GELE Photogrammetry & Cartography — Map ProjectionsConcept Map

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

To

Properties Preserved by Projections

From

Projection Fundamentals

Strength

strong

Relationship

Projections must choose which geographic property to preserve because all four cannot be preserved simultaneously

To

Projection Selection Criteria

From

Properties Preserved by Projections

Strength

strong

Relationship

The property to preserve is determined by the map purpose and application type

To

Transverse Mercator Projection

From

Developable Surfaces

Strength

strong

Relationship

Transverse Mercator uses a cylindrical developable surface rotated 90° around the ellipsoid

To

Transverse Mercator Projection

From

Scale Factor k

Strength

strong

Relationship

Scale factor is set at the central meridian (k₀ = 0.9996 for UTM) and varies with distance from the central meridian

To

Coordinate Transformation

From

Scale Factor k

Strength

strong

Relationship

Scale factor is applied to convert between ellipsoidal and grid distances; grid distance = k × ellipsoidal distance

To

Philippine Coordinate Systems

From

Transverse Mercator Projection

Strength

strong

Relationship

Both PPCS and UTM are based on the Transverse Mercator projection with conformal properties

To

Coordinate Transformation

From

Philippine Coordinate Systems

Strength

strong

Relationship

Philippine coordinate systems use specific transformation procedures to convert between geographic (WGS84/PRS92) and grid coordinates

To

Scale Factor k

From

Distortion Analysis

Strength

strong

Relationship

Distortion is primarily quantified through scale factor variation across the projection zone

To

Transverse Mercator Projection

From

Projection Selection Criteria

Strength

moderate

Relationship

Transverse Mercator is selected for surveying and engineering work where conformal properties and accurate angles are required

To

Projection Selection Criteria

From

Distortion Analysis

Strength

moderate

Relationship

Acceptable distortion limits inform whether a projection is suitable for the required accuracy and application

To

Distortion Analysis

From

Properties Preserved by Projections

Strength

moderate

Relationship

A projection's preserved property directly influences which other properties experience the greatest distortion

To

Common Exam Topics and Board Problems

From

Coordinate Transformation

Strength

moderate

Relationship

Coordinate transformations and scale factor applications are frequent topics in PRC Geodetic Engineer Licensure Examinations

To

Common Exam Topics and Board Problems

From

Scale Factor k

Strength

moderate

Relationship

Grid distance calculation using scale factor is a standard board exam problem type

To

Common Exam Topics and Board Problems

From

Philippine Coordinate Systems

Strength

strong

Relationship

Practical application of PPCS and UTM, zone selection, and coordinate conversion are central examination topics

To

Conformal Property Explanation

From

Transverse Mercator Projection

Strength

strong

Relationship

Transverse Mercator is specifically selected for surveying because it preserves angles and local shape, critical for bearing and angle computations

To

Scale Factor k

From

Developable Surfaces

Strength

moderate

Relationship

The choice of developable surface (cylindrical, conic, or azimuthal) affects how scale factor varies across the projection