Map Projections - Concept Map
Map Projections — Flattening the Curved Earth onto a Plane
Related concepts
Projection Fundamentals
Sub concepts
- Three-dimensional ellipsoid to two-dimensional plane conversion
- Inevitable distortion of geographic properties
- Trade-off principle: no projection preserves all four properties simultaneously
Relationship to central
Defines what a projection is and why it is necessary in cartography and surveying
Properties Preserved by Projections
Sub concepts
- Conformal (Orthomorphic) — preserves angles and local shape; used in surveying and navigation
- Equal-Area (Equivalent) — preserves area; used in thematic and statistical maps
- Equidistant — preserves distance along specific lines or from a central point
- Compromise — balances distortion across multiple properties
Relationship to central
Classifies projections by the geographic property they prioritize
Developable Surfaces
Sub concepts
- Cylindrical projections — wrapping a cylinder around the ellipsoid (e.g. Mercator, Transverse Mercator)
- Conic projections — cone placed over the poles or along a parallel (e.g. Albers, Lambert)
- Azimuthal (Planar) projections — plane touching the ellipsoid at a single point (e.g. Stereographic, Orthographic)
Relationship to central
Describes the geometric surface onto which the ellipsoid is projected
Scale Factor (k)
Sub concepts
- Definition: k = projected distance / true ellipsoidal distance
- Standard lines: k = 1.000 (no distortion along standard lines or points)
- Transverse Mercator behavior: k < 1 at central meridian (set to 0.9996 for UTM), k > 1 at zone edges
- Grid distance conversion: grid distance = k × ellipsoidal distance
- Scale factor variation across the projection zone
Relationship to central
Quantifies the distortion of linear distances introduced by any projection
Transverse Mercator Projection
Sub concepts
- Cylindrical surface rotated 90° with axis aligned to a central meridian
- Conformal property preserves surveying angles and bearings locally
- Central meridian scale factor k₀ = 0.9996 (UTM standard) or per PPCS specification
- Zone structure: 6° longitude or 3° longitude zones (depending on application)
- False easting and false northing to avoid negative coordinates
Relationship to central
The primary conformal projection used by Philippine surveying and mapping authorities
Philippine Coordinate Systems
Sub concepts
- Philippine Plane Coordinate System (PPCS) — nation-wide conformal grid based on Transverse Mercator
- Universal Transverse Mercator (UTM) — global 6° zone system; Zones 50–52 cover the Philippines
- WGS84 (World Geodetic System 1984) — reference ellipsoid for modern Philippine surveys
- PRS92 (Philippine Reference System 1992) — national geodetic datum tied to WGS84
- Legal framework: RA 4374 (Surveying profession), RA 8560 (Consumers Act), PD 1529 (Professions Regulation), CA 141 (Public Land Act)
Relationship to central
Practical implementation of projections specific to Philippine surveying and mapping
Distortion Analysis
Sub concepts
- Angular distortion: deviation from true bearings and angles
- Linear distortion: change in distance represented by scale factor variation
- Areal distortion: percentage difference in area (minimal for equal-area projections)
- Maximum scale factors and distortion limits within a zone
- Acceptable distortion thresholds for surveying (±1:10,000 typical) versus mapping applications
Relationship to central
Evaluates and quantifies how projections alter geographic properties
Projection Selection Criteria
Sub concepts
- Map extent and shape (large area vs. strip surveys)
- Accuracy requirements (millimeter-level surveying vs. regional overview)
- Intended use (navigation, area statistics, engineering surveys, cadastral work)
- Zone extent and central meridian selection
- Compliance with Philippine standards (PPCS, UTM) or project specifications
Relationship to central
Framework for choosing the appropriate projection for a given cartographic or surveying purpose
Coordinate Transformation
Sub concepts
- Geographic (latitude, longitude) to grid (Easting, Northing) transformation
- Application of scale factor in distance computations
- Convergence of meridians and grid/true azimuth conversion
- Datum transformations (WGS84 to PRS92, vice versa)
- Software and formulae for transformation (Redfearn equations for Transverse Mercator)
Relationship to central
Process of converting between geographic and projected coordinates, or between projection systems
Common Exam Topics and Board Problems
Sub concepts
- Grid distance calculation from ellipsoidal distance using scale factor
- Projection property identification and justification
- Selection of projection for specific cartographic scenarios
- Zone determination for Philippine coordinates (PPCS/UTM)
- Angular and linear distortion assessment
- Coordinate conversions and scaling corrections
Relationship to central
Key concepts and problem types appearing in PRC Geodetic Engineer Licensure Examinations
Concept connections
- Projection FundamentalsProperties Preserved by ProjectionsProjections must choose which geographic property to preserve because all four cannot be preserved simultaneously
- Properties Preserved by ProjectionsProjection Selection CriteriaThe property to preserve is determined by the map purpose and application type
- Developable SurfacesTransverse Mercator ProjectionTransverse Mercator uses a cylindrical developable surface rotated 90° around the ellipsoid
- Scale Factor kTransverse Mercator ProjectionScale factor is set at the central meridian (k₀ = 0.9996 for UTM) and varies with distance from the central meridian
- Scale Factor kCoordinate TransformationScale factor is applied to convert between ellipsoidal and grid distances; grid distance = k × ellipsoidal distance
- Transverse Mercator ProjectionPhilippine Coordinate SystemsBoth PPCS and UTM are based on the Transverse Mercator projection with conformal properties
- Philippine Coordinate SystemsCoordinate TransformationPhilippine coordinate systems use specific transformation procedures to convert between geographic (WGS84/PRS92) and grid coordinates
- Distortion AnalysisScale Factor kDistortion is primarily quantified through scale factor variation across the projection zone
- Projection Selection CriteriaTransverse Mercator ProjectionTransverse Mercator is selected for surveying and engineering work where conformal properties and accurate angles are required
- Distortion AnalysisProjection Selection CriteriaAcceptable distortion limits inform whether a projection is suitable for the required accuracy and application
- Properties Preserved by ProjectionsDistortion AnalysisA projection's preserved property directly influences which other properties experience the greatest distortion
- Coordinate TransformationCommon Exam Topics and Board ProblemsCoordinate transformations and scale factor applications are frequent topics in PRC Geodetic Engineer Licensure Examinations
- Scale Factor kCommon Exam Topics and Board ProblemsGrid distance calculation using scale factor is a standard board exam problem type
- Philippine Coordinate SystemsCommon Exam Topics and Board ProblemsPractical application of PPCS and UTM, zone selection, and coordinate conversion are central examination topics
- Transverse Mercator ProjectionConformal Property ExplanationTransverse Mercator is specifically selected for surveying because it preserves angles and local shape, critical for bearing and angle computations
- Developable SurfacesScale Factor kThe choice of developable surface (cylindrical, conic, or azimuthal) affects how scale factor varies across the projection
Diagrams
Map Projections — Complete Concept Hierarchy
Comprehensive mind map showing all major concepts in Map Projections, organized hierarchically from the central idea through projection types, properties, Philippine applications, and examination topics. This visual overview helps students understand how all concepts interconnect within the chapter.
Projection Selection Process — Decision Flowchart
Decision flowchart guiding geodetic engineers through the projection selection process. This diagram helps students and professionals systematically choose the appropriate projection based on map purpose, geographic extent, accuracy requirements, and Philippine regulatory frameworks.
Scale Factor Application in Grid Distance Calculation
Process flowchart detailing the step-by-step application of scale factor in converting ellipsoidal distances to grid distances. This diagram emphasizes the practical calculation routine essential for surveying and mapping work within projected coordinate systems.
Projection Property Classification and Use Cases
Classification flowchart showing the four main projection properties, their defining characteristics, typical use cases, and practical applications. Students use this diagram to quickly identify which projection property best suits a given cartographic or surveying scenario.
Philippine Coordinate Systems — PPCS vs. UTM
Comparison flowchart distinguishing the Philippine Plane Coordinate System (PPCS) from the Universal Transverse Mercator (UTM), showing their respective characteristics, zone structures, scale factors, and appropriate applications. This diagram helps students understand when to use each system in Philippine surveying practice.
Projection Distortion Budget in Transverse Mercator Zones
Pie chart illustrating the typical distribution of scale factor distortion within a Transverse Mercator projection zone. The chart shows that most of the zone (40%) experiences near-unity scale near the center, while edges and peripheries experience measurable distortion (k > 1.0005). This helps students understand why zones are limited to about 6° longitude in UTM and why zone selection is critical.
Projection Transformation States — From Ellipsoid to Grid
State diagram showing the transformation sequence from geographic coordinates on the WGS84 ellipsoid through projection calculations, false coordinate application, and final grid coordinate generation. The bidirectional arrows indicate forward and inverse transformations, essential for coordinate system conversions in Philippine surveying.