Elementary Surveying: An Introduction to Geomatics

1 Introduction   1.1 Definition of Surveying   1.2 Geomatics   1.3 History of Surveying   1.4 Geodetic and Plane Surveys   1.5 Importance of Surveying   1.6 Specialized Types of Surveys   1.7 Surveying Safety   1.8 Land and Geographic Information Systems   1.9 Federal Surveying and Mapping Agencies   1.10 The Surveying Profession   1.11 Professional Surveying Organizations   1.12 Surveying on the Internet   1.13 Future Challenges in Surveying Problems Bibliography 2 Units, Significant Figures, and Field Notes Part I Units and Significant Figures   2.1 Introduction   2.2 Units of Measurement 25t   2.3 International System of Units (SI)   2.4 Significant Figures   2.5 Rounding Off Numbers Part II Field Notes   2.6 Field Notes   2.7 General Requirements of Handwritten Field Notes   2.8 Types of Field Books   2.9 Kinds of Notes   2.10 Arrangements of Notes   2.11 Suggestions for Recording Notes   2.12 Introduction to Data Collectors   2.13 Transfer of Files from Data Collectors   2.14 Digital Data File Management   2.15 Advantages and Disadvantages of Data Collectors Problems Bibliography 3 Theory of Errors in Observations   3.1 Introduction   3.2 Direct and Indirect Observations   3.3 Errors in Measurements   3.4 Mistakes   3.5 Sources of Errors in Making Observations   3.6 Types of Errors   3.7 Precision and Accuracy   3.8 Eliminating Mistakes and Systematic Errors   3.9 Probability   3.10 Most Probable Value   3.11 Residuals   3.12 Occurrence of Random Errors   3.13 General Laws of Probability   3.14 Measures of Precision   3.15 Interpretation of Standard Deviation   3.16 The 50, 90, and 95 Percent Errors   3.17 Error Propagation 3.17.1 Error of a Sum 3.17.2 Error of a Series 3.17.3 Error in a Product 3.17.4 Error in the Mean   3.18 Applications   3.19 Conditional Adjustment of Observations   3.20 Weights of Observations   3.21 Least-Squares Adjustment Problems Bibliography 4 Leveling–Theory, Methods, and Equipment Part I Leveling–Theory and Methods   4.1 Introduction   4.2 Definitions   4.3 North American Vertical Datum   4.4 Curvature and Refraction   4.5 Methods for Determining Differences in Elevation 4.5.1 Measuring Vertical Distances by Taping or Electronic Methods 4.5.2 Differential Leveling 4.5.3 Barometric Leveling 4.5.4 Trigonometric Leveling Part II Equipment for Differential Leveling   4.6 Categories of Levels   4.7 Telescopes   4.8 Level Vials   4.9 Tilting Levels   4.10 Automatic Levels   4.11 Digital Levels   4.12 Tripods   4.13 Hand Level   4.14 Level Rods   4.15 Testing and Adjusting Levels 4.15.1 Requirements for Testing and Adjusting Instruments 4.15.2 Adjusting for Parallax 4.15.3 Testing and Adjusting Level Vials 4.15.4 Preliminary Adjustment of the Horizontal Cross Hair 4.15.5 Testing and Adjusting the Line of Sight Problems Bibliography 5 Leveling—Field Procedures and Computations   5.1 Introduction   5.2 Carrying and Setting Up a Level   5.3 Duties of a Rodperson   5.4 Differential Leveling   5.5 Precision   5.6 Adjustments of Simple Level Circuits   5.7 Reciprocal Leveling   5.8 Three-Wire Leveling   5.9 Profile Leveling 5.9.1 Staking and Stationing the Reference Line 5.9.2 Field Procedures for Profile Leveling 5.9.3 Drawing and Using the Profile   5.10 Grid, Cross-Section, or Borrow-Pit Leveling   5.11 Use of the Hand Level   5.12 Sources of Error in Leveling 5.12.1 Instrumental Errors 5.12.2 Natural Errors 5.12.3 Personal Errors   5.13 Mistakes   5.14 Reducing Errors and Eliminating Mistakes Problems Bibliography 6 Distance Measurement Part I Methods for Measuring Distances   6.1 Introduction   6.2 Summary of Methods for Making Linear Measurements   6.3 Pacing   6.4 Odometer Readings   6.5 Optical Rangefinders   6.6 Tacheometry   6.7 Subtense Bar Part II Distance Measurements by Taping   6.8 Introduction to Taping   6.9 Taping Equipment and Accessories   6.10 Care of Taping Equipment   6.11 Taping on Level Ground 6.11.1 Lining In 6.11.2 Applying Tension 6.11.3 Plumbing 6.11.4 Marking Tape Lengths 6.11.5 Reading the Tape 6.11.6 Recording the Distance   6.12 Horizontal Measurements on Sloping Ground   6.13 Slope Measurements   6.14 Sources of Error in Taping 6.14.1 Incorrect Length of Tape 6.14.2 Temperature Other Than Standard 6.14.3 Inconsistent Pull 6.14.4 Sag 6.14.5 Tape Not Horizontal and Tape Off-Line 6.14.6 Improper Plumbing 6.14.7 Faulty Marking 6.14.8 Incorrect Reading or Interpolation 6.14.9 Summary of Effects of Taping Errors   6.15 Tape Problems   6.16 Combined Corrections in a Taping Problem Part II Electronic Distance Measurement   6.17 Introduction   6.18 Propagation of Electromagnetic Energy   6.19 Principles of Electronic Distance Measurement   6.20 Electro-Optical Instruments   6.21 Total Station Instruments   6.22 EDM Instruments Without Reflectors   6.23 Computing Horizontal Lengths From Slope Distances 6.23.1 Reduction of Short Lines by Elevation Differences 6.23.2 Reduction of Short Lines by Zenith or Altitude Angle   6.24 Errors in Electronic Distance Measurement 6.24.1 Personal Errors 6.24.2 Instrumental Errors 6.24.3 Natural Errors Problems Bibliography 7 Angles, Azimuths, and Bearings   7.1 Introduction   7.2 Units of Angle Measurement   7.3 Kinds of Horizontal Angles   7.4 Direction of a Line   7.5 Azimuths   7.6 Bearings   7.7 Comparison of Azimuths and Bearings   7.8 Computing Azimuths   7.9 Computing Bearings   7.10 The Compass and The Earth’s Magnetic Field   7.11 Magnetic Declination   7.12 Variations in Magnetic Declination   7.13 Software for Determining Magnetic Declination   7.14 Local Attraction   7.15 Typical Magnetic Declination Problems   7.16 Mistakes Problems Bibliography 8 Total Station Instruments: Angle Measurements Part I Total Station Instruments   8.1 Introduction   8.2 Characteristics of Total Station Instruments   8.3 Functions Performed by Total Station Instruments   8.4 Parts of a Total Station Instrument   8.5 Handling and Setting Up a Total Station Instrument   8.6 Servo-Driven and Remotely Operated Total Station Instruments Part II Angle Measurements   8.7 Relationship of Angles and Distances   8.8 Observing Horizontal Angles with Total Station Instruments   8.9 Observing Horizontal Angles by the Direction Method   8.10 Closing the Horizon   8.11 Observing Deflection Angles   8.12 Observing Azimuths   8.13 Observing Vertical Angles   8.14 Sights and Marks   8.15 Prolonging a Straight Line   8.16 Balancing-In   8.17 Random Traverse   8.18 Total Stations for Determining Elevation Differences   8.19 Adjustment of Total Station Instruments and Their Accessories 8.19.1 Adjustment of Plate-Level Vials 8.19.2 Adjustment of Tripods 8.19.3 Adjustment of Tribrachs 8.19.4 Adjustment of Optical Plummets 8.19.5 Adjustment of Circular Level Bubbles   8.20 Sources of Error in Total Station Work 8.20.1 Instrumental Errors 8.20.2 Natural Errors 8.20.3 Personal Errors   8.21 Propagation of Random Errors in Angle Observations   8.22 Mistakes Problems Bibliography 9 Traversing   9.1 Introduction   9.2 Observation of Traverse Angles or Directions 9.2.1 Traversing by Interior Angles 9.2.2 Traversing by Angles to the Right 9.2.3 Traversing by Deflection Angles 9.2.4 Traversing by Azimuths   9.3 Observation of Traverse Lengths   9.4 Selection of Traverse Stations   9.5 Referencing Traverse Stations   9.6 Traverse Field Notes   9.7 Angle Misclosure   9.8 Traversing with Total Station Instruments   9.9 Radial Traversing   9.10 Sources of Error in Traversing   9.11 Mistakes in Traversing Problems 10 Traverse Computations   10.1 Introduction   10.2 Balancing Angles   10.3 Computation of Preliminary Azimuths or Bearings   10.4 Departures and Latitudes   10.5 Departure and Latitude Closure Conditions   10.6 Traverse Linear Misclosure and Relative Precision   10.7 Traverse Adjustment 10.7.1 Compass (Bowditch) Rule 10.7.2 Least-Squares Method   10.8 Rectangular Coordinates   10.9 Alternative Methods for Making Traverse Computations 10.9.1 Balancing Angles by Adjusting Azimuths or Bearings 10.9.2 Balancing Departures and Latitudes by Adjusting Coordinates   10.10 Lengths and Directions of Lines from Departures and Latitudes or Coordinates   10.11 Computing Final Adjusted Traverse Lengths and Directions   10.12 Coordinate Computations in Boundary Surveys   10.13 Use of Open Traverses   10.14 State Plane Coordinate Systems   10.15 Traverse Computations Using Computers   10.16 Locating Blunders in Traverse Measurements   10.17 Mistakes in Traverse Computations Problems Bibliography 11 Coordinate Geometry in Surveying Calculations   11.1 Introduction   11.2 Coordinate Forms of Equations for Lines and Circles   11.3 Perpendicular Distance from a Point to a Line   11.4 Intersection of Two Lines, Both Having Known Directions   11.5 Intersection of a Line with a Circle   11.6 Intersection of Two Circles   11.7 Three-Point Resection   11.8 Two-Dimensional Conformal Coordinate Transformation   11.9 Inaccessible Point Problem   11.10 Three-Dimensional Two-Point Resection   11.11 Conclusions Problems Bibliography 12 Area   12.1 Introduction   12.2 Methods of Measuring Area   12.3 Area by Division into Simple Figures   12.4 Area by Offsets from Straight Lines 12.4.1 Regularly Spaced Offsets 12.4.2 Irregularly Spaced Offsets   12.5 Area by Coordinates   12.6 Area by Double Meridian Distance Method   12.7 Area of Parcels with Circular Boundaries   12.8 Partitioning of Lands 12.8.1 Trial and Error Method 12.8.2 Use of Simple Geometric Figures 12.8.3 Coordinate Method   12.9 Area by Measurements from Maps 12.9.1 Area by Counting Coordinate Squares 12.9.2 Area by Scaled Lengths 12.9.3 Area by Digitizing Coordinates 12.9.4 Area by Planimeter   12.10 Sources of Error in Determining Areas   12.11 Mistakes in Determining Areas Problems Bibliography 13 The Global Positioning System–Introduction and Principles of Operation   13.1 Introduction   13.2 Overview of GPS   13.3 The GPS Signal   13.4 Reference Coordinate Systems for GPS 13.4.1 The Satellite Reference Coordinate System 13.4.2 The Geocentric Coordinate System 13.4.3 The Geodetic Coordinate System   13.5 Fundamentals of GPS Positioning 13.5.1 Code Ranging 13.5.2 Carrier Phase-Shift Measurements   13.6 Errors in GPS Observations 13.6.1 Clock Bias 13.6.2 Refraction 13.6.3 Other Error Sources 13.6.4 Geometry of Observed Satellites 13.6.5 Selective Availability   13.7 Differential GPS   13.8 Kinematic GPS Methods   13.9 Relative Positioning 13.9.1 Single Differencing 13.9.2 Double Differencing 13.9.3 Triple Differencing   13.10 Other Satellite Navigation Systems 13.10.1 The GLONASS Constellation 13.10.2 Galileo System 13.10.3 Compass   13.11 The Future Problems Bibliography 14 The Global Positioning System–Static surveys   14.1 Introduction   14.2 Field Procedures in GPS Surveys 14.2.1 Static Relative Positioning 14.2.2 Rapid Static Relative Positioning 14.2.3 Pseudokinematic Surveys 14.2.4 Kinematic Surveys   14.3 Planning GPS Surveys 14.3.1 Preliminary Considerations 14.3.2 Selecting the Appropriate Survey Method 14.3.3 Field Reconnaissance 14.3.4 Developing an Observation Scheme 14.3.5 Availability of Reference Stations   14.4 Performing Static GPS Surveys   14.5 Data Processing and Analysis 14.5.1 Specifications for GPS Surveys 14.5.2 Analysis of Fixed Baseline Measurements 14.5.3 Analysis of Repeat Baseline Measurements 14.5.4 Analysis of Loop Closures 14.5.5 Baseline Network Adjustment 14.5.6 The Survey Report   14.6 Sources of Errors in GPS Work 14.6.1 Instrumental Errors 14.6.2 Natural Errors 14.6.3 Personal Errors   14.7 Mistakes in GPS Work   14.8 Future Outlook for GPS Problems Bibliography 15 The Global Positioning System–Kinematic GPS   15.1 Introduction   15.2 Initialization   15.3 Equipment Used in Kinematic Surveys   15.4 Methods Used in Kinematic Surveys   15.5 Performing Post-Processed Kinematic Surveys   15.6 Communication in Real-Time Kinematic Surveys   15.7 Real-Time Networks   15.8 Performing Real-Time Kinematic Surveys   15.9 Machine Control   15.10 Errors in Kinematic Surveys   15.11 Mistakes in Kinematic Surveys Problems Bibliography 16 Adjustments by Least Squares   16.1 Introduction   16.2 Fundamental Condition of Least Squares   16.3 Least-Squares Adjustment by the Observation Equation Method   16.4 Matrix Methods in Least-Squares Adjustment   16.5 Matrix Equations for Precisions of Adjusted Quantities   16.6 Least-Squares Adjustment of Leveling Circuits   16.7 Propagation of Errors   16.8 Least-Squares Adjustment of GPS Baseline Vectors   16.9 Least-Squares Adjustment of Traditional Horizontal Plane Surveys 16.9.1 Linearizing Nonlinear Equations 16.9.2 The Distance Observation Equation 16.9.3 The Azimuth Observation Equation 16.9.4 The Angle Observation Equation 16.9.5 A Traverse Example Using WOLFPACK   16.10 Error Ellipses   16.11 Adjustment Procedures   16.12 Other Measures of Precision for Horizontal Stations   16.13 Conclusions Problems Bibliography 17 Mapping Surveys   17.1 Introduction   17.2 Basic Methods for Performing Mapping Surveys   17.3 Map Scale   17.4 Control for Mapping Surveys   17.5 Contours   17.6 Characteristics of Contours   17.7 Direct and Indirect Methods of Locating Contours 17.7.1 Direct Method 17.7.2 Indirect Method   17.8 Digital Elevation Models and Automated Contouring Systems   17.9 Basic Field Methods for Locating Topographic Details 17.9.1 Radiation by Total Station 17.9.2 Radiation by Stadia 17.9.3 Coordinate Squares or “Grid” Method 17.9.4 Offsets from a Reference Line 17.9.5 Topographic Detailing with GPS 17.9.6 Laser-Scanning   17.10 Three-Dimensional Conformal Coordinate Transformation   17.11 Selection of Field Method   17.12 Working with Data Collectors and Field-to-Finish Software   17.13 Hydrographic Surveys 17.13.1 Equipment for Making Soundings 17.13.2 Locating Soundings 17.13.3 Hydrographic Mapping   17.14 Sources of Error in Mapping Surveys   17.15 Mistakes in Mapping Surveys Problems Bibliography 18 Mapping   18.1 Introduction   18.2 Availability of Maps and Related Information   18.3 National Mapping Program   18.4 Accuracy Standards for Mapping   18.5 Manual and Computer-Aided Drafting Procedures   18.6 Map Design   18.7 Map Layout   18.8 Basic Map Plotting Procedures 18.8.1 Manually Plotting by Coordinates 18.8.2 Plotting Using CADD   18.9 Contour Interval   18.10 Plotting Contours   18.11 Lettering   18.12 Cartographic Map Elements   18.13 Drafting Materials   18.14 Automated Mapping and Computer-Aided Drafting Systems   18.15 Impacts of Modern Land and Geographic Information Systems on Mapping   18.16 Sources of Error in Mapping   18.17 Mistakes in Mapping Problems Bibliography 19 Control Surveys and Geodetic Reductions   19.1 Introduction   19.2 The Ellipsoid and Geoid   19.3 The Conventional Terrestrial Pole   19.4 Geodetic Position and Ellipsoidal Radii of Curvature   19.5 Geoid Undulation and Deflection of The Vertical   19.6 U.S. Reference Frames 19.6.1 North American Horizontal Datum of 1927 (NAD27) 19.6.2 North American Horizontal Datum of 1983 (NAD83) 19.6.3 Later Versions of NAD83 19.6.4 National Geodetic Vertical Datum of 1929 (NGVD29) 19.6.5 North American Vertical Datum of 1988 (NAVD88) 19.6.6 Transforming Coordinates between Reference Frames   19.7 Accuracy Standards and Specifications For Control Surveys   19.8 The National Spatial Reference System   19.9 Hierarchy of the National Horizontal Control Network   19.10 Hierarchy of the National Vertical Control Network   19.11 Control Point Descriptions   19.12 Field Procedures For Traditional Horizontal Control Surveys 19.12.1 Triangulation 19.12.2 Precise Traverse 19.12.3 Trilateration 19.12.4 Combined Networks   19.13 Field Procedures for Vertical Control Surveys   19.14 Reduction of Field Observations to Their Geodetic Values 19.14.1 Reduction of Distance Observations Using Elevations 19.14.2 Reduction of Distance Observations Using Vertical Angles 19.14.3 Reduction of Directions and Angles 19.14.4 Leveling and Orthometric Heights   19.15 Geodetic Position Computations 19.15.1 Direct Geodetic Problem 19.15.2 Inverse Geodetic Problem   19.16 The Local Geodetic Coordinate System   19.17 Three-Dimensional Coordinate Computations   19.18 Conclusions Problems Bibliography 20 State Plane Coordinates   20.1 Introduction   20.2 Projections Used in State Plane Coordinate Systems   20.3 Lambert Conformal Conic Projection   20.4 Transverse Mercator Projection   20.5 State Plane Coordinates in NAD27 and NAD83   20.6 Computing SPCS83 Coordinates in the Lambert Conformal Conic System 20.6.1 Zone Constants 20.6.2 The Direct Problem 20.6.3 The Inverse Problem   20.7 Computing SPCS83 Coordinates in the Transverse Mercator System 20.7.1 Zone Constants 20.7.2 The Direct Problem 20.7.2 The Inverse Problem   20.8 Reduction of Distances and Angles to State Plane Coordinate Grids 20.8.1 Grid Reduction of Distances 20.8.2 Grid Reduction of Azimuths and Angles   20.9 Computing State Plane Coordinates of Traverse Stations   20.10 Surveys Extending from One Zone to Another   20.11 Conversions between SPCS27 and SPCS83   20.12 The Universal Transverse Mercator Projection   20.13 Other Map Projections 20.13.1 Oblique Stereographic Map Projection 20.13.2 Oblique Mercator Map Projection Problems Bibliography 21 Boundary Surveys   21.1 Introduction   21.2 Categories of Land Surveys   21.3 Historical Perspectives   21.4 Property Description by Metes and Bounds   21.5 Property Description by Block and Lot System   21.6 Property Description by Coordinates   21.7 Retracement Surveys   21.8 Subdivision Surveys   21.9 Partitioning Land   21.10 Registration of Title   21.11 Adverse Possession and Easements   21.12 Condominium Surveys   21.13 Geographic and Land Information Systems   21.14 Sources of Error in Boundary Surveys   21.15 Mistakes Problems Bibliography 22 Surveys of the Public Lands   22.1 Introduction   22.2 Instructions for Surveys of the Public Lands   22.3 Initial Point   22.4 Principal Meridian   22.5 Baseline   22.6 Standard Parallels (Correction Lines)   22.7 Guide Meridians   22.8 Township Exteriors, Meridional (Range) Lines, and Latitudinal (Township) Lines   22.9 Designation of Townships   22.10 Subdivision of a Quadrangle Into Townships   22.11 Subdivision of a Township Into Sections   22.12 Subdivision of Sections   22.13 Fractional Sections   22.14 Notes   22.15 Outline of Subdivision Steps   22.16 Marking Corners   22.17 Witness Corners   22.18 Meander Corners   22.19 Lost and Obliterated Corners   22.20 Accuracy of Public Lands Surveys   22.21 Descriptions by Township Section and Smaller Subdivision   22.22 BLM Land Information System   22.23 Sources of Error   22.24 Mistakes Problems Bibliography 23 Construction Surveys   23.1 Introduction   23.2 Specialized Equipment for Construction Surveys 23.2.1 Visible Laser-Beam Instruments 23.2.2 Reflectorless Total Stations   23.3 Horizontal and Vertical Control   23.4 Staking Out A Pipeline   23.5 Staking Pipeline Grades   23.6 Staking Out a Building   23.7 Staking Out Highways   23.8 Other Construction Surveys   23.9 Construction Surveys Using Total Station Instruments   23.10 Construction Surveys Using GPS Equipment   23.11 Machine Control   23.12 As-Built Surveys with Laser Scanning   23.13 Sources of Error in Construction Surveys   23.14 Mistakes Problems Bibliography 24 Horizontal Curves   24.1 Introduction   24.2 Degree of Circular Curve   24.3 Definitions and Derivation of Circular Curve Formulas   24.4 Circular Curve Stationing   24.5 General Procedure of Circular Curve Layout by Deflection Angles   24.6 Computing Deflection Angles and Chords   24.7 Notes for Circular Curve Layout by Deflection Angles and Incremental Chords   24.8 Detailed Procedures for Circular Curve Layout by Deflection Angles and Incremental Chords   24.9 Setups on Curve   24.10 Metric Circular Curves by Deflection Angles and Incremental Chords   24.11 Circular Curve Layout by Deflection Angles and Total Chords   24.12 Computation of Coordinates on a Circular Curve   24.13 Circular Curve Layout by Coordinates   24.14 Curve Stakeout Using GPS and Robotic Total Stations   24.15 Circular Curve Layout by Offsets   24.16 Special Circular Curve Problems 24.16.1 Passing a Circular Curve through a Fixed Point 24.16.2 Intersection of a Circular Curve and a Straight Line 24.16.3 Intersection of Two Circular Curves   24.17 Compound and Reverse Curves   24.18 Sight Distance on Horizontal Curves   24.19 Spirals 24.19.1 Spiral Geometry 24.19.2 Spiral Calculation and Layout   24.20 Computation of “As-Built” Circular Alignments   24.21 Sources of Error in Laying Out Circular Curves   24.22 Mistakes Problems Bibliography 25 Vertical Curves   25.1 Introduction   25.2 General Equation of a Vertical Parabolic Curve   25.3 Equation of an Equal Tangent Vertical Parabolic Curve   25.4 High or Low Point on a Vertical Curve   25.5 Vertical Curve Computations Using the Tangent Offset Equation 25.5.1 Example Computations Using the English System of Units 25.5.2 Example Computations Using the Metric System   25.6 Equal Tangent Property of a Parabola   25.7 Curve Computations by Proportion   25.8 Staking a Vertical Parabolic Curve   25.9 Machine Control in Grading Operations   25.10 Computations for an Unequal Tangent Vertical Curve   25.11 Designing a Curve to Pass through a Fixed Point   25.12 Sight Distance   25.13 Sources of Error in Laying Out Vertical Curves   25.14 Mistakes Problems Bibliography 26 Volumes   26.1 Introduction   26.2 Methods of Volume Measurement   26.3 The Cross-Section Method   26.4 Types of Cross Sections   26.5 Average End Area Formula   26.6 Determining End Areas 26.6.1 End Areas by Simple Figures 26.6.2 End Areas by Coordinates   26.7 Computing Slope Intercepts   26.8 Prismoidal Formula   26.9 Volume Computations   26.10 Unit-Area, or Borrow-Pit, Method   26.11 Contour-Area Method   26.12 Measuring Volumes of Water Discharge   26.13 Sources of Error in Determining Volumes   26.14 Mistakes Problems Bibliography 27 Photogrammetry   27.1 Introduction   27.2 Uses of Photogrammetry   27.3 Aerial Cameras   27.4 Types of Aerial Photographs   27.5 Vertical Aerial Photographs   27.6 Scale of a Vertical Photograph   27.7 Ground Coordinates from a Single Vertical Photograph   27.8 Relief Displacement on a Vertical Photograph   27.9 Flying Height of a Vertical Photograph   27.10 Stereoscopic Parallax   27.11 Stereoscopic Viewing   27.12 Stereoscopic Measurement of Parallax   27.13 Analytical Photogrammetry   27.14 Stereoscopic Plotting Instruments 27.14.1 Direct Optical Projection Stereoplotters 27.14.2 Mechanical Projection Stereoplotters 27.14.3 Analytical Stereoplotters 27.14.4 Softcopy Stereoplotters   27.15 Orthophotos   27.16 Ground Control for Photogrammetry   27.17 Flight Planning   27.19 Airborne Laser-Mapping Systems   27.20 Remote Sensing   27.21 Sources of Error in Photogrammetry   27.22 Mistakes Problems Bibliography 28 Introduction to Geographic Information Systems   28.1 Introduction   28.2 Land Information Systems   28.3 GIS Data Sources and Classifications   28.4 Spatial Data 28.4.1 Simple Spatial Objects 28.4.2 Vector and Raster Formats 28.4.3 Topology   28.5 Nonspatial Data   28.6 Data Format Conversions 28.6.1 Vector-to-Raster Conversion 28.6.2 Raster-to-Vector Conversion   28.7 Creating GIS Databases 28.7.1 Generating Digital Data from Field Surveys 28.7.2 Digitizing from Aerial Photos with Stereoplotters 28.7.3 Digitizing Existing Graphic Materials 29.7.4 Keyboard Entry 29.7.5 Existing Digital Data Sets 29.7.6 Scanning   28.8 Metadata   28.9 GIS Analytical Functions 28.9.1 Proximity Analysis 28.9.2 Boundary Operations 28.9.3 Spatial Joins 28.9.4 Logical Operations 28.9.5 Other GIS Functions   28.10 GIS Applications Problems Bibliography A Dumpy Levels, Transits, and Theodolites   A.1 Introduction   A.2 The Dumpy Level   A.3 Introduction to the Transit and Theodolite   A.4 The Transit A.4.1 Parts of a Transit A.4.2 Circle Scales and Verniers A.4.3 Properties of the Transit A.4.4 Handling, Setting up, and using a Transit   A.5 The Theodolite A.5.1 Characteristics of Theodolites A.5.2 Repeating Theodolites A.5.3 Directional Theodolites A.5.4 Handling, Setting Up, and Using a Theodolite B Example Noteforms C Astronomical Observations   C.1 Introduction   C.2 Overview of Usual Procedures for Astronomical Azimuth Determination   C.3 Ephemerides   C.4 Definitions   C.5 Time   C.6 Timing Observations   C.7 Computations for Azimuth from Polaris Observations by the Hour Angle Method   C.8 Azimuth from Solar Observations D Using the Worksheets on the Companion Disk   D.1 Introduction   D.2 Using the Files   D.3 Using the Worksheets as an Aid in Learning E Introduction to Matrices   E.1 Introduction   E.2 Definition of a Matrix   E.3 The Dimensions of a Marix   E.4 The Transpose of a Matrix   E.5 Matrix Addition   E.6 Matrix Multiplication   E.7 Matrix Inverse F U.S. State Plane Coordinate System Defining Parameters   F.1 Introduction   F.2 Defining Parameters for States Using the Lambert Conformal Conic Map Projection   F.3 Defining Parameters for States Using the Transverse Mercator Map Projection G Answers to Selected Problems Index