PEC EPE Geoinformatics cheat sheet

Geoid: the equipotential surface of Earth's gravity field that best approximates mean sea level; it is the physical height reference (orthometric heights H).

Ellipsoid: mathematically defined surface of revolution with semi-major axis a and flattening f = (a−b)/a; used as the geometric reference for geodetic coordinates (φ, λ, h).

Relationship between heights: h = H + N, where h is ellipsoidal height, H orthometric height, and N geoid undulation.

Geodetic datum: an ellipsoid plus its position and orientation relative to the Earth; a change of datum alters coordinates, not the physical points.

Datum transformation: 3-parameter (translation only), 7-parameter Helmert/Bursa-Wolf (3 translations, 3 rotations, scale), or grid-based (NTv2); accuracy depends on the transformation model and the extent of the network.

Geocentric vs geodetic latitude: geodetic latitude is the angle between the ellipsoid normal and the equatorial plane; geocentric latitude is the angle to the Earth's centre - they differ by up to about 0.19°.

Vertical deflection: the angle between the ellipsoid normal and the gravity vector (plumb line); it reflects local gravity-field anomalies.

Modern global frames (ITRF, WGS84) are dynamic: coordinates change with plate motion, so an epoch must accompany coordinates (e.g. ITRF2014 epoch 2010.0).

ED50 vs ETRS89 in Europe: ED50 is a local, non-geocentric datum; ETRS89 is aligned with ITRF at epoch 1989.0 and is the basis for ETRS89/UTM coordinates.

Levelling: height difference between two points = sum of backsights − sum of foresights; closing error = ΣBS − ΣFS, distributed proportionally to distance or number of setups.

Trigonometric levelling: ΔH = S·cos z + (1−k)·S²·sin²z/(2R), where z is zenith angle, k the refraction coefficient (≈0.13), R Earth radius; curvature and refraction correction is essential for long sights.

Traverse: linear misclosure = √(ΔE² + ΔN²); relative precision = misclosure / total traverse length; angular misclosure is checked against n·√(allowance) for n angles.

Bowditch (compass) rule distributes misclosure proportional to leg length; transit rule distributes proportional to coordinate increment - use Bowditch for compass traverses.

Resection (three-point problem): the position of an unknown station is computed from angles to three known points; the danger circle is the locus where the solution is indeterminate.

Total station: measures slope distance, zenith angle and horizontal direction; coordinates computed as E = E₀ + S·sin z·sin Az, N = N₀ + S·sin z·cos Az.

Setting out: coordinates of a design point are computed from the design and then staked by polar (angle + distance) or by offsets from a baseline; check with an independent measurement.

GNSS + total station integration: GNSS provides control coordinates in a projected CRS; total station provides local precision for detail and setting out.

Error propagation: the standard deviation of a sum/difference is √(σ₁² + σ₂²); for a product/quotient the relative errors add in quadrature.

GNSS pseudorange: P = c·(t_received − t_transmitted) + c·(receiver clock error) + atmospheric delays + noise; four satellites are the minimum for a 3D fix with clock estimation.

Positioning modes: absolute (single point, metre-level), relative/DGPS (code, decimetre), RTK (carrier phase, cm), PPP (precise orbits/clocks, cm after convergence).

RTK requires a base station or network (VRS) and a radio/internet link; the baseline length limits ambiguity resolution accuracy (ionosphere/troposphere decorrelation).

Integer ambiguity resolution: carrier-phase observations contain an unknown integer number of cycles N; fixing N converts cm-level phase to cm-level position.

DOP (dilution of precision): HDOP, VDOP, PDOP, GDOP; PDOP = √(HDOP² + VDOP²); lower DOP = better geometry; satellites clustered in one part of the sky give poor DOP.

Multipath: signal reflection from surfaces near the antenna; mitigated by choke-ring antennas, elevation mask, and longer observation sessions.

Ionosphere delay is frequency-dependent and removed by the ionosphere-free linear combination (L1/L2 or L1/L5); troposphere delay is frequency-independent and modelled.

GNSS height: ellipsoidal height h from the receiver; orthometric height H = h − N requires a geoid model.

Constellations: GPS (US), GLONASS (Russia, FDMA), Galileo (EU), BeiDou (China); multi-constellation improves availability and DOP.

Scale of a vertical aerial photograph: s = f / H, where f is focal length and H is flying height above ground; for a tilted photo scale varies across the frame.

Relief displacement: d = r·h / H, where r is radial distance from the principal point, h object height, H flying height; displacement is radial from the nadir/principal point.

Stereo overlap: forward overlap (typically 60%) and side overlap (typically 20–30%) are needed for stereo viewing and matching.

Parallax: p = x_left − x_right; height difference from parallax: Δh = H·Δp / (b + Δp), where b is the photo base.

Bundle block adjustment: simultaneously solves camera pose and object point coordinates using tie points and GCPs; uses collinearity equations.

Orthophoto: a rectified image with relief and tilt displacement removed; requires a DEM/DSM for true orthorectification in urban areas.

LiDAR: measures range from laser pulse time-of-flight; produces dense point clouds; intensity and multiple returns help classify vegetation and ground.

Remote sensing indices: NDVI = (NIR − Red)/(NIR + Red); NDWI uses green/NIR or NIR/SWIR for water; indices are ratio-based and reduce illumination effects.

Resolution types: spatial (pixel size), spectral (number and width of bands), radiometric (bit depth), temporal (revisit interval) - they are independent and all matter for a task.

Map scale: representative fraction (1:25,000), graphic bar, and verbal scale; scale is only constant on conformal projections at the standard parallel(s) or along the central meridian.

Conformal projections preserve angles and local shape (Mercator, Transverse Mercator, Lambert Conformal Conic); equal-area projections preserve area (Albers, Lambert Azimuthal Equal-Area); no flat map preserves both.

UTM: 60 zones, 6° of longitude each, central meridian scale factor 0.9996, false easting 500,000 m, false northing 10,000,000 m in the southern hemisphere.

Mercator: conformal cylindrical; exaggerates area and distance with latitude; unsuitable for global area statistics.

Map generalisation operators: selection, simplification, smoothing, aggregation, displacement, exaggeration, classification - applied to reduce detail at smaller scales.

Cartographic symbolisation: visual variables are position, size, shape, value (lightness), colour hue, orientation, and texture; each encodes a different kind of data.

Choropleth maps require normalised data (rates, densities), not raw counts; graduated symbols suit absolute quantities.

Contour lines: never cross (except overhangs), spacing inversely proportional to slope; index contours are labelled every fifth line typically.

Map projection parameters (central meridian, standard parallels, false origin) must be recorded with any projected coordinate dataset.

Vector data model: points, lines, polygons with attribute tables; topology defines adjacency, connectivity and containment.

Raster data model: grid of cells with a value per cell; cell size determines spatial resolution and storage volume.

Overlay operations: point-in-polygon, line-in-polygon, polygon-on-polygon (union, intersection, identity, erase, clip); output attributes combine inputs.

Spatial join: attaches attributes from one layer to another based on a spatial relationship (intersects, contains, within, nearest).

Buffer: polygon at a fixed distance from a feature; fixed-distance, variable-distance and multiple-ring buffers; projection distortion affects buffer shape.

Network analysis: shortest path, service area, closest facility, origin-destination matrix; requires connectivity and impedance attributes.

Spatial interpolation: IDW (inverse distance weighting), kriging (geostatistical, with variogram), spline, Thiessen polygons, natural neighbour; choice depends on data and assumed spatial process.

Geodatabase vs shapefile: geodatabases support topology, domains, subtypes, relationship classes and larger feature counts; shapefiles are limited (2 GB, no true curves, no topology).

Metadata: describes data lineage, accuracy, projection, and contact; essential for fitness-for-use assessment and data sharing.

Spatial index structures: R-tree, quadtree, and grid indexes speed up spatial queries by bounding-box filtering before exact geometry tests.

Topology rules: polygons must not overlap or have gaps (depending on the rule set); lines must not dangle or self-intersect; enforcing topology supports data quality.

Coordinate precision: storing coordinates at excessive precision wastes storage and can create false precision; match precision to survey accuracy.

Versioning and archiving: versioned geodatabases allow multiple editors and historical states; archiving records changes without overwriting history.

Data quality dimensions: positional accuracy, attribute accuracy, completeness, logical consistency, temporal accuracy, and lineage.

Spatial ETL: extract, transform, load pipelines convert between formats and CRS; reprojection must be explicit and documented.

Compression and tiling: raster tiling (e.g. COG) and vector tiling improve web delivery; lossy compression affects analytical results.

Backup and integrity: regular backups, checksums, and validation of geometry and attribute domains protect against corruption and silent errors.

Relational model: tables (relations), primary keys (unique row identifier), foreign keys (referential integrity), and normal forms (1NF, 2NF, 3NF, BCNF) reduce redundancy and update anomalies.

SQL spatial extension: geometry/geography types, spatial predicates (ST_Intersects, ST_Contains, ST_Within), and spatial functions (ST_Buffer, ST_Area, ST_Length, ST_Transform).

OGC Simple Features: standard geometry model (Point, LineString, Polygon, MultiPoint, MultiLineString, MultiPolygon, GeometryCollection) and WKT/WKB encodings.

OGC web services: WMS (map images), WFS (features), WCS (coverages), WMTS (tiles), CSW (catalogue); each has a distinct capability document.

ISO 19115 metadata standard and ISO 19139 XML encoding define discovery and use metadata for geographic data.

INSPIRE (EU) requires harmonised spatial data themes, metadata, network services and data-sharing arrangements; it builds on ISO/OGC standards.

Spatial database indexing: GiST or R-tree indexes on geometry columns; query planners use bounding-box filters before exact predicates.

Transactions: ACID properties (atomicity, consistency, isolation, durability) protect multi-user edits; spatial databases extend this to geometry edits.

Spatial autocorrelation: measures whether nearby values are similar; Moran's I (global) and local indicators (LISA) identify clustering and outliers.

Spatial weights matrix: defines neighbour relationships (queen, rook, distance band, k-nearest); the choice changes autocorrelation and regression results.

Spatial regression: OLS assumes independent errors; spatial lag and spatial error models address dependence; check residuals for autocorrelation.

Hot spot analysis: Getis-Ord Gi* identifies statistically significant clusters of high or low values; results depend on the analysis scale and weights.

Terrain analysis: slope = rise/run; aspect = downslope direction; hillshade uses slope, aspect and sun azimuth/altitude; viewshed identifies visible cells from a viewpoint.

Hydrological analysis: flow direction (D8, multiple flow direction), flow accumulation, watershed delineation; requires a hydrologically corrected DEM (sinks filled).

Cost surface analysis: least-cost path uses a friction surface (slope, land cover, roads); path minimises accumulated cost, not Euclidean distance.

Uncertainty: results depend on input accuracy, scale, classification scheme, and model assumptions; sensitivity analysis tests robustness.

Cadastre: a systematic register of land parcels with geometry, ownership and value; a land registry records rights and transactions.

Torrens system: title by registration - the register is conclusive evidence of title, and the state guarantees title (indefeasibility), subject to statutory exceptions.

Boundary types: natural (rivers, coastlines), artificial (walls, fences), and mathematical (coordinates); riparian boundaries can shift with accretion but not avulsion.

Adverse possession: occupation without permission for a statutory period can confer title; requirements typically include open, exclusive, continuous and hostile possession.

Easement vs covenant: an easement grants a right over another's land (e.g. right of way); a covenant restricts use; both are registered interests.

Boundary evidence hierarchy: monument (physical mark) usually prevails over measurement (distance/coordinate) when the two conflict, depending on jurisdiction.

Cadastral surveying standards: accuracy classes (e.g. relative positional tolerance), coordinate datum, and monumentation requirements are set by statute or regulation.

Expropriation/compulsory acquisition: requires statutory authority, public purpose, notice, and compensation; valuation principles vary by jurisdiction.

Professional duty: act within competence and disclose limitations; a surveyor who lacks expertise in a specialised area must refer or obtain specialist input.

Conflict of interest: disclose any interest that could influence professional judgement; do not accept work where independence is compromised.

Confidentiality: client data and personal information are protected; disclosure requires consent or legal obligation (e.g. court order).

Quality assurance: documented procedures, independent checks, calibration records, and peer review reduce error and support liability defence.

Contract types: lump sum, time and materials, and cost-plus; scope, deliverables, payment terms and limitation of liability should be explicit.

Risk management: identify, assess, mitigate and monitor risks; keep a risk register and contingency for schedule and budget.

Project scheduling: critical path method (CPM) identifies the longest path and float; resource levelling balances workload against constraints.

Ethical codes typically require honesty, integrity, public safety, competence, and fair dealing; professional misconduct can lead to discipline or loss of licence.

Data and intellectual property: clarify ownership of survey data, software and deliverables in the contract; respect copyright and licensing.