Study guide
7.3 Terrain Representation & 3D Visualization: Shaded Relief, Slope, Aspect, Curvature & Oblique Views
GISP Geospatial Core Technical Knowledge Exam Study Guide Exam
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1 Chapter 1: GISP Exam Structure, Policies & Preparation Strategy
1.1 GISP Certification Framework, Pearson VUE Delivery & Passing Standard 1.2 The 10 Official GISCI Knowledge Categories & Diagnostic Study Planning 1.3 Question Reasoning, Vendor-Neutral Concepts & Test-Taking Tactics
2 Chapter 2: Geodesy, Datums & Earth Geometry
2.1 Earth Geometry: Geoid, Reference Ellipsoids, and Heights 2.2 Horizontal & Vertical Datums: NAD27, NAD83, WGS84, NAVD88, and Modernized NSRS 2.3 Geomatics Disciplines, Geodetic Control Networks, and Monumentation
3 Chapter 3: Coordinate Systems & Map Projections
3.1 Geographic (GCS) vs. Projected (PCS) Coordinate Systems & Angles 3.2 Projection Families & Distortion Properties 3.3 Standard Projected Systems: State Plane (SPCS), UTM, and Web Mercator
4 Chapter 4: Vector & Raster Spatial Data Models
4.1 Vector Data Architecture: Points, Lines, Polygons, Multipart Features & Curves 4.2 Raster Architecture: Grid Structures, Pixel Dimensions & Multi-Dimensional Resolutions 4.3 Modeling Geographic Phenomena: Discrete Objects vs. Continuous Fields 4.4 Elevation and Surface Representations: DEMs, DSMs, DTMs, TINs, and Point Clouds
5 Chapter 5: Topology, Data Quality & Geospatial Standards
5.1 Spatial Topology: Planar Enforcement, Adjacency, Connectivity & DE-9IM 5.2 Data Quality Dimensions and Positional Accuracy Standards (ISO 19157-1, NSSDA, RMSE) 5.3 Geospatial Metadata Standards: FGDC CSDGM and the ISO 19115 Family 5.4 Open Standards and Interoperability: OGC Web Services & Open Formats
6 Chapter 6: Cartographic Design & Visual Variables
6.1 Visual Variables (Bertin's Semiology of Graphics) and Map Symbology 6.2 Map Design Hierarchy, Common Elements, Layout Balance & Typography 6.3 Color Theory, Palette Types & Accessible Cartographic Design
7 Chapter 7: Thematic Mapping & Data Classification
7.1 Thematic Map Types: Choropleth, Proportional/Graduated Symbol, Dot Density, Isarithmic & Cartograms 7.2 Data Classification Methods: Natural Breaks, Quantile, Equal Interval, Geometric Interval & Standard Deviation 7.3 Terrain Representation & 3D Visualization: Shaded Relief, Slope, Aspect, Curvature & Oblique Views
8 Chapter 8: Field Data Acquisition & GNSS
8.1 GNSS Constellations, Signal Structures, Error Budgets & Differential Correction (DGPS, RTK, PPP) 8.2 Heads-Up & Tablet Digitizing, Snapping Tolerances, Stream Mode & Boundary Capture 8.3 Mobile Field GIS Workflows, Disconnected Editing, GNSS Integration & Crowdsourced/VGI Data
9 Chapter 9: Remote Sensing & Imagery
9.1 The Electromagnetic Spectrum, Atmospheric Windows, Spectral Signatures & Sensor Types 9.2 Aerial Photogrammetry: Relief Displacement, Parallax, Orthorectification & Ground Control 9.3 Active Remote Sensing: LiDAR, RADAR, Synthetic Aperture Radar (SAR) & UAS/Drone Mapping
10 Chapter 10: Georeferencing, Transformations & Resampling
10.1 Georeferencing: Control Points, Root Mean Square Error & Transformation Models (Affine, Similarity, Projective, Spline) 10.2 Raster Resampling Techniques: Nearest Neighbor, Bilinear Interpolation & Cubic Convolution 10.3 Datum Transformations: 3-Parameter, 7-Parameter Helmert, and Grid-Based Shifts (NADCON, HARN)
11 Chapter 11: Data Integration & Spatial Generalization
11.1 Geospatial ETL: Format Conversion, Schema Mapping & Coordinate Translation 11.2 Spatial Generalization: Selection, Simplification, Smoothing, Aggregation, Collapse & Displacement 11.3 Conflation, Edge-Matching, Rubber-Sheeting & Data Harmonization
12 Chapter 12: Vector Analysis & Overlay Operations
12.1 Attribute and Spatial Query Languages: SQL WHERE Clauses and Spatial Predicates 12.2 Vector Geometric Overlay: Intersect, Union, Identity, Erase, Symmetrical Difference & Update 12.3 Proximity Analysis: Euclidean Distance, Fixed & Variable Buffers, Voronoi/Thiessen Polygons
13 Chapter 13: Raster Analysis, Surfaces & Spatial Statistics
13.1 Map Algebra & Raster Overlay: Local, Focal, Zonal & Global Operations 13.2 Surface Analysis & Spatial Interpolation: IDW, Kriging, Spline & Viewshed Analysis 13.3 Network Analysis: Geometric Networks, Utility Networks & Routing 13.4 Spatial Statistics & Pattern Analysis: Spatial Autocorrelation, Hot Spots & Regression
14 Chapter 14: Geospatial Database Design & Multiuser Architecture
14.1 Relational Database Foundations & Geospatial Extensions (SQL, PostGIS, SpatiaLite) 14.2 Geodatabase Schema Architecture: Feature Datasets, Subtypes & Attribute Domains 14.3 Spatial Indexing & Storage Structures: R-Tree, Quadtree, Geohash & Vector Tiles 14.4 Multiuser Geodatabase Architecture: Traditional Versioning, Branch Versioning & Archiving
15 Chapter 15: GIS Programming, Automation & Web Services
15.1 Python for GIS Automation: Scripting, Spatial DataFrames & Geospatial Libraries 15.2 Visual Programming, Workflow Modeling & Script Tools 15.3 Web GIS Architecture: REST APIs, Feature Services, Vector Tiles & Cloud Platforms
16 Chapter 16: Enterprise Architecture, Systems Security & Cloud Platforms
16.1 Enterprise GIS Architecture, Server Tiers, Sizing & Capacity Planning 16.2 Cloud GIS, Virtualization, Containers & High Availability (HA) 16.3 Enterprise GIS Security, Authentication, Authorization & System Auditing
17 Chapter 17: GIS Ethics, Legal Frameworks & Professional Practice
17.1 GISCI Code of Ethics & Rules of Conduct: Obligations to Society, Employers, Colleagues & Individuals 17.2 Legal Frameworks: Copyright, Intellectual Property, Licensing & Liability 17.3 Location Privacy, Geoprivacy & Spatial Data Confidentiality 17.4 GIS Project Management, Governance, Data Custodianship & Professional Practice
7.3 Terrain Representation & 3D Visualization: Shaded Relief, Slope, Aspect, Curvature & Oblique Views
Key Takeaways Explain This Topic AI
Analytical hillshading calculates surface illumination based on light source solar azimuth (standard 315° NW) and solar altitude (standard 45°); illuminating from the south causes the pseudoscopic illusion (relief inversion).
Slope calculates the maximum rate of elevation change across a 3x3 moving window kernel, expressed either in angular degrees (0° to 90°) or percentage rise (rise / run * 100, where 45° equals 100% slope).
Aspect identifies the compass azimuth direction (0° to 360°) that the downslope surface faces, with flat areas assigned a special flag value of -1 or null.
Surface curvature decomposes into profile curvature (parallel to slope direction, governing flow velocity and acceleration/deceleration) and plan curvature (perpendicular to slope direction, governing flow convergence/divergence).
3D perspective visualization requires careful calibration of vertical exaggeration, viewing azimuth, pitch/tilt, field of view (FOV), and surface drape texture alignment to avoid geometric misinterpretation.
Last updated: September 2026
Terrain Representation & 3D Visualization: Shaded Relief, Slope, Aspect, Curvature & Oblique Views
Quick Summary: Digital terrain modeling extracts primary morphometric derivatives (slope and aspect) and secondary derivatives (profile and plan curvature) from elevation surfaces using 3x3 moving focal window kernels. Visualizing three-dimensional topography on two-dimensional screens or printed maps requires specialized cartographic techniques, including analytical hillshading (shaded relief), hypsometric tinting, and oblique 3D perspective draping. Understanding illumination geometry, the pseudoscopic illusion, vertical exaggeration factors, and coordinate system unit conversions (Z-factors) is critical for accurate spatial analysis and landscape visualization.
Digital Elevation Models and Focal Operations
Digital terrain modeling represents continuous topographic surfaces using several primary data models:
Digital Elevation Model (DEM): A regularly spaced raster grid where each cell stores a single elevation value representing the bare-earth ground surface (devoid of vegetation canopy and human structures).
Digital Surface Model (DSM): Captures the elevation of the highest reflective surface, including tree canopies, building roofs, and infrastructure.
Digital Terrain Model (DTM): A bare-earth elevation model augmented with vector breaklines (e.g., ridge crests, stream centerlines, road cuts) to maintain linear topographic discontinuities.
Triangulated Irregular Network (TIN): A vector-based surface composed of contiguous, non-overlapping triangular facets constructed via Delaunay triangulation from irregularly spaced point samples.
The 3x3 Moving Window Kernel
Most raster terrain derivatives are calculated using a 3x3 cell moving window (kernel) centered over target cell e 5 e_5 e 5 : 3x3 FOCAL NEIGHBORHOOD KERNEL
- [ e1 e2 e3 ]
- [ e4 e5 e6 ]
- [ e7 e8 e9 ]
* Cell e5 is the target processing cell.
- * Cell size in X direction = Δx (cell width)
- * Cell size in Y direction = Δy (cell height)
Using Horn's algorithm (the standard formulation in modern GIS software), the first partial derivatives of elevation with respect to the east-west ( X X X ) and north-south ( Y Y Y ) directions are computed using weighted finite differences: ∂ z ∂ x = ( e 3 + 2 e 6 + e 9 ) − ( e 1 + 2 e 4 + e 7 ) 8 × Δ x \frac{\partial z}{\partial x} = \frac{(e_3 + 2e_6 + e_9) - (e_1 + 2e_4 + e_7)}{8 \times \Delta x} ∂ x ∂ z = 8 × Δ x ( e 3 + 2 e 6 + e 9 ) − ( e 1 + 2 e 4 + e 7 ) ∂ z ∂ y = ( e 7 + 2 e 8 + e 9 ) − ( e 1 + 2 e 2 + e 3 ) 8 × Δ y \frac{\partial z}{\partial y} = \frac{(e_7 + 2e_8 + e_9) - (e_1 + 2e_2 + e_3)}{8 \times \Delta y} ∂ y ∂ z = 8 × Δ y ( e 7 + 2 e 8 + e 9 ) − ( e 1 + 2 e 2 + e 3 )
Horn's algorithm weights orthogonal adjacent neighbors ( e 2 , e 4 , e 6 , e 8 e_2, e_4, e_6, e_8 e 2 , e 4 , e 6 , e 8 ) twice as heavily as diagonal corner neighbors ( e 1 , e 3 , e 7 , e 9 e_1, e_3, e_7, e_9 e 1 , e 3 , e 7 , e 9 ), providing superior noise damping over older simple difference algorithms.
Analytical Hillshading (Shaded Relief)
Analytical hillshading (shaded relief) simulates the visual appearance of sunlight casting shadows across three-dimensional terrain onto a two-dimensional map display.
Illumination Geometry
Hillshading is governed by two user-specified solar illumination parameters:
Solar Azimuth: The compass direction of the simulated light source, measured clockwise from true north ( 0 ∘ 0^\circ 0 ∘ to 360 ∘ 360^\circ 36 0 ∘ ). The universal cartographic default is 315 ∘ 315^\circ 31 5 ∘ (Northwest) .
Solar Altitude (Elevation Angle): The angle of the light source above the horizon, measured from 0 ∘ 0^\circ 0 ∘ (at the horizon) to 90 ∘ 90^\circ 9 0 ∘ (directly overhead at zenith). The standard default is 45 ∘ 45^\circ 4 5 ∘ .
Zenith Angle: The complement of altitude, defined as Zenith = 90 ∘ − Altitude \text{Zenith} = 90^\circ - \text{Altitude} Zenith = 9 0 ∘ − Altitude . For a standard 45 ∘ 45^\circ 4 5 ∘ altitude, the zenith angle is also 45 ∘ 45^\circ 4 5 ∘ ( 0.7854 0.7854 0.7854 radians). HILLSHADE ILLUMINATION GEOMETRY
- North (0° / 360°)
- |
- Sun Azimuth |
- 315° (NW) \ |
- \ |
- \ |
- West (270°) ----------+---------- East (90°)
- |
- |
- |
- South (180°)
- Solar Altitude: 45° above horizon (Zenith = 45°)
- Illumination formula: Intensity = 255 * [(cos(Zenith) * cos(Slope)) +
- (sin(Zenith) * sin(Slope) * cos(Azimuth - Aspect))]
- Lambert's Cosine Law of Illumination
Hillshading algorithms compute the illumination value ( 0 0 0 to 255 255 255 integer grayscale) of each cell based on Lambert's Cosine Law : the radiant intensity reflected from a diffuse surface is directly proportional to the cosine of the angle of incidence ( i i i ) between the incoming illumination vector and the surface normal vector: Illumination = 255 × cos ( i ) \text{Illumination} = 255 \times \cos(i) Illumination = 255 × cos ( i )
Where the angle of incidence is calculated from the cell's local slope and aspect relative to solar zenith and azimuth: cos ( i ) = ( cos ( Zenith ) × cos ( Slope ) ) + ( sin ( Zenith ) × sin ( Slope ) × cos ( Azimuth − Aspect ) ) \cos(i) = \left(\cos(\text{Zenith}) \times \cos(\text{Slope})\right) + \left(\sin(\text{Zenith}) \times \sin(\text{Slope}) \times \cos(\text{Azimuth} - \text{Aspect})\right) cos ( i ) = ( cos ( Zenith ) × cos ( Slope ) ) + ( sin ( Zenith ) × sin ( Slope ) × cos ( Azimuth − Aspect ) )
If the resulting illumination value is ≤ 0 \le 0 ≤ 0 , the cell lies in complete cast shadow (assigned a value of 0 0 0 ). Fully illuminated slopes facing directly into the light source approach 255 255 255 .
The Pseudoscopic Illusion (Relief Inversion)
One of the most critical perceptual rules in cartography is the prevention of the pseudoscopic illusion , commonly known as relief inversion :
The human visual cortex has evolved under the subconscious perceptual assumption that overhead light arrives from above and slightly to the left (the upper-left quadrant of visual space).
If a GIS analyst attempts to model "realistic" Northern Hemisphere solar illumination by setting the light source from the south (e.g., solar azimuth 135 ∘ 135^\circ 13 5 ∘ to 180 ∘ 180^\circ 18 0 ∘ , representing true midday sun in North America or Europe), the human visual system inverts the topography.
Mountain ridges appear as sunken canyons or valleys, while river valleys and meteor craters appear as elevated mountain ridges.
Caution
The Universal Northwest Rule: To prevent relief inversion, cartographers universally illuminate analytical hillshades from the Northwest ( 315 ∘ 315^\circ 31 5 ∘ ) , regardless of the map's actual geographic hemisphere or true solar ephemeris. Even in the Southern Hemisphere, where the real sun shines from the north, human cognitive physiology requires top-left illumination on printed or digital screens.
Advanced Hillshading: Multidirectional and Swiss-Style Shading
Standard single-source hillshades suffer from visual saturation on northwest-facing slopes and pitch-black shadows on southeast-facing slopes. Modern cartographers employ multidirectional hillshading , which computes weighted illumination from multiple light sources (e.g., 225 ∘ , 270 ∘ , 315 ∘ , 225^\circ, 270^\circ, 315^\circ, 22 5 ∘ , 27 0 ∘ , 31 5 ∘ , and 360 ∘ 360^\circ 36 0 ∘ ) simultaneously. When blended with hypsometric tinting (elevation color ramps) using a Multiply layer blending mode, the resulting display conveys rich relief without obscuring base vector themes.
Slope: Angular Degrees vs. Percent Rise
Slope represents the first spatial derivative of elevation, quantifying the maximum rate of change in elevation across each cell relative to its immediate neighbors.
Measurement Formats
Slope is expressed in two distinct formats that must never be confused:
Degree of Slope ( 0 ∘ 0^\circ 0 ∘ to 90 ∘ 90^\circ 9 0 ∘ ): The angular incline of the terrain surface relative to a horizontal plane: Slope degrees = arctan ( ( ∂ z ∂ x ) 2 + ( ∂ z ∂ y ) 2 ) × 180 ∘ π \text{Slope}_{\text{degrees}} = \arctan\left(\sqrt{\left(\frac{\partial z}{\partial x}\right)^2 + \left(\frac{\partial z}{\partial y}\right)^2}\right) \times \frac{180^\circ}{\pi} Slope degrees = arctan ( ∂ x ∂ z ) 2 + ( ∂ y ∂ z ) 2 × π 18 0 ∘
Percentage Rise ( 0 % 0\% 0% to ∞ % \infty\% ∞% ): The ratio of vertical rise to horizontal run, multiplied by 100: Slope percent = tan ( Slope degrees ) × 100 = ( Rise Run ) × 100 \text{Slope}_{\text{percent}} = \tan(\text{Slope}_{\text{degrees}}) \times 100 = \left(\frac{\text{Rise}}{\text{Run}}\right) \times 100 Slope percent = tan ( Slope degrees ) × 100 = ( Run Rise ) × 100 DEGREES VS. PERCENT RISE
- Flat Surface: 0° = 0% Rise (Rise = 0, Run = 100)
- Moderate Slope: 14.04°= 25% Rise (Rise = 25, Run = 100)
- Steep Slope: 26.57°= 50% Rise (Rise = 50, Run = 100)
45-Degree Incline: 45° = 100% Rise (Rise = 100, Run = 100) <-- EXAM TRAP!
- Precipitous: 63.43°= 200% Rise (Rise = 200, Run = 100)
- Vertical Wall: 90° = Approaches Infinity
Important
The 45-Degree / 100% Rise Trap: A common exam misconception is assuming that a 100 % 100\% 100% slope represents a vertical 90 ∘ 90^\circ 9 0 ∘ cliff. This is mathematically incorrect. A 100 % 100\% 100% slope occurs when vertical rise equals horizontal run ( Rise / Run = 1.0 \text{Rise} / \text{Run} = 1.0 Rise / Run = 1.0 ), which corresponds to an angle of exactly 45 ∘ 45^\circ 4 5 ∘ . A vertical wall ( 90 ∘ 90^\circ 9 0 ∘ ) has a run of zero, resulting in a slope that approaches infinity.
The Critical Z-Factor (Unit Conversion Multiplier)
The Z-factor is an essential conversion parameter applied when the horizontal ground coordinate units ( X , Y X, Y X , Y ) differ from the vertical elevation units ( Z Z Z ): Effective Surface Gradient = ( ∂ z ∂ x ) 2 + ( ∂ z ∂ y ) 2 × Z -factor \text{Effective Surface Gradient} = \sqrt{\left(\frac{\partial z}{\partial x}\right)^2 + \left(\frac{\partial z}{\partial y}\right)^2} \times Z\text{-factor} Effective Surface Gradient = ( ∂ x ∂ z ) 2 + ( ∂ y ∂ z ) 2 × Z -factor
Common unit mismatch scenarios include:
Geographic Coordinates: Horizontal coordinates are stored in Decimal Degrees (WGS84 or NAD83), but elevation is recorded in meters or feet. Because one degree of latitude equals approximately 111,320 meters at the equator, running slope without a Z-factor treats one degree as one meter, resulting in slope calculations exaggerated by more than 100,000x! The analyst must calculate the latitude-appropriate Z-factor ( Z = 1 / [ 111 , 320 × cos ( latitude ) ] Z = 1 / [111,320 \times \cos(\text{latitude})] Z = 1/ [ 111 , 320 × cos ( latitude )] ) or reproject the DEM into a conformal projected coordinate system (e.g., UTM or State Plane).
Feet vs. Meters: Horizontal coordinates are in UTM meters, but elevation is recorded in US Survey Feet ( 1 foot = 0.3048 meters 1 \text{ foot} = 0.3048 \text{ meters} 1 foot = 0.3048 meters ). A Z-factor of 0.3048 0.3048 0.3048 must be applied to convert feet to meters prior to slope computation.
Aspect: Compass Orientation and Azimuths
Aspect is the compass direction that the maximum downslope gradient faces. It represents the downhill orientation of the terrain surface face.
Mathematical Computation
Aspect is computed from the directional derivatives using the two-argument arctangent function: Aspect = atan2 ( − ∂ z ∂ y , − ∂ z ∂ x ) \text{Aspect} = \text{atan2}\left(-\frac{\partial z}{\partial y}, -\frac{\partial z}{\partial x}\right) Aspect = atan2 ( − ∂ y ∂ z , − ∂ x ∂ z )
The resulting angle is converted into standard compass azimuth degrees ranging clockwise from 0 ∘ 0^\circ 0 ∘ to 360 ∘ 360^\circ 36 0 ∘ :
- North: 0 ∘ 0^\circ 0 ∘ (or 360 ∘ 360^\circ 36 0 ∘ )
- East: 90 ∘ 90^\circ 9 0 ∘
- South: 180 ∘ 180^\circ 18 0 ∘
- West: 270 ∘ 270^\circ 27 0 ∘
- Handling Flat Terrain: The -1 Value
When a cell and its 3x3 neighbors have zero elevation change ( ∂ z / ∂ x = 0 \partial z/\partial x = 0 ∂ z / ∂ x = 0 and ∂ z / ∂ y = 0 \partial z/\partial y = 0 ∂ z / ∂ y = 0 ), slope is zero. On a flat surface, the downhill direction is undefined. GIS software assigns flat terrain cells a special flag value of − 1 -1 − 1 (or NoData / null).
Environmental Applications
Microclimate and Insolation: In the Northern Hemisphere, south-facing slopes ( 135 ∘ 135^\circ 13 5 ∘ to 225 ∘ 225^\circ 22 5 ∘ ) receive significantly higher solar irradiance, resulting in warmer, drier soils, sparse vegetation, and accelerated snowmelt. North-facing slopes ( 315 ∘ 315^\circ 31 5 ∘ to 45 ∘ 45^\circ 4 5 ∘ ) remain cooler and wetter, fostering denser forest canopy.
Wildfire Behavior: Aspect dictates fuel moisture levels and wind-exposure dynamics.
Avalanche Risk Modeling: Windward versus leeward aspect orientations govern dangerous snow slab accumulation.
Terrain Curvature: Profile vs. Plan Curvature
Curvature represents the second spatial derivative of elevation (the rate of change of slope). Curvature characteristically decomposes into two orthogonal directional components that govern surface hydrology and sediment transport: TERRAIN CURVATURE COMPONENTS
- [Profile Curvature] [Plan (Planform) Curvature]
- Measured parallel to slope Measured perpendicular to slope
- (Downslope) (Along Contours)
- Convex: \ Convex: / \
- \_ (Accelerating Flow) / \ (Diverging Flow)
- -------- (Ridges/Spurs)
- Concave: \_ Concave: \ /
- \ (Decelerating Flow) \ / (Converging Flow)
- -------- (Gullies/Ravines)
Curvature Type Measurement Direction Morphological Surface Hydrological & Geomorphic Impact
Profile Curvature Parallel to maximum slope gradient (downslope direction) Convex: Slope increases downslope; Concave: Slope decreases downslope Flow Velocity: ; • Convex profile: Water accelerates downslope, driving soil erosion.; • Concave profile: Water decelerates downslope, driving sediment deposition.
Plan (Planform) Curvature Perpendicular to maximum slope gradient (along horizontal contours) Convergent (Concave): Valleys, ravines; Divergent (Convex): Ridges, spurs, noses Flow Trajectory: ; • Convergent plan: Runoff concentrates into drainage channels.; • Divergent plan: Runoff spreads outward across landscape.
Modern landscape morphometry software also derives Tangential Curvature (plan curvature multiplied by the sine of slope) and Total Curvature to model complex soil moisture indices.
3D Perspective and Oblique Views
Visualizing geographic datasets in three dimensions involves projecting 3D ( X , Y , Z ) (X, Y, Z) ( X , Y , Z ) coordinates onto a two-dimensional camera viewing plane using perspective projection geometry.
Primary Camera Parameters 3D PERSPECTIVE VIEWING GEOMETRY
- Camera Position (Observer X,Y,Z)
- \
- \ Pitch / Tilt Angle
- \ (0° = Horizon, 90° = Nadir Looking Down)
- \
- \
- +------------------> Look-at Target Point
- (Center of View)
* View Azimuth (Heading): Compass direction of camera line-of-sight.
* Field of View (FOV): Angular viewing cone (narrow = telephoto, wide = perspective distortion).
* Vertical Exaggeration (VE): Multiplier applied to Z values relative to X,Y.
Observer Coordinates ( X , Y , Z ) (X, Y, Z) ( X , Y , Z ) and Target Point: Define camera location and focal look-at center.
Pitch / Tilt Angle: The inclination angle between the camera optical axis and the horizontal ground plane ( 0 ∘ 0^\circ 0 ∘ represents looking horizontally toward the horizon; 90 ∘ 90^\circ 9 0 ∘ represents looking straight down at nadir).
View Azimuth (Heading): The compass direction of the camera line-of-sight ( 0 ∘ 0^\circ 0 ∘ to 360 ∘ 360^\circ 36 0 ∘ ).
Field of View (FOV): The angular cone captured by the virtual camera. A narrow FOV ( 15 ∘ 15^\circ 1 5 ∘ to 30 ∘ 30^\circ 3 0 ∘ ) resembles a telephoto lens, minimizing perspective distortion; a wide FOV ( 60 ∘ 60^\circ 6 0 ∘ to 90 ∘ 90^\circ 9 0 ∘ ) expands peripheral visibility but causes distortion near screen edges.
Vertical Exaggeration (VE)
Vertical Exaggeration (VE) is an artificial scaling factor applied to the vertical elevation axis ( Z Z Z ) relative to the horizontal ground coordinates ( X , Y X, Y X , Y ): VE = Vertical Scale Factor Horizontal Scale Factor \text{VE} = \frac{\text{Vertical Scale Factor}}{\text{Horizontal Scale Factor}} VE = Horizontal Scale Factor Vertical Scale Factor
When to Apply VE: In flat or gently rolling regions (such as coastal plains or interior prairies), natural topography appears completely flat in 3D perspective views. Applying a VE of 2 × , 5 × , 2\times, 5\times, 2 × , 5 × , or 10 × 10\times 10 × accentuates subtle geomorphic features (paleo-channels, dunes, escarpments).
Exam Trap & Risk: Applying excessive VE in mountainous terrain produces precipitous, unnatural needle-peaks, exaggerates apparent slope angles, and misleads geotechnical hazard assessments.
Surface Draping
Surface draping projects two-dimensional planimetric themes (such as multispectral satellite imagery, aerial orthophotographs, vector parcel boundaries, or classified thematic rasters) over a three-dimensional elevation mesh (DEM or TIN). The rendering engine applies texture coordinate mapping, interpolating Z Z Z -elevations for every draped vertex to conform the 2D imagery to the undulating terrain surface.
Summary of Terrain Derivatives & Visualization Rules
Terrain Derivative Derivative Order Primary Output Units Critical Setting / Rule Primary Analytical Use
Hillshade Radiative Modeling 0 to 255 Grayscale Solar Azimuth 315° NW , Altitude 45° Relief visualization; base shading for vector draping.
Slope 1st Derivative Degrees ( 0 ∘ – 90 ∘ 0^\circ–90^\circ 0 ∘ –9 0 ∘ ) or % Rise ( 0 % – ∞ 0\%–\infty 0%–∞ ) Z-factor required if horizontal/vertical units differ Soil erosion, transport routing, hazard risk.
Aspect 1st Derivative Azimuth Degrees ( 0 ∘ – 360 ∘ 0^\circ–360^\circ 0 ∘ –36 0 ∘ ) Flat areas assigned -1 Solar radiation, wildfire spread, ecological habitats.
Profile Curvature 2nd Derivative 1 / meter 1/\text{meter} 1/ meter (Convex/Concave) Measured parallel to slope Flow acceleration/deceleration; erosion/deposition.
Plan Curvature 2nd Derivative 1 / meter 1/\text{meter} 1/ meter (Convergent/Divergent) Measured perpendicular to slope Flow convergence/divergence; channel delineation.
3D Perspective Coordinate Projection Screen Coordinates Calibrate Vertical Exaggeration (VE) Visual impact assessment, flight simulation, public outreach.
Common Exam Traps
Caution
Exam Trap 7.3.1: Pseudoscopic Relief Inversion from Southern Light. Questions frequently test the result of setting the hillshade solar azimuth to the south (e.g., 180 ∘ 180^\circ 18 0 ∘ or 135 ∘ 135^\circ 13 5 ∘ ). The correct answer is the pseudoscopic illusion (relief inversion) : valleys appear as ridges, and ridges appear as valleys. Illumination must be set to the Northwest ( 315 ∘ 315^\circ 31 5 ∘ ).
Caution
Exam Trap 7.3.2: Percent Slope vs. Degrees (The 45-Degree Trap). An exam question asks for the percent rise of a 45 ∘ 45^\circ 4 5 ∘ incline. Many examinees guess 50 % 50\% 50% . The correct answer is 100 % 100\% 100% because rise = run \text{rise} = \text{run} rise = run ( tan ( 45 ∘ ) × 100 = 100 % \tan(45^\circ) \times 100 = 100\% tan ( 4 5 ∘ ) × 100 = 100% ). A 90 ∘ 90^\circ 9 0 ∘ slope approaches infinity.
Caution
Exam Trap 7.3.3: Missing Z-Factor in Geographic Coordinate Systems. Calculating slope or shaded relief directly on a DEM projected in WGS84 decimal degrees without applying a Z-factor produces wildly distorted results (slopes near 89 ∘ 89^\circ 8 9 ∘ everywhere) because degrees are treated as linear meters. A conversion Z-factor or projected coordinate system is required.
Caution
Exam Trap 7.3.4: Confusing Profile vs. Plan Curvature. Remember: Profile curvature governs flow acceleration/deceleration (velocity downslope), while Plan curvature governs flow convergence/divergence (horizontal spreading or concentrating across contours).