionsfor a low level missile would be examples of acomputer utilizing photogrammetric data. C. L. MILLER

* Presented at the Society's 24th Annual Meeting, Hotel Shoreham, Washington, D. C.March 27, 1958.

433

434 PHOTOGRAMMETRIC ENGINEERING

As a technical specialist, the photogram­metric engineer is primarily concerned withthe first area of application. However,since these two areas are closely related,one giving direction to the other, theycannot be entirely separated. Stated moregenerally, an entirely new solution to aproblem often comes from an integrationof the technological advances made inmany related or unrelated fields; also,consideration of the over-all problem fromraw data to final answer will often lead tomore efficient solutions.

During the last two years, the Photo­grammetry Laboratory of the M.LT. CivilEngineering Department has been con­ducting research on the subject of "newapproaches to highway engineeringthrough the application of photogram­metry, automation instrumentation, andelectronic computers." The program issponsored by the Massachusetts Depart­ment of Public Works in cooperation withthe Bureau of Public Roads. The purposeof this paper is to describe one develop­men t by the project-the theory andapplication of the digital terrain model.Although it is primarily an advance in theuse of the photogrammetric output, theimplications to the practice of photo­grammetry are important.

THE TERRAIN DATA PROBLEM

A convenient representation of the sur­face of the earth is a common requirementfor many engineering, scientific, and mili­tary problems. The use and nature ofterrain data storage and presentationforms such as the topographic map, thephysical model, the three dimensionalstereo model, and the profile and cross­section are all common examples. Theseare all essentially analog forms of terraindata and are designed primarily for humaninterpretation and utilization in mentaland manual processes. Obviously, many ofthe mental and manual processes for whichthe human utilizes such terrain data inobtaining numerical answers to problemscan be efficiently handled by the elec­tronic digital computer.

A fundamental requirement for using acomputer efficiently is to have the terraindata in a form which the machine under­stands. In the case of the electronic digitalcomputer, this form is of course digital dataon computer input material such aspunched cards, punched tape, or magnetictape. Therefore, re-stating the first re-

quirement, a machine data form counter­part of the engineer's topographic map orgraphical cross section is needed.

Before the second requirement can bestated, certain characteristics of the mod­ern computer should be examined. Aseveryone has heard, computers performarithmetic operations at fantastic speeds.However, few people, even engineers,comprehend the significance of such com­puting speed on the impact the computersshould have and will have in the approachto future problems. Such an impact isgradually being felt in the field of highwayengineering where the initial efforts wereto have the electronic computer do theidentical work formerly handled by man­ual methods. Now that the "power underthe hood" is being felt, radical changes inapproaches can be expected.

One way to take advantage of the speedof the electronic computer is to numericallyevaluate perhaps a hundred solutions to aproblem where only one or two were con­sidered previously. Another use for thespeed is to take advantage of more exactand rigorous mathematical formulations ofthe problem instead of being limited to thesimple approximations dictated by manualmethods. Such changes in approach areeconomically justified as long as cost re­flects a correspondingly more economicalsolution. For example, if a computer candetermine a mile of earthwork in tenminutes at say $10 in computing cost, itcertainly makes sense to spend 16 hours or$1000 in computing time if $10,000 can besaved in construction costs by a more eco­nomical location.

We now come to our second requirementfor the efilcient storage of terrain data. Totake full advantage of the computer, ourdigital terrain data should permit the ef­ficient consideration of a large number ofpossible solutions to the problem at handand preferably more exact or correctsolutions.

The digital terrain model system dis­cussed in the remainder of the paper is onepossible approach to realizing more of thepotential value of photogrammetry andelectronic computers in such fields as civilengineering.

THE DIGITAL TERRAIN MODEL

THE CONCEPT

The digital terrain model (DTM) issimply a statistical representation of the

DIGITAL TERRAIN MODEL-THEORY AND APPLICATION 435

continuous surface of the ground by alarge number of selected points withknown xyz coordinates in an arbitrary co­ordinate field. Storing the DTM data oncomputer input material makes it avail­able to the computer for an analysis of awide variety of terrain problems, and alsofor the evaluation of an unlimited numberof independent solutions to each type ofproblem.

THE COORDINATE SYSTEM

The origin and direction of xy horizontalaxes of the DTM coordinate system andthe z datum may be selected at will withdue regard to convenience and the re­quirements of the particular problem athand. This coordinate system is independ­ent but should be related to an estab­lished system such as state plane-coordi­nates and mean sea-level datum. By arbi­trarily specifying the DTM coordinates oftwo points of known state plane-coordi­nates, the state plane-coordinates of allDTM points may easily be computed,when required, using simple rotation andtranslation of axes formulae. Normally,the DTM datum will be mean sea-level ora parallel datum. For a given project, anumber of different but related DTM co­ordinate systems might be used for differ­ent parts of the project area. In general,the engineer has rather complete freedomand considerable flexibility in selecting themost convenient DTM coordinate system.

DIGITAL REPRESENTATION SYSTEMS

The surface of the ground may berepresented, in the DTM, by anyone of a

number of possible sets of selected points.The only requirement the set must meetis that it be stored systematically to facil­itate recovery by the computer. Thiscould be accomplished by specifying thatthe points be stored sequentially in orderof increasing x (or y or z). Such a sequencemight be used if a system of points such asused by the plane tahle topographer wasselected.

By requiring that the points be locatedalong a system of parallel scan lines, amore practical sequence of data results(Figure 1). Such scan lines will normally belines of constant x (y scan lines) or lines ofconstant y (x scan lines). The distance be­tween or spacing of the scan lines may bevariable or constant, and the frequency ofthe poi nts along the scan lines may bevariable or constant. \iVith constant spac­ing of the scan lines and constant fre­quency of points along the scan lines, asq uare or rectangular grid would resul t.Such a system would permit (1) the high­est degree of automation in the data pro­curement phase, (2) the simplest process­ing of the data by the computer.

With a variable frequency of pointsalong the scan lines, the selected pointsmight be on (a) equal increments of z orcontour line crossings, (b) incrementscorresponding to a constant product of yzincrements, (c) terrain control points suchas high and low points and slope breaks.Here again, the engineer has completefreedom in selecting the system of pointsbest suited to the problem at hand. Hischoice might consider the type of terrain,available data procurement equipment,

DATA BASELlliE "x _ .-'./ / Ltl/I,£x, j~

FIG. 1. This illustrates the arrangement of the Baseline, Scan lines, and Data Points. DataPoints are shown at each contour line, but more or less points may be used as dictated by systemrequirements.

436 PHOTOGRAMMETRIC ENGINEERING

and the nature and requirements of his ap­plication of the DTM. In any of the sys­tems, the density of the points for a giventype of terrain will depend on the accuracyrequirements associated with the applica­tion. Different applications will requiredifferent accuracy levels or degrees of per­missive terrain approximation. In someengineering problems, a series of DTM'swith progressively higher densities ofpoints for smaller areas might be advisablecorresponding, for example, to the variousstages in the location and design of a high­way.

THE MATHEMATICAL TERRAIN MODEL

The DTM, like the topographic map,uses a sample of data to represent the con­tinuous surface of the ground. The DTMuses a sample of the infinite number ofsurface points, and the topographic mapuses a sample of the infinite number ofcontour lines of the surface. Just as theengineer must interpolate on the topo­graphic map, the computer will have tointerpolate with the DTM. And in bothcases straight line interpolation will oftenbe quite satisfactory.

Since with the high-speed electroniccomputer, much more sophisticated inter­polation with the DTM is quite practical,it is proposed that the actual model uti­lized by the computer be a mathematicalmodel of the surface generated with thedata furnished by the DTM. Instead ofconnecting each successive pair of pointswith a straight line, a third degree poly­nomial will be generated by the computer(Figure 2). A scan line will then consist of anumber of continuous curves, each goodfor a specified range of y val ues. Theequation for the section between yz and Y3is of the form:

z = z, + A (y - Yl) + B (y - Yl) (y - yz)

+ C(y - Yl)(Y - yz) (y - Y3)

where the constants are computed by thefollowing equations in terms of the yz's ofthe four points bracketing the range ofusefulness of the individual polynomial:

(zz - Zl) (Z3 - Zl) - A ()13 - Yl)A = -- B = ::....::---:.:--..,.-"'''--~

(yz - )'1) (Y3 - Yl) (Y3 - yz)

~-~-A~-~-B~-~~-~C = ..:-c.._2-,--~-:-:-,'--'----:-':--~

(y, - y,)(y< - yz)(y, - Y3)

By differentiating the equation of thepolynomial, the slope at any point along

the scan line may be obtained. By settingthe differentiated form equal to zero, thelocation of the high and low points may beobtained. By integrating the polynomial,the area under the curve may be obtained.The following equations result.

dz [ .Slope - = A + B (y - Yl) + (y - yz) ]dy

+ C[(y - Yl)(Y - yz) + (y - y,)(y - y,)

+ (y - yz) (y - Y3)]

Areay"..-y, = (y, - yz) [Zl - AYI - By,yz - CY1YZY3]

()"z _ yzZ)+---- [A - B(y, + yz)2

+ C(YlYZ + y,y, + y,y,) ](y,,3 _ yz3)

+ --:3-- [B - C(YI + yz + Y3)]

+ ~~- yz') [C]4

Interpolation between the scan linesmay be accomplished in a similar mannerby evaluating the polynomials across thescan lines and parallel to the scan lineswhich pass through the desired point frompoints previously interpolated on thepolynomials along the scan lines. An alter­nate approach, and one which shows prom­ise, is to evaluate the equation of a seriesof surfaces which will fit the DTM points.Considerable work is being performed onthis subject but it has not yet reached astage far enough advanced for reporting atthis ti me.

The mathematical terrain model can bejustified if the number of DTM pointsnecessary to represent an area of interestcan be greatly reduced. A single third de­gree polynomial might, for example,represent a given profile as accurately aswould 50 straight line interpolations.(Figure 2) The speed and efficiency of theelectronic computer permits one to thinkin terms of representing the surface of aproject area by thousands or literally tensof thousands of mathematical equations.

DTM DATA INSTRUMENTATION

The most important contribution ofphotogrammetry to the DTM concept isthe practicality of obtaining the tre·mendous amount of terrain data neces­sary. It would be quite impractical to ob­tain the coordinates of, for example,10,000 points in a one square mile area inany other way. Using photogrammetry,

DIGITAL TERRAIN MODEL-THEORY AND APPLICATION

REPRESENTATION OF TERRAIN PROFILE BY THIRD DEGREE POLYNOMIAL

z ' 1000 + 0.31 y - 0.9 X 16~2 +0.5 X 166y'

1040r----,r--r----r--,---r---,---,----,r--r--r--,---,

960

940

'no

900

437

0+00 2+00 12+00

FIG. 2. This illustrates how terrain which would be reprcscnted by many points, using straightline interpolation, may be reprcsented by fewer points using a third degree polynomial.

the data procurement problem is reducedto one of obtaining the coordinates ofmany points from the stereo model in afast, efficient, and accurate manner.

One approach to this problem is to pre­pare the standard topographic map tophotogrammetric methods. The DTM dataare readily obtainable from the contourmap by graphically plotting the scan lines,manually scaling and recording the data,and manually punching the results. Suchan approach has the advantage that aminimum additional investment in instru­mentation is required-the price of a sim­ple scale. For limited and special use of theDTM system, such an approach might beeconomical. However, the totally manualapproach is of course the slowest and mostcostly in manpower expenses. It would notbe practical for extensive use of the DTMconcept. Two men, one scaling and one re­cording, will take about 200 points perhour on the average. Hence, our exampleof 10,000 points would take 50 hours at acost of 100 manhours plus the cost ofpunching and verifying the results.

Semi-automatic scanning and outputinstrumentation for operation with a mapas the source of data is quite possible andis the subject of current research and de­velopment at M.LT. Several different ap­proaches to the problem are being investi­gated and will be reported on at a laterdate. ]. A. Stieber, of the U. S. NavalTraining Device Center, is doing some re-

lated work on the procurement of digitaldata from maps to operate a numericallycontrolled milling machine for the produc­tion of physical terrain models.

A second manual approach to obtainingthe DTkf data would be to scale the datadirectly from the stereoplotter manuscript.Any of the systems of data along scanlines could be selected. \Vi th some plottersit is possible to plot continuous pro/ilesacross the stereo model. This is being ac­complished in the M.LT. PhotogrammetryLaboratory by means of a Nistri coordina­tometer and coordinatograph unit, operat­ing on either the Kelsh or Balplex plotter.These plots may then be digitized manu­ally or automatically with a scanning andoutput system.

The /irst real step in automation of thedata procurement is obtained by digitizingone or more of the x, y, and z scanning mo­tions of the stereoplotter. If a rigid gridsystem is being used, it would only be nec­essary to digitize the z axis, the x and ypositions being furnished by a projected orplotted grid. If the x increments are con­stant, and/or plotted, digitizing of the yand z axes would be sufficient. Completeflexibility and automation isonly achievedby digi tizing all three axes.

A basic requirement for a scanning sys­tem is that the scanning motions and themeasurements they represent be convertedto a form which can be digitized. This maybe accomplished by converting the linear

438 PHOTOGRAMMETRIC ENGINEERING

FIG. 3. The Nistri Coordinatometer shown on the Balplex Plotter. This unit is used toobtain the x, Y, and z coordinates of points. rt is also L1sed on the Kelsh Plotter.

motions to equivalent shaft rotations bysuch means as a lead screw, rack andpinion, continuous wire or chain, or odom­eter type wheel. There are a number ofcommercial components for convertingshaft rotations to digital output. A systemof measuring and digitizing based on theuse of a diffraction grating might also beused. A scanning, measuring, and digitiz­ing system of unique design based on send­ing sound waves down a wire, has been de­veloped by the Physics Department atM.LT. for photographic data reductionand shows potential for stereoplotter ap­plication. As a matter of convenience, it isdesirable to have the scanning axes parallelto the DTM data coordinate axes in orderto directly read DTM coordinates. There­fore, either the stereomodel or the scan­ning unit axes should be capable of beingrotated about a vertical axes.

For experimental work, the M.LT.Photogrammetry Laboratory is using thepreviously mentioned Nistri unit as athree-dimensional scanning unit for doubleprojection plotters (Figure 3). The unit isrotated in stereomodel space to align theaxes.

An odometer type scanning unit for usewith maps or plotters is being built. TheNistri unit may also be used for map scan­ning.

Two basic types of readout systems maybe used. The slowest but simplest would be

a static type, meaning that the operatormust stop for each point, and press abutton to accomplish the automatic read­out and recording. Two such systems havebeen designed and are being developed inthe M.LT. Photogrammetry Laboratory,one using electronic counters (Figure 4)and the other, high speed relays. Althoughthere are several commercial readout sys­tems available which are adaptable tophotogrammetry, the M.LT. systems arebeing built to obtain a number of specialexperimental features for research work.

The second basic type of readout sys­tem which might be used would permitreadout "on-the-f1y" meaning that theoperator could scan the model with a con­stant or variable but continuous drive. Thecoordinates of points at equal y, z, or yzincrements would automatically be readout and recorded. Although the initial costwould be greater than for a static readoutsystem, the increased speed would eco­nomically justify such a system in manycases. The actual data recording unit cantake many commercial forms such as atape punch, card punch, electric type­wri ter, magnetic tape recorder, or combi­nation of such units.

The final degree of au tomation would beachieved by substituting an automaticscanning system for the human operator.Vlie can also expect to see radical changesin the stereoplotter itself as more advan-

DIGITAL TERRAIN MODEL-THEORY AND APPLICATION 439

FIG. 4. The console, in the center of the photograph, gives a visual readout of the coordinatesobtained from the Nistri Coordinatometer. The readout is by means of electronic counting tubeswhich also drive the Bendix tape punch, shown in the lower right-hand corner of the photograph.

tage is taken of the technological develop­ments in automatic instrumentation.From the above paragraphs, it can be seenthat the photogrammetric engineer hasmany possibilities for increasing the effi­ciency and speed of data procurement inconjunction with the DTM system. TheM.LT. research staff is concerned with theinvestigation of the over-all field of auto­matic instrumentation in photogrammetrywith particular emphasis on highway en­gineering applications and is exploringmany new possibilities in this direction.Since many other private, institutional,and governmental groups are working inthe same and related fields, many new de­velopments are anticipated.

ELECTRONIC COMPUTER OPERATIONS

With the DTM data or the mathemati­cal terrain model data stored on computerinput material, they may be read into in­ternal computer storage in blocks as re­quired. Hence, the represented surface isessentially available "on demand" atelectronic speeds for operations by thecomputer. Most applications of the DT Mare concerned with mathematically re­lating some spatial surface of interest tothe DTM represented surface. The spatialsurface of interest may be that of a pro­posed highway, the surface of a reservoir,

or the path of a microwave. A series ofmathematical equations must be writtento represent the geometry of such surfacesin a three dimensional coordinate systemwhich coincides with or is related to theDTM coordinate system. When this hasbeen accomplished, a program is preparedto give the computer a set of instructionsto follow in relating the two surfaces andcomputing the answers of interest.

Although each application of the DTMwill have unique requirements and specialcontrols on the necessary computer pro­grams, there are a number of problemswhich are common to many applications.For example, the coordinates of the inter­section of a given plane and the surface ofthe model is fundamental to the solution ofmany engineering problems. The inter­section of a vertical plane and the model isa terrain profile; a horizontal plane and themodel, a terrain contour; and a slopingplane and the model, perhaps the limits ofa highway cut or fill. Such surfaces inter­secting the model might also commonly becylindrical or conical. Once the intersec­tions of the two surfaces have been com­puted, a common problem is to determinethe enclosed areas or volume. Hence, it ispossible to write general computer pro­grams which can be adapted easily to awide range of applications.

440 PHOTOGRAMMETRIC ENGINEERING

Three basic electronic computer pro­grams have been written at M.LT. forapplying the DTM to highway engineering.The Phase I program gives a generalhorizontal alignment solution for the prob­lem of relating any alignment to the DTMdata. The input data are the coordinatesand radius of curvature at each point ofintersection-the P.L-and an origin ofcenterline stationing. The input data canbe referenced to a coordinate system dif­ferent from that of the DTM data andusually will be stated plane coordi na tes. Theoutput of the Phase I program is the D.TMcoordinates and centerline stationing ofselected points along the alignment, usu­ally at stated intervals such as every 50feet. The program also serves as a generalsolution to the profile problem, furnishinga terrain profile defined by the intersectionof a series of plane and cylindrical verticalsurfaces ,with the model.

The Phase II program gives a solutionto the vertical alignment problem and re­lates the profile reference line of the high­way surface to the DTM data. The inputto Phase II consists of the station, eleva­tion, and length of parabolic curve associ­ates with each P.I. The output is the refer­ence elevations at the same points com­puted in Phase I.

After the reference line for the proposedhighway surface has been completelyfixed in three dimensional space and re­lated to the DTM data, the Phase III pro­gram generates the highway surface, com­putes intersections of the surface and themodel, and determines the enclosed areasand volumes.

In the present program, the surface gen­erated or the cross-section templet can becomposed of a series of 20 planes, all ofwhich are variable from job to job, andsix of which are variables selected by thecomputer. Although these programs haveimmediate practical application to a vari­ety of problems, they represent only thecrude beginning of the programs which willultimately be used with the DTM.

The programs described above requirethat the engineer specify to a great extentthe shape and location of his surface of in­terest. In many cases it will be possibleand desirable for the computer to assist inselecting the location of the engineeringsurface, according to limits and controlsset by the engineer. An example would be aproblem in which the computer is required

to select the highway profile or grade lineto meet specified optimization conditionsand according to controls on gradient,curvature, sight distance, design practice,and similar geometric control specifica­tions. AI though the mathematical formu­lation and programming of such problemswill be quite complex and costly, they areentirely practical and economically justi­fied.

MULTIPLE VARIABLE EVALUATION

The usefulness of the DTM approachcan be greatly extended by simultaneouslyconsidering additional variables related tothe problem at hand. This can be accom­plished by attaching classification infor­mation and quantitative data describingother variables at each point. For example,the total data associated with each terrainpoint in the M.I.T. experimental work andautomatically recorded by the output in­strumentation take the form:

pppp xxxxxx YYYYY ZZZZZ CCNN

comprised of four identification digits, sixdigits of the x coordinate, five of y, five ofz, a classification and two digits of quanti­tative data. Six different formatsof the out­put data are presently possible by means ofa six position switch for different IBMcard, Remington Rand card, and Bendixtape punch data formats.

The classification and quantitative dataassociated with a given point can takemany forms and includes a number of dif­ferent types of variables. For example, theclassification might be the type of soil atthe point, and the quantitative digits thedepth of overburden to bedrock. Such datamight be obtained by airphoto analysisand geophysical methods. The computerprogram using such DTM data would com­pute the volumes of each type of materialincluded in the construction requirements.Alternately, the quantitative data mightrepresent the unit right-of-way cost andthe computer would be expected to deter­mine the relative land acquisition cost foreach alignment evaluated. The solution ofthe ul timate forms of such problems will bebased on the digital cost model previouslyproposed by the senior author. In solvingthe problems, the computer will evaluatethe most economical solution consideringall cost and benefit variables. Admittedly,such problems become quite complex and

DIGITAL TERRAIN MODEL-THEORY AND APPLICATION 441

have immediate practical restrictions butcertainly should be the subject of activeresearch.

PRESENTATION AND UTILIZATION

OF THE OUTPUT DATA

The output of the electronic computerwill be a digital or numerical form of data.Quite often the result of interest will be inthe form of a numerical answer and no fur­ther transformation of the data will benecessary. However, in many cases theengineer will require an analog form ofdata presentation for human study. Agraphical plot will be the most commonlyused analog form.

Continuous line plotters are now avail­able for graphically plotting the results ofDTM problems. The potential applica­tions of the DTM will call for a family ofsuch plotters. For example, the output ofthe mathematical terrain model approachwould call for a system which would per­mit plotting of the continuous third orhigher degree polynomial equations de­fining surface profiles.

Note that the computer analysis of themathematical terrain model could furnishoutput data for the plotting of contourlines either in terms of the coordinates of alarge number of points on each contour orin terms of a series of equations definingeach contour line. Such output could beautomatically plotted to obtain contourmaps of the DTM area.

An electronic computer program hasbeen written by the M.LT. ComputationCenter for plotting and recording a contourmap of a matrix of digital values with theType 740 Cathode Ray tube output re­corder of the IBM type 704 computer.This program is being extensively used atM.LT. in scientific data reduction andillustrates a number of possibilities in theengineering field. In addition to two di­mensional continuous plots, the outputdata can be used for controlling three-di­mensional cutting machines for carvingphysical models of the DTM area.

In all of the previous examples, theequations defining the engineering sur­faces of interest will furnish the data forthe plotting or carving of such surfacesalong with the DTM surface. There aremany other possible forms and uses for theoutput of the DTM system in solving en­gineering problems.

RESUME OF ApPLICATIONS

A number of application examples havealready been mentioned to illustrate char­acteristics of the DTM approach. A re­sume of these and several other civil en­gineering areas of application follows.

a. Location, design, and quantity anal­ysis for highways, railroads, canals,levees, dams, dredging, airports,building develop men ts, etc.

b. Quantity determinations for borrowpits, quarries, open pit mines, coaland ore piles, and other types of man­made and natural cuts and embank­ments.

c. Surface change studies related tosettlement, erosion, silting, etc.

d. Clearance studies for airport ap­proach zones, microwave systems,radar and missile installations, etc.

e. Terrain analysis problems associatedwith reservoirs, drainage problems,transmission lines of all types, etc.

In essence it may be said that whenevertwo surfaces of interest are to be relatedand computations are required, the DTMoffers a possible approach. Photogram­metry will usually offer the only practicalapproach to the problem of obtaining therequired data, and the electronic com­puter makes it possible to consider com­puting problems which would require anarmy of men with desk calculators.

ACKNOWLEDGMENTS

The research described in this paper issponsored by the Massachusetts Depart­ment of Public Works and is directed byAnthony N. DiNatale, Commissioner ofPublic Works; E. J. McCarthy, ChiefEngineer; Patrick F. Cox, Deputy ChiefEngineer; Joseph O'Neil, Supervisor of Re­search; and Charles Whitcomb, Locationand Surveys Engineer. The program isconducted in cooperation with the U. S.Bureau of Public Roads under the super­sision of Charles Hall, District Engineer,and John Swanson, Regional Engineer.Encouragement and technical advice fromthe office of H. A. Radzikowski, Chief, Di­vision of Development, Bureau of PublicRoads, is gratefully acknowledged. Thefollowing firms have actively assisted theprogram in arranging for instrumenta­tion facilities: I BM Corporation, BendixComputer Division, Remington Rand,

442 PHOTOGRAMMETRIC ENGINEERING

a.M.L Corporation of America, Bauschand Lomb. Finally, the authors pay trib­ute to their colleagues on the project staffincluding D. R. Schur;,:, E. P. Gladding,and T. H. Kaalstad.

REFERENCES

Addjtional material on the subject paper willbe found in the following publications of theM.l.T. Photogrammetry Laboratory.

1. No. 107-Preliminary Report, IntegratedAerial Photogrammetric and ElectronicComputer System

2. No. 109-Digital Readout Systems andComponents for Photogrammetric Instru­men ta tion

3. No. 110-A Study of Directional ScanningTechniques

4. No. 111-Digital Terrain Model Approachto Highway Earthwork Analysis

5. No. 112-An Automatic Digital OutputSystem for Double Projection Stereoplot­tel's

6. No. 113-The Skew System for HighwayEarthwork Analysis

7. o. 114-Electronic Computer Program-ming of the Skew System

8. TO. liS-Earthwork Data Procurement byPhotogrammetric Methods

Previous papers by the project staff whichdiscuss some of the concepts presented in th ispaper include:

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Beginning in 1917, the manufactur of opticalglass in this country has been closely allied withnational defense. Until 1917 all of the opticalglass used in the United States was importedfrom Germany. By the end of 1917, the Bausch& Lomb Glass Plant had multiplied its volume

9. Miller, C. L. and R. D. Schurz, "Educa­tional and Research Activities in Photo­grammetry at M.LT." PHOTOGRAMMETRICENGINEERING, March 1958.

10. Miller, C. L., "Impact of the ExpandedHighway Program on Photogrammetry,"PHOTOGRAMMETRIC ENGINEERING, Decem­ber 1956.

II. Roberts, P.O., "Using New Methods inHighway Location," PHOTOGRAMMETRICENGINEERING, June 1957.

Information on developments by othergroups which are related to the subject matterinclude:

12. ROSENBERG, P., "I nformation Theory andElectronic Photogrammetry," PHOTO­GRAMMETRIC ENGINEERING, September1955.

13. Esten, R. D., "Automatic Contouring,"PHOTOGRAMMETRIC ENGINEERING, March1957.

14. Spooner, Dossi, and Misulia, "Let's GoOver the Hill-Potential Benefits of ProfileScanning the Stereo-Model," PHOTOGRAM­METRIC ENGINEERING, December 1957.

IS. Schwidefsky, K., "New Aids for umericalPhotogrammetry," Photogrammetria, Vol.XIV, No. I, 1957-58.

16. Stieber, j. A., "The Master Terrain ModelSystem," paper presented at 1957 JointEastern Computer Conference. To be pub­lished in proceedings of conference.

by twenty times, and was manufacturing opticaglass at the rate of 40,000 pounds per monthAt the close of ''''orld War I, B&L had pro­duced 450,000 pounds, or 65% of all the opticalglass used by the military forces. Twenty yearslater with the outbreak of World War II,Bausch & Lomb was again ready for militaryproduction. During the war, the Glass Plantmanufactured high quality optical glass atabout 1200% of the pre-war production.

Since 1918 B&L has continued to produce itsown optical glass, and at the present time is theonly manufacturer in the Western Hemisphereproducing optical elements from sand to fin­ished product. The requirements for the opticalproducts made by Bausch & Lomb, includingboth ophthalmic goods and scientific instru­ments, numbers more than 120 different typesof optical glass.

It has manufactured its own optical glassfor years. Because the research experts haveselected only the best raw ingredients and chem­icals and the engineers and craftsmen controlevery operation in the processing, the Bausch &Lomb Optical Company has earned a reputa­tion for the manufacture of optical glass of thevery highest quality.